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{{distinguish|Grapheme|Graphane|Graphyne}}
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{{technical|date=December 2013}}


[[File:Graphen.jpg|thumb|300px|Graphene is an [[Chicken wire (chemistry)|atomic-scale honeycomb lattice]] made of carbon atoms.]]
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'''Graphene''' is a 2-dimensional, [[crystal]]ine [[allotrope]] of [[carbon]]. In graphene, carbon atoms are densely packed in a regular [[Sp2 bond|sp<sup>2</sup>-bonded]] [[chicken wire (chemistry)|atomic-scale chicken wire]] ([[Hexagonal tiling|hexagonal]]) pattern. Graphene can be described as a one-atom thick layer of [[graphite]]. It is the basic structural element of other allotropes, including graphite, [[charcoal]], [[carbon nanotube]]s and [[fullerene]]s. It can also be considered as an indefinitely large [[Aromaticity|aromatic]] molecule, the limiting case of the family of flat [[polycyclic aromatic hydrocarbon]]s.
  <li>[http://im.cnhs114.com/bbs/forum.php?mod=viewthread&tid=3301560 http://im.cnhs114.com/bbs/forum.php?mod=viewthread&tid=3301560]</li>
 
 
High-quality graphene is strong, light, nearly transparent and an excellent conductor of heat and electricity. Its interactions with other materials and with light and its inherently two-dimensional nature produce unique properties, such as the [[Bipolar junction transistor|bipolar transistor]] effect, [[ballistic transport]] of charges and large quantum oscillations.
  <li>[http://www.coreculture.com/index.php?option=com_kunena&func=view&catid=13&id=88547&Itemid=12#88547 http://www.coreculture.com/index.php?option=com_kunena&func=view&catid=13&id=88547&Itemid=12#88547]</li>
 
 
At the time of its isolation in 2004,<ref name="APS News">
  <li>[http://bbs.0738.cc/forum.php?mod=viewthread&tid=7241501&fromuid=70455 http://bbs.0738.cc/forum.php?mod=viewthread&tid=7241501&fromuid=70455]</li>
{{cite journal
 
| year=2009
  <li>[http://www.tc139.cn/news/html/?227410.html http://www.tc139.cn/news/html/?227410.html]</li>
| url=http://www.aps.org/publications/apsnews/200910/loader.cfm?csModule=security/getfile&pageid=187967
 
| title=This Month in Physics History: October 22, 2004: Discovery of Graphene
</ul>
| page=2
| series=Series II |volume=18 |issue=9
| journal=[[APS News]]
}}</ref> many researchers studying [[carbon nanotubes]] were already familiar with graphene's composition, structure and properties, which had been calculated decades earlier. The combination of familiarity, extraordinary properties and surprising ease of isolation enabled a rapid increase in graphene research. [[Andre Geim]] and [[Konstantin Novoselov]] at the [[University of Manchester]] won the [[Nobel Prize in Physics]] in 2010 "for groundbreaking experiments regarding the [[Two-dimensional space|two-dimensional]] material graphene".<ref>
{{cite web
|title=The Nobel Prize in Physics 2010
|url=http://nobelprize.org/nobel_prizes/physics/laureates/2010/
|publisher=[[The Nobel Foundation]]
|accessdate=2013-12-03
}}</ref>
{{toclimit|3}}
 
==Definition==
 
"Graphene" is a combination of [[graphite]] and the suffix [[-ene]], named by [[Hanns-Peter Boehm]],<ref name="termorigin">{{cite journal |doi= 10.1351/pac199466091893 |author= H. P. Boehm, R. Setton, E. Stumpp |title= Nomenclature and terminology of graphite intercalation compounds | url = http://www.iupac.org/publications/pac/1994/pdf/6609x1893.pdf | journal = Pure and Applied Chemistry |volume=66 |issue=9 |year=1994 |pages=1893–1901}}</ref> who described single-layer carbon foils in 1962.<ref name="Boehm1962">
{{cite journal |author= H. P. Boehm, A. Clauss, G. O. Fischer, U. Hofmann |title= Das Adsorptionsverhalten sehr dünner Kohlenstoffolien | journal = Zeitschrift für anorganische und allgemeine Chemie |volume=316 |issue=3–4 |year=1962 |pages=119–127 | doi=10.1002/zaac.19623160303}}
</ref>
 
The term ''graphene'' first appeared in 1987<ref name="Mouras87">
{{Cite journal |author =Mouras, S. ''et al.'' |title = Synthesis of first stage graphite intercalation compounds with fluorides |journal = Revue de Chimie Minerale |url=http://cat.inist.fr/?aModele=afficheN&cpsidt=7578318 |volume = 24 | page = 572 |year = 1987}}
</ref> to describe single sheets of graphite as one of the constituents of [[graphite intercalation compound]]s (GICs); conceptually a GIC is a crystalline salt of the intercalant and graphene. The term was also used in early descriptions of [[carbon nanotube]]s,<ref name="Saito92">{{Cite journal |author =Saito, R. ''et al.'' |title = Electronic structure of graphene tubules based on C60|doi=10.1103/PhysRevB.46.1804 |journal = Physical Review B | volume = 46 | page = 1804 |year =1992|bibcode = 1992PhRvB..46.1804S |issue =3 |first2 =Mitsutaka |first3 =G. |first4 =M. }}</ref> as well as for epitaxial graphene<ref name="Forbeaux98">{{Cite journal | author = Forbeaux, I. ''et al.''|title = Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure |doi=10.1103/PhysRevB.58.16396 |journal = Physical Review B | volume = 58 | page = 16396 |year = 1998 |bibcode = 1998PhRvB..5816396F | issue = 24 | first2 = J.-M. | first3 = J.-M. }}
</ref> and polycyclic aromatic hydrocarbons.<ref name="Wang00">
{{Cite journal | author = Wang, S. ''et al.'' |title = A new carbonaceous material with large capacity and high efficiency for rechargeable Li-ion batteries |doi=10.1149/1.1393559 |journal = Journal of the Electrochemical Society | volume = 147 | page = 2498 |year = 2000 | issue = 7 | first2 = S. | first3 = J. | first4 = Y. | first5 = H. | first6 = H. | first7 = T.}}</ref>
 
The [[International Union of Pure and Applied Chemistry|IUPAC]] compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene... it is incorrect to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed."<ref name=iupac-gold-book>{{cite web |title=graphene layer |url=http://goldbook.iupac.org/G02683.html |work=IUPAC Gold Book |publisher=International Union of Pure and Applied Chemistry |accessdate=31 March 2012}}</ref>
 
Graphene can be considered an "infinite alternant" (only six-member carbon ring) [[polycyclic aromatic hydrocarbon]] (PAH). The largest known isolated PAH molecule consists of 222 atoms and is 10 [[benzene ring]]s across.<!--why is this relevant to graphene?--><ref>{{Cite journal |author = Simpson, C. D. ''et al.'' |title = Synthesis of a Giant 222 Carbon Graphite Sheet | doi = 10.1002/1521-3765(20020315)8:6<1424::AID-CHEM1424>3.0.CO;2-Z | journal = Chemistry&nbsp;– A European Journal |volume = 6 | page = 1424 |year =2002 |issue = 6 |first2 = J. Diedrich |first3 = Alexander J. |first4 = Laurence |first5 = Hans Joachim |first6 = Klaus}}</ref> It has proven difficult to synthesize even slightly bigger molecules, and they still remain "a dream of many organic and polymer chemists".<ref name=2Dpolymers>{{Cite journal |author = Sakamoto J. ''et al'' |title = Two-Dimensional Polymers: Just a Dream of Synthetic Chemists? |year = 2009 |journal = Angew. Chem. Int. Ed. |pmid = 19130514 |volume = 48 |issue = 16 | doi = 10.1002/anie.200801863 |pages = 1030–69 |first2 = Jeroen |first3 = Oleg |first4 = A. Dieter}}</ref>
 
A definition of "isolated or free-standing graphene" was proposed: "graphene is a single atomic plane of graphite, which &nbsp;– and this is essential&nbsp;– is sufficiently isolated from its environment to be considered free-standing."<ref name=Sciencerev09>{{Cite journal |author = Geim A. |year = 2009 |title = Graphene: Status and Prospects |journal = Science |pmid = 19541989 |volume = 324 |issue = 5934 |doi = 10.1126/science.1158877 |bibcode = 2009Sci...324.1530G |pages = 1530–4 |arxiv = 0906.3799 }}</ref> This definition is narrower than the definition given above and refers to cleaved, transferred and suspended graphene monolayers.{{Citation needed|date=December 2011}} Other forms of graphene, such as graphene grown on various metals, can become free-standing if, for example, suspended or transferred to [[silicon dioxide]] ({{chem|SiO|2}}) or [[silicon carbide]] (after its [[Passivation (chemistry)|passivation]] with hydrogen).<ref name=SiCplusH2>{{Cite journal |author = Riedl C., Coletti C., Iwasaki T., Zakharov A.A., Starke U. |year = 2009 |title = Quasi-Free-Standing Epitaxial Graphene on SiC Obtained by Hydrogen Intercalation |journal = Physical Review Letters |volume = 103 |page = 246804 |doi = 10.1103/PhysRevLett.103.246804 |pmid=20366220 |bibcode=2009PhRvL.103x6804R |issue = 24|arxiv = 0911.1953 }}</ref>
 
==History==
In 1859 [[Sir Benjamin Collins Brodie, 2nd Baronet|Benjamin Collins Brodie]] was aware of the highly [[Lamella (materials)|lamellar]] structure of thermally reduced [[graphite oxide]].<ref>
{{cite journal
|last1=Brodie |first1=B. C.
|year=1859
|title=On the Atomic Weight of Graphite
|journal=[[Philosophical Transactions of the Royal Society of London]]
|volume=149 |issue= |pages=249–259
|bibcode=1859RSPT..149..249B
|jstor=108699
}}</ref>
 
The structure of [[graphite]] was solved in 1916.<ref>{{cite journal|author=[[Peter Debye|Debije P]], Scherrer P|year = 1916|title=Interferenz an regellos orientierten Teilchen im Röntgenlicht I|journal=Physikalische Zeitschrift|volume=17|page=277}}</ref> by the related method of [[powder diffraction]],<ref>{{cite journal|author=Friedrich W|year = 1913|title=Eine neue Interferenzerscheinung bei Röntgenstrahlen|journal=Physikalische Zeitschrift|volume=14|page=317}}</ref><ref>{{cite journal|author=Hull AW|authorlink=Albert Hull|year = 1917|title=A New Method of X-ray Crystal Analysis|journal=Phys. Rev.|volume=10|page=661|doi=10.1103/PhysRev.10.661|issue=6|bibcode = 1917PhRv...10..661H }}</ref> It was studied in detail by V. Kohlschütter and P. Haenni in 1918, who also described the properties of [[graphene oxide paper|graphite oxide paper]].<ref name=Kohlschuttler1918>
{{cite journal
|last1=Kohlschütter |first1=V.
|last2=Haenni |first2=P.
|year=1919
|title=Zur Kenntnis des Graphitischen Kohlenstoffs und der Graphitsäure
|journal=[[Zeitschrift für anorganische und allgemeine Chemie]]
|volume=105 |issue=1 |pages=121–144
|doi=10.1002/zaac.19191050109
}}</ref> Its structure was determined from single-crystal diffraction in 1924.<ref>{{cite journal|author=Bernal JD|authorlink=John Desmond Bernal|year = 1924|title=The Structure of Graphite|jstor=94336|journal= Proc. R. Soc. Lond.|volume=A106|issue=740|pages=749–773}}</ref><ref>{{cite journal|author=Hassel O, Mack H|year = 1924|title=Über die Kristallstruktur des Graphits|journal=Zeitschrift für Physik|volume=25|page=317|doi=10.1007/BF01327534|bibcode = 1924ZPhy...25..317H }}</ref>
 
The theory of graphene was first explored by [[P. R. Wallace]] in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by [[Gordon Walter Semenoff]] and David P. DeVincenzo and Eugene J. Mele.<ref name="devincenzo">{{Cite journal |author = DiVincenzo, D. P. and Mele, E. J. |title = Self-Consistent Effective Mass Theory for Intralayer Screening in Graphite Intercalation Compounds|doi=10.1103/PhysRevB.29.1685 |journal = Physical Review B |volume = 295 | page = 1685 |year =1984|bibcode = 1984PhRvB..29.1685D |issue = 4 }}</ref> Semenoff emphasized the occurrence in a magnetic field of an electronic [[Landau level]] precisely at the Dirac point. This level is responsible for the anomalous integer quantum Hall effect.<ref name="2dgasDiracFermions"/><ref name="Gusynin"/><ref name="Berry'sPhase"/>
 
The earliest TEM images of few-layer graphite were published by G. Ruess and F. Vogt in 1948.<ref name=RuessTEM>
{{cite journal
|last1=Ruess |first1=G.
|last2=Vogt |first2=F.
|year=1948
|title=Höchstlamellarer Kohlenstoff aus Graphitoxyhydroxyd
|journal=[[Monatshefte für Chemie]]
|volume=78 |issue=3–4 |page=222
|doi=10.1007/BF01141527
}}</ref> Later, single graphene layers were also observed directly by electron microscopy.<ref name=Meyer07>{{Cite journal | author = Meyer, J. ''et al.'' |title = The structure of suspended graphene sheets | journal = Nature | volume = 446 | pages = 60–63 | year =2007 |doi = 10.1038/nature05545 | pmid = 17330039 | issue = 7131 |arxiv = cond-mat/0701379 |bibcode = 2007Natur.446...60M | first2 = A. K. | first3 = M. I. | first4 = K. S. | first5 = T. J. | first6 = S. }}</ref> Before 2004 intercalated graphite compounds were studied under a [[Transmission electron microscopy|transmission electron microscope]] (TEM). Researchers occasionally observed thin graphitic flakes ("few-layer graphene") and possibly even individual layers. An early, detailed study on few-layer graphite dates to 1962.<ref name=GroxTEM>
{{cite book
|last1=Boehm |first1=H. P.
|last2=Clauss |first2=A.
|last3=Fischer |first3=G.
|last4=Hofmann  |first4=U.
|year=1962
|chapter=Surface Properties of Extremely Thin Graphite Lamellae
|url=http://graphenetimes.com/wp-content/uploads/1961/09/BoehmProcCarbon1962.pdf
|booktitle=Proceedings of the Fifth Conference on Carbon
|publisher=[[Pergamon Press]]
}}</ref>{{#tag:ref|This paper reports graphitic flakes that give an additional contrast equivalent of down to ~0.4&nbsp;nm or 3 atomic layers of amorphous carbon. This was the best possible resolution for 1960 TEMs. However, neither then nor today it is possible to argue how many layers were in those flakes. Now we know that the TEM contrast of graphene most strongly depends on focusing conditions.<ref name=Meyer07/> For example, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known way is to analyse relative intensities of various diffraction spots. The first reliable TEM observations of monolayers are probably given in refs. 24 and 26 of {{harvnb|Geim|Novoselov|2007}}}}
 
Starting in the 1970s single layers of graphite were grown epitaxially on top of other materials.<ref name="Oshima97">{{Cite journal |author =Oshima, C. and Nagashima, A. |title =Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces | doi = 10.1088/0953-8984/9/1/004 |journal = J. Phys.: Condens. Matter | volume = 9 | page = 1 |year =1997 |bibcode = 1997JPCM....9....1O }}</ref> This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of [[sp2 bond|sp<sup>2</sup>-bonded]] carbon atoms, as in free-standing graphene. However, there is significant charge transfer from the substrate to the epitaxial graphene, and, in some cases, hybridization between the [[d-orbital]]s of the substrate atoms and [[Pi orbital|π orbitals]] of graphene, which significantly alters the electronic structure of epitaxial graphene.
 
Single layers of graphite were also observed by [[transmission electron microscopy]] within bulk materials, in particular inside soot obtained by chemical exfoliation. Efforts to make thin films of graphite by mechanical exfoliation started in 1990,<ref name=SciAm/> but nothing thinner than 50 to 100 layers was produced before 2004.
[[File:Nobelpriset i fysik 2010.tif|thumb|A lump of graphite, a graphene transistor and a tape dispenser. Donated to the [[Nobel Museum]] in Stockholm by Andre Geim and Konstantin Novoselov in 2010.]]
 
Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10&nbsp;nm in thickness were obtained.{{sfn|Geim|Novoselov|2007}} Old papers were unearthed<ref name=GroxTEM/> in which researchers tried to isolate graphene starting with intercalated compounds. These papers reported the observation of very thin graphitic fragments (possibly monolayers) by transmission electron microscopy. Neither of the earlier observations was sufficient to "spark the graphene gold rush", which awaited macroscopic samples of extracted atomic planes.
 
One of the very first patents pertaining to the production of graphene was filed in October, 2002 (US Pat. 7071258).<ref>[http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2F7071258 United States Patent: 7071258]. Patft.uspto.gov. Retrieved on 2014-01-12.</ref> Entitled, "Nano-scaled Graphene Plates", this patent detailed one of the very first large scale graphene production processes. Two years later, in 2004 [[Andre Geim]] and [[Kostya Novoselov]] at University of Manchester extracted single-atom-thick crystallites from bulk graphite.<ref name="Nov 04"/> They pulled graphene layers from graphite and transferred them onto thin {{chem|SiO|2}} on a silicon wafer in a process called either micromechanical cleavage or the [[Scotch tape]] technique. The {{chem|SiO|2}} electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the {{chem|SiO|2}} could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. They may not have been the first to use this technique—{{citation|patent|US|6667100}}, filed in 2002, describes how to process commercially available flexible expanded graphite to achieve a graphite thickness of 0.01 thousandth of an inch. The key to success was high-throughput visual recognition of graphene on a properly chosen substrate, which provides a small but noticeable optical contrast.
 
The cleavage technique led directly to the first observation of the [[anomalous quantum Hall effect]] in graphene,<ref name="2dgasDiracFermions"/><ref name="Berry'sPhase"/> which provided direct evidence of graphene's theoretically predicted [[Berry's phase]] of massless [[Dirac fermion]]s. The effect was reported soon after by [[Philip Kim]] and Yuanbo Zhang in 2005. These experiments started after the researchers observed colleagues who were looking for the quantum Hall effect<ref>{{cite journal |last=Kopelevich, |title=Reentrant Metallic Behavior of Graphite in the Quantum Limit |journal=Physical Review Letters |year=2003 |volume=90|page=156402 |doi=10.1103/PhysRevLett.90.156402|url=http://link.aps.org/doi/10.1103/PhysRevLett.90.156402 |first1=Y. |last2=Torres |first2=J.|last3=Da Silva |first3=R. |last4=Mrowka |first4=F. |last5=Kempa |first5=H. |last6=Esquinazi|first6=P. |issue=15 |pmid=12732058|arxiv = cond-mat/0209406 |bibcode = 2003PhRvL..90o6402K }}</ref> and Dirac fermions<ref>{{cite journal |last=Igor A. Luk’yanchuk and Yakov Kopelevich |title=Phase Analysis of Quantum Oscillations in Graphite |journal=Physical Review Letters |year=2004 |volume=93|page=166402 |doi=10.1103/PhysRevLett.93.166402|url=http://link.aps.org/doi/10.1103/PhysRevLett.93.166402 |issue=16 |pmid=15525015 |first1=Igor|last2=Kopelevich |first2=Yakov|arxiv = cond-mat/0402058 |bibcode = 2004PhRvL..93p6402L }}</ref> in bulk graphite.
 
Even though graphene on nickel and on silicon carbide have both existed in the laboratory for decades, graphene mechanically exfoliated on {{chem|SiO|2}} provided the first proof of the Dirac fermion nature of electrons.{{Citation needed|date=September 2010}}
 
[[File:Nobel Prize 2010-Press Conference KVA-DSC 8009.jpg|thumb|Andre Geim and Konstantin Novoselov, 2010]]
Geim and Novoselev received several awards for their pioneering research on graphene, notably the 2010 [[Nobel Prize in Physics]].<ref>{{cite web |url=http://physicsworld.com/cws/article/news/43939 |title=Graphene pioneers bag Nobel prize |publisher=[[Institute of Physics]], UK |date=October 5, 2010 |accessdate=October 6, 2010}}</ref>
 
==Properties==
 
===Structure===
 
The [[atomic structure]] of isolated, single-layer graphene was studied by [[transmission electron microscope|transmission electron microscopy]] (TEM) on sheets of graphene suspended between bars of a metallic grid.<ref name=Meyer07/> Electron diffraction patterns showed the expected honeycomb lattice. Suspended graphene also showed "rippling" of the flat sheet, with amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals,{{sfn|Geim|Novoselov|2007}}<ref name="Carlsson">{{Cite journal | author = Carlsson, J. M. |title = Graphene: Buckle or break |doi=10.1038/nmat2051 |journal = Nature Materials | volume = 6 | year = 2007 | pmid = 17972931 | issue = 11 |bibcode = 2007NatMa...6..801C | pages = 801–2 }}</ref><ref name="Fasolino">{{Cite journal | author = Fasolino, A., Los, J. H., & Katsnelson, M. I. |title = Intrinsic ripples in graphene |doi=10.1038/nmat2011 |journal = Nature Materials | volume = 6 | year = 2007 | pmid = 17891144 | issue = 11 |bibcode = 2007NatMa...6..858F | pages = 858–61 |arxiv = 0704.1793 }}</ref> or may originate from the ubiquitous dirt seen in all TEM images of graphene. Atomic resolution real-space images of isolated, single-layer graphene on {{chem|SiO|2}} substrates are available<ref name=Ishigami07>{{Cite journal |last = Ishigami |first = Masa |coauthors = et al. |year = 2007 |volume = 7 |issue = 6 |pages = 1643–1648 |title = Atomic Structure of Graphene on SiO<sub>2</sub> |journal = Nano Lett |doi = 10.1021/nl070613a |pmid = 17497819 |bibcode = 2007NanoL...7.1643I }}</ref><ref name="Stolyarova">{{Cite journal |last = Stolyarova |first = Elena |coauthors = et al. |year = 2007 |volume = 104 |pages = 9209–9212 |title = High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface |journal = Proceedings of the National Academy of Sciences |doi = 10.1073/pnas.0703337104 |pmid = 17517635 |issue = 22 |pmc = 1874226 |bibcode = 2007PNAS..104.9209S |arxiv = 0705.0833 }}</ref> via [[scanning tunneling microscope|scanning tunneling microscopy]]. [[Photoresist]] residue, which must be removed to obtain atomic-resolution images, may be the "[[adsorbate]]s" observed in TEM images, and may explain the observed rippling. Rippling on  {{chem|SiO|2}} is caused by conformation of graphene to the underlying {{chem|SiO|2}}, and is not intrinsic.<ref name=Ishigami07/>
 
Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures.<ref>{{Cite journal | author = Kasuya, D.; Yudasaka, M.; Takahashi, K.; Kokai, F.; Iijima, S. |title = Selective Production of Single-Wall Carbon Nanohorn Aggregates and Their Formation Mechanism | doi =10.1021/jp020387n |journal = J. Phys. Chem. B |volume = 106 | year = 2002 | page = 4947 | issue = 19}}</ref> However, unlayered graphene with only (hk0) rings has been found in the core of [[presolar grains|presolar]] graphite onions.<ref>{{Cite journal | author = Bernatowicz |year = 1996 |title = Constraints on stellar grain formation from presolar graphite in the Murchison meteorite | journal = Astrophysical Journal | volume = 472 |pages =760–782 | doi = 10.1086/178105 | bibcode=1996ApJ...472..760B | issue = 2 | author2 = T. J. | display-authors = 2 | last3 = Gibbons | first3 = Patrick C. | last4 = Lodders | first4 = Katharina | last5 = Fegley | first5 = Bruce | last6 = Amari | first6 = Sachiko | last7 = Lewis | first7 = Roy S.}}</ref> TEM studies show faceting at defects in flat graphene sheets<ref>{{Cite journal |author = Fraundorf, P. and Wackenhut, M. |year = 2002 |title = The core structure of presolar graphite onions | journal = Astrophysical Journal Letters | volume = 578 | page = L153–156 |arxiv=astro-ph/0110585 |doi = 10.1086/344633 | bibcode=2002ApJ...578L.153F |issue = 2}}</ref> and suggest a role for two-dimensional crystallization from a melt.
 
Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as [[hydrocarbon]]s.  Bombarded with pure carbon atoms, the atoms perfectly align into [[hexagon]]s, completely filling the holes.<ref name=Manchester>{{Cite journal |year = 2012 |doi=10.1021/nl300985q |title = Graphene re-knits its holes |journal = Mesoscale and Nanoscale Physics |arxiv = 1207.1487v1 |author=Recep Zan, Quentin M. Ramasse, Ursel Bangert, Konstantin S. Novoselov |volume = 12 |issue = 8 |page = 3936|bibcode = 2012NanoL..12.3936Z }}</ref><ref>Puiu, Tibi (July 12, 2012) [http://www.zmescience.com/research/studies/graphene-can-repair-self-automatically-12072012/ Graphene sheets can repair themselves naturally]. zmescience.com</ref>
 
===Chemical===
Graphene is the only form of carbon (and generally all solid materials) in which each single atom is in exposure for chemical reaction from two sides (due to the 2D structure). It is known that carbon atoms at the edge of graphene sheets have special chemical reactivity, and graphene has the highest ratio of edgy carbons (in comparison with similar materials such as carbon nanotubes). In addition, various types of defects within the sheet, which are very common, increase the chemical reactivity.<ref name="Denis">{{Cite journal |author = Denis, P. A.; Iribarne F. |title = Comparative Study of Defect Reactivity in Graphene |doi=10.1021/jp4061945 |journal = Journal of Physical Chemistry C |volume = 117 | page = 19048 | year =2013 |issue = 37}}</ref> The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below 260°C <ref name="Yamada3">{{Cite journal |author = Yamada, Y.; Murota, K; Fujita, R; Kim, J; et al. |title = Subnanometer vacancy defects introduced on graphene by oxygen gas|doi= 10.1021/ja4117268 |journal = Journal of American Chemical Society}}</ref> and the graphene burns at very low temperature (e.g., 350 °C).<ref name="Eftekhari">{{Cite journal |author = Eftekhari, A.; Jafarkhani P. |title = Curly Graphene with Specious Interlayers Displaying Superior Capacity for Hydrogen Storage |doi=10.1021/jp410044v |journal = Journal of Physical Chemistry C |volume = 117 | page = 25845 | year =2013 |issue = 48}}</ref> In fact, graphene is chemically the most reactive form of carbon, owing to the lateral availability of carbon atoms.
Graphene is commonly modified with oxygen- and nitrogen-containing functional groups and analyzed by infrared spectroscopy and X-ray photoelectron spectroscopy. But, determination of structures of graphene with oxygen-<ref name="Yamada">{{Cite journal |author = Yamada, Y.; Yasuda, H.; Murota, K.; Nakamura, M.; Sodesawa, T.; Sato, S. |title = Analysis of heat-treated graphite oxide by X-ray photoelectron spectroscopy |doi=10.1007/s10853-013-7630-0 |journal = Journal of Material Science |volume = 48 | page = 8171 | year =2013 |issue = 23}}</ref> and nitrogen-<ref name="Yamada2">{{Cite journal |author = Yamada, Y.; Kim, J.; Murota, K.; Matsuo, S.; Sato, S. |title = Nitrogen-containing graphene analyzed by X-ray photoelectron spectroscopy |doi=10.1016/j.carbon.2013.12.061 |journal = Carbon}}</ref> containing functional groups is a difficult task unless the structures are well controlled.
 
In 2013, [[Stanford University]] physicists reported that sheets of Graphene one atom thick are a hundred times more chemically reactive than thicker sheets.<ref>{{cite web|url=http://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html|title=Thinnest graphene sheets react strongly with hydrogen atoms; thicker sheets are relatively unaffected|publisher=Phys.org|date=1 February 2013|accessdate=1 February 2013}}</ref>
 
===Physical===
 
The [[carbon–carbon bond]] length in graphene is about 0.142 [[nanometer]]s.<ref>{{cite arXiv |eprint=0804.4086 |author = Raji Heyrovska|title=Atomic Structures of Graphene, Benzene and Methane with Bond Lengths as Sums of the Single, Double and Resonance Bond Radii of Carbon |class=physics.gen-ph |year=2008}}</ref>  Graphene sheets stack to form graphite with an interplanar spacing of 0.335&nbsp;nm.
 
===Electronic===
 
[[File:cnt zz v3.gif|thumb|350px|right|[[Graphene nanoribbon|GNR]] band structure for zig-zag orientation. Tightbinding calculations show that zigzag orientation is always metallic.]]
 
[[File:cnt gnrarm v3.gif|thumb|350px|right|[[Graphene nanoribbon|GNR]] band structure for armchair orientation. Tightbinding calculations show that armchair orientation can be semiconducting or metallic depending on width (chirality).]]
 
Graphene differs from most three-dimensional materials. Intrinsic graphene is a [[semi-metal]] or zero-gap [[semiconductor]]. Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. The energy-momentum relation ([[dispersion relation]]) is linear for low energies near the six corners of the two-dimensional hexagonal [[Brillouin zone]], leading to zero [[effective mass (solid-state physics)|effective mass]] for electrons and [[Electron hole|holes]].<ref name="E-Phonon">{{Cite book | author = Charlier, J.-C.; Eklund, P.C.; Zhu, J. and Ferrari, A.C. | chapter = Electron and Phonon Properties of Graphene: Their Relationship with Carbon Nanotubes | title = from Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications, Ed. A. Jorio, G. Dresselhaus, and M.S. Dresselhaus | location = Berlin/Heidelberg | publisher =Springer-Verlag | year = 2008}}</ref> Due to this linear (or “[[conical intersection|conical]]") dispersion relation at low energies, electrons and holes near these six points, two of which are inequivalent, behave like [[theory of relativity|relativistic]] particles described by the [[Dirac equation]] for spin-1/2 particles.<ref name="Semenoff">{{Cite journal |author = Semenoff, G. W. |title = Condensed-Matter Simulation of a Three-Dimensional Anomaly |doi=10.1103/PhysRevLett.53.2449 |journal = Physical Review Letters |volume = 53 | page = 2449 | year =1984 |bibcode=1984PhRvL..53.2449S |issue = 26}}</ref><ref name=CBE>{{Cite journal |author = Avouris, P., Chen, Z., and Perebeinos, V. |title = Carbon-based electronics |doi=10.1038/nnano.2007.300 |journal = Nature Nanotechnology | volume = 2 | year =2007 |pmid = 18654384 |issue = 10 |bibcode = 2007NatNa...2..605A |pages = 605–15 }}</ref> Hence, the electrons and holes are called Dirac [[fermions]] and the six corners of the Brillouin zone are called the Dirac points.<ref name="Semenoff"/> The equation describing the electrons' linear dispersion relation is <math>E = \hbar v_F\sqrt{k_x^2+k_y^2}</math>; where the [[Fermi velocity]] ''v<sub>F</sub>'' ~ {{val|e=6|u=m/s}}, and the [[wavevector]] ''k'' is measured from the Dirac points (the zero of energy is chosen here to coincide with the Dirac points).<ref name=CBE/>
 
==="Massive" electrons===
 
Graphene's unit cell has two identical carbon atoms and two zero-energy states: one in which the electron resides on atom A, the other in which the electron resides on atom B. Both states exist at exactly zero energy. However, if the two atoms in the unit cell are not identical, the situation changes. Hunt et al. show that placing hBN in contact with graphene can alter the potential felt at atom A versus atom B enough that the electrons develop a mass and accompanying band gap of about 30 meV.<Ref name=sci1306>{{cite doi|10.1126/science.1240317}}</ref>
 
The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via [[optical spectroscopy]]. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators.<Ref name=sci1306/>
 
If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of [[quantum dot]]s, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against [[backscatter]]ing and could carry currents without dissipation.<Ref name=sci1306/>
 
====Electron transport====
 
Experimental results from transport measurements show that graphene has a remarkably high [[electron mobility]] at room temperature, with reported values in excess of {{val|15000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}}.{{sfn|Geim|Novoselov|2007}} Additionally, the symmetry of the experimentally measured conductance indicates that hole and electron mobilities should be nearly the same.<ref name="E-Phonon"/> The mobility is nearly independent of temperature between {{val|10|u=K}} and {{val|100|u=K}},<ref name="2dgasDiracFermions">{{Cite journal | author=Novoselov, K. S. ''et al.'' |title = Two-dimensional gas of massless Dirac fermions in graphene |doi=10.1038/nature04233 |journal = Nature | volume = 438 | pages = 197–200 |year =2005 | pmid= 16281030 | issue= 7065 |arxiv = cond-mat/0509330 |bibcode = 2005Natur.438..197N | first2=A. K. | first3=S. V. | first4=D. | first5=M. I. | first6=I. V. | first7=S. V. | first8=A. A. }}</ref><ref name="GiantMobility">{{Cite journal | author = Morozov, S.V. ''et al.'' |title = Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer |doi=10.1103/PhysRevLett.100.016602 |journal = Physical Review Letters| volume = 100 |page = 016602 |year =2008 |pmid=18232798 |bibcode=2008PhRvL.100a6602M | issue = 1 | first2 = K. | first3 = M. | first4 = F. | first5 = D. | first6 = J. | first7 = A.|arxiv = 0710.5304 }}</ref><ref name=E-ph>{{Cite journal | author = Chen, J. H. ''et al.'' |title = Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO<sub>2</sub> |doi=10.1038/nnano.2008.58 |journal = Nature Nanotechnology | volume = 3 | year =2008 | pmid = 18654504 | issue = 4 | pages = 206–9 | first2 = Chaun | first3 = Shudong | first4 = Masa | first5 = Michael S.}}</ref> which implies that the dominant scattering mechanism is [[defect scattering]]. Scattering by the acoustic [[phonon]]s of graphene intrinsically limits room temperature mobility to {{val|200000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}} at a carrier density of {{val|e=12|u=cm<sup>−2</sup>}}.<ref name=E-ph/><ref name="GrapheneMC">{{Cite journal | author = Akturk, A. and Goldsman, N. |title = Electron transport and full-band electron–phonon interactions in graphene |doi=10.1063/1.2890147 |journal = Journal of Applied Physics | volume = 103 | page = 053702 |year = 2008 |bibcode = 2008JAP...103e3702A | issue = 5 }}</ref> The corresponding [[resistivity]] of the graphene sheet would be {{val|e=-6|u=Ω·cm}}. This is less than the resistivity of [[silver]], the lowest known at room temperature.<ref name="UMDnews">[https://newsdesk.umd.edu/scitech/release.cfm?ArticleID=1621 Physicists Show Electrons Can Travel More Than 100 Times Faster in Graphene :: University Communications Newsdesk, University of Maryland]. Newsdesk.umd.edu (2008-03-24). Retrieved on 2014-01-12.</ref> However, for graphene on {{chem|SiO|2}} substrates, scattering of electrons by optical phonons of the substrate is a larger effect at room temperature than scattering by graphene’s own phonons. This limits mobility to {{val|40000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}}.<ref name=E-ph/>
 
Despite zero carrier density near the Dirac points, graphene exhibits a minimum [[Electrical conductivity|conductivity]] on the order of <math>4e^2/h</math>. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the {{chem|SiO|2}} substrate may lead to local puddles of carriers that allow conduction.<ref name="E-Phonon"/> Several theories suggest that the minimum conductivity should be <math>4e^2/{(\pi}h)</math>; however, most measurements are of order <math>4e^2/h</math> or greater{{sfn|Geim|Novoselov|2007}} and depend on impurity concentration.<ref name=K>{{Cite journal | author = Chen, J. H. ''et al.'' |title = Charged Impurity Scattering in Graphene |doi=10.1038/nphys935 |journal = Nature Physics | volume = 4 | pages = 377–381 |year = 2008 |bibcode = 2008NatPh...4..377C | issue=5 | first2 = C. | first3 = S. | first4 = M. S. | first5 = E. D. | first6 = M.|arxiv = 0708.2408 }}</ref>
 
Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in vacuum.<ref name=K/><ref name="ChemDoping">{{Cite journal | author = Schedin, F. ''et al.'' |title = Detection of individual gas molecules adsorbed on graphene |doi=10.1038/nmat1967 |journal = Nature Materials |volume = 6 | pages = 652–655 |year = 2007 | pmid = 17660825 | issue = 9 |bibcode = 2007NatMa...6..652S |first2 = A. K. | first3 = S. V. | first4 = E. W. | first5 = P. | first6 = M. I. | first7 = K. S. }}</ref> Even for [[dopant]] concentrations in excess of 10<sup>12</sup> cm<sup>2</sup> carrier mobility exhibits no observable change.<ref name="ChemDoping"/> Graphene doped with [[potassium]] in [[ultra-high vacuum]] at low temperature can reduce mobility 20-fold.<ref name=K/><ref name="GrapheneCharge">{{Cite journal | author = Adam, S. ''et al.'' |title = A self-consistent theory for graphene transport |journal = Proc. Nat. Acad. Sci. USA | volume = 104 |arxiv=0705.1540 |year = 2007 | doi = 10.1073/pnas.0704772104 | pmid = 18003926 | issue = 47 | pmc = 2141788 |bibcode = 2007PNAS..10418392A | pages = 18392–7 | first2 = E. H. | first3 = V. M. | first4 = S. }}</ref> The mobility reduction is reversible on heating the graphene to remove the potassium.
 
Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum<ref>{{Cite journal | author=Hadar Steinberg, Gilad Barak, Amir Yacoby, et al |title=Charge fractionalization in quantum wires (Letter) |journal=Nature Physics |volume=4 |issue=2 |year=2008 |pages=116–119 |doi = 10.1038/nphys810 |bibcode = 2008NatPh...4..116S |arxiv = 0803.0744 }}</ref>) is thought to occur. It may therefore be a suitable material for constructing [[quantum computer]]s<ref>{{Cite journal |arxiv=1003.4590 |title=Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force |author=Agung Trisetyarso |journal=Quantum Information & Computation |url=http://dl.acm.org/citation.cfm?id=2481569.2481576 |volume=12 |year=2012 |page=989 |bibcode = 2010arXiv1003.4590T |issue=11–12 }}</ref> using [[anyon]]ic circuits.<ref>{{Cite journal |arxiv=0812.1116 |title=Manifestations of topological effects in graphene |author=Jiannis K. Pachos |journal=Contemporary Physics |doi=10.1080/00107510802650507 |volume=50 |year=2009 |page=375 |bibcode = 2009ConPh..50..375P |issue=2 }}<br/>[http://www.int.washington.edu/talks/WorkShops/int_08_37W/People/Franz_M/Franz.pdf Fractionalization of charge and statistics in graphene and related structures], M. Franz, University of British Columbia, January 5, 2008</ref>
 
===Optical===
 
[[File:graphene visible.jpg|left|300px|thumb|{{anchor|photoopt|reason=linked by [[#Drawing method]] above}}Photograph of graphene in transmitted light. This one-atom-thick crystal can be seen with the naked eye because it absorbs approximately 2.3% of white light.]]
 
Graphene's unique optical properties produce an unexpectedly high [[Opacity (optics)|opacity]] for an atomic monolayer in vacuum, absorbing ''πα'' ≈ 2.3% of white [[light]], where ''α'' is the [[fine-structure constant]].<ref>{{Cite journal |title=Universal infrared conductance of graphite |first1=A. B. |last1=Kuzmenko |first2=E. |last2=Van Heumen |first3=F. |last3=Carbone |first4=D. |last4=Van Der Marel |journal=Physical Review Letters |volume=100 |page=117401 | doi=10.1103/PhysRevLett.100.117401 |year=2008 |pmid=18517825 |issue=11 |bibcode=2008PhRvL.100k7401K|arxiv = 0712.0835 }}</ref> This is a consequence of the "unusual low-energy electronic structure of monolayer graphene that features electron and hole [[conical intersection|conical bands]] meeting each other at the [[graphene#Electronic properties|Dirac point]]... [which] is qualitatively different from more common [[quadratic massive band]]s".<ref>{{Cite journal |title=Fine Structure Constant Defines Visual Transparency of Graphene |url = http://onnes.ph.man.ac.uk/nano/Publications/Science_2008fsc.pdf | author=Nair, R. R. ''et al.'' |journal=[[Science (journal)|Science]] |year=2008 |doi=10.1126/science.1156965 |volume=320 |page=1308 |pmid=18388259 |issue=5881 |bibcode = 2008Sci...320.1308N |first2=P. |first3=A. N. |first4=K. S. |first5=T. J. |first6=T. |first7=N. M. R. |first8=A. K. }} [http://optics.unige.ch/vdm/marel_files/publications/uni08.pdf]</ref> Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, the interatomic distance, hopping value and frequency cancel when optical conductance is calculated using [[Fresnel equations]] in the thin-film limit.
 
Although confirmed experimentally, the measurement is not precise enough to improve on other techniques for determining the [[fine-structure constant]].<ref>{{Cite news |title=Graphene Gazing Gives Glimpse Of Foundations Of Universe |url=http://www.sciencedaily.com/releases/2008/04/080403140918.htm |publisher=ScienceDaily |date=2008-04-04 |accessdate=2008-04-06}}</ref>
 
Graphene's [[band gap]] can be tuned from 0 to 0.25 eV (about 5 micrometre wavelength) by applying voltage to a dual-gate bilayer graphene [[field-effect transistor]] (FET) at room temperature.<ref>{{Cite journal | doi = 10.1038/nature08105 | journal=Nature | author = Zhang, Y. ''et al.'' | volume = 459 | pages = 820–823 |date = 11 June 2009 | title= Direct observation of a widely tunable bandgap in bilayer graphene | pmid = 19516337 | issue = 7248 |bibcode = 2009Natur.459..820Z | first2 = Tsung-Ta | first3 = Caglar | first4 = Zhao | first5 = Michael C. | first6 = Alex | first7 = Michael F. | first8 = Y. Ron | first9 = Feng }}</ref> The optical response of [[graphene nanoribbons]] is tunable into the [[terahertz]] regime by an applied magnetic field.<ref>{{Cite journal | doi = 10.1063/1.2964093 | journal=Appl Phys Lett | author = Junfeng Liu, A. R. Wright, Chao Zhang, and Zhongshui Ma | volume = 93 | pages = 041106–041110 |date = 29 July 2008 | title= Strong terahertz conductance of graphene nanoribbons under a magnetic field |bibcode = 2008ApPhL..93d1106L | issue = 4 }}</ref> Graphene/graphene oxide systems exhibit [[Graphene#Electrochromic devices|electrochromic behavior]], allowing tuning of both linear and ultrafast optical properties.<ref name="Kurum2011">{{Cite journal |author=Kurum, U. ''et al.'' |title=Electrochemically tunable ultrafast optical response of graphene oxide |journal=Applied Physics Letters |volume=98 |page=141103 |year=2011 |bibcode = 2011ApPhL..98b1103M |doi = 10.1063/1.3540647 |issue=2 |first2=Bo |first3=Kailiang |first4=Yan |first5=Hao}}</ref>
 
A graphene-based [[Bragg grating]] (one-dimensional [[photonic crystal]]) has been fabricated and demonstrated its capability for excitation of surface electromagnetic waves in the periodic structure by using 633&nbsp;nm He-Ne laser as the light source.<ref>{{cite journal |author=K.V.Sreekanth ''et al.'' |title=Excitation of surface electromagnetic waves in a graphene-based Bragg grating |journal=Scientific Reports |year=2012 |doi=10.1038/srep00737 |last2=Zeng |first2=Shuwen |last3=Shang |first3=Jingzhi |last4=Yong |first4=Ken-Tye |last5=Yu |first5=Ting |volume=2|bibcode = 2012NatSR...2E.737S }}</ref>
 
====Saturable absorption====
 
Such unique absorption could become saturated when the input optical intensity is above a threshold value. This nonlinear optical behavior is termed [[saturable absorption]] and the threshold value is called the saturation fluence. Graphene can be saturated readily under strong excitation over the visible to [[near-infrared]] region, due to the universal optical absorption and zero band gap. This has relevance for the mode locking of [[fiber laser]]s, where fullband mode locking has been achieved by graphene-based saturable absorber. Due to this special property, graphene has wide application in ultrafast [[photonics]]. Moreover, the optical response of graphene/graphene oxide layers can be tuned electrically.<ref name="Kurum2011" /><ref>{{cite journal |author=Bao, Qiaoliang et al. |title=Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers |url=http://www3.ntu.edu.sg/home2006/zhan0174/AFM.pdf |archiveurl=http://web.archive.org/web/20110717122454/http://www3.ntu.edu.sg/home2006/zhan0174/AFM.pdf |archivedate=2011-07-17 |journal=Advanced Functional Materials |volume=19 |page=3077 |year=2009 |doi=10.1002/adfm.200901007 |issue=19 |first2=Han |first3=Yu |first4=Zhenhua |first5=Yongli |first6=Ze Xiang |first7=Kian Ping |first8=Ding Yuan}}<br/>{{Cite journal |author=Zhang, H. ''et al.'' |title=Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene |journal=Optics Express |volume=17 |page=P17630 |url=http://www3.ntu.edu.sg/home2006/zhan0174/OE_graphene.pdf |archiveurl=http://web.archive.org/web/20110717122606/http://www3.ntu.edu.sg/home2006/zhan0174/OE_graphene.pdf |archivedate=2011-07-17 |bibcode=2009OExpr..1717630Z |last2=Tang |last3=Zhao |last4=Bao |last5=Loh |year=2009 |doi=10.1364/OE.17.017630 |issue=20 |first2=D. Y. |first3=L. M. |first4=Q. L. |first5=K. P.|arxiv = 0909.5536 }}<br/>{{Cite journal |author=Zhang, H. ''et al.'' |title=Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker |journal=Applied Physics Letters |volume=95 |page=P141103 |url=http://www3.ntu.edu.sg/home2006/zhan0174/apl.pdf |archiveurl=http://web.archive.org/web/20110717122745/http://www3.ntu.edu.sg/home2006/zhan0174/apl.pdf |archivedate=2011-07-17 |bibcode=2009ApPhL..95n1103Z |last2=Bao |last3=Tang |last4=Zhao |last5=Loh |year=2009 |doi=10.1063/1.3244206 |issue=14 |first2=Qiaoliang |first3=Dingyuan |first4=Luming |first5=Kianping|arxiv = 0909.5540 }}<br/>
{{Cite journal |author=Zhang, H. ''et al.'' |title=Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser |journal=Applied Physics Letters |volume=96 |page=111112 |url=http://www.sciencenet.cn/upload/blog/file/2010/3/20103191224576536.pdf |archiveurl=http://www.webcitation.org/5pt6I3oAm |archivedate=2010-05-21 |doi=10.1063/1.3367743 |bibcode=2010ApPhL..96k1112Z |year=2010 |issue=11|arxiv = 1003.0154 |first2=Dingyuan |first3=R. J. |first4=Luming |first5=Qiaoliang |first6=Kian Ping }}, {{cite journal |last1=Zhang |title=Graphene: Mode-locked lasers |journal=NPG Asia Materials |year=2009 |doi=10.1038/asiamat.2009.52}}</ref>
Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave saturable absorption in graphene demonstrates the possibility of graphene microwave and terahertz photonics devices, such as microwave saturable absorber, modulator, polarizer, microwave signal processing and broad-band wireless access networks.<ref name=Zheng>{{Cite journal | author = Zheng, Z. ''et al.'' | title = Microwave and optical saturable absorption in graphene | journal = Optics Express | year = 2012 | volume = 20 | issue = 21 | pages = 23201–23214 | doi = 10.1364/OE.20.023201 | url = http://www.opticsinfobase.org/view_article.cfm?gotourl=http%3A%2F%2Fwww.opticsinfobase.org%2FDirectPDFAccess%2FDDD3E2E7-B65E-B0FE-CE508B2B58C39140_242486%2Foe-20-21-23201.pdf%3Fda%3D1%26id%3D242486%26seq%3D0%26mobile%3Dno&org= | format = PDF | pmid = 23188285 | first2 = Chujun | first3 = Shunbin | first4 = Yu | first5 = Ying | first6 = Han | first7 = Shuangchun|bibcode = 2012OExpr..2023201Z }}</ref>
 
====Nonlinear Kerr effect====
 
Under more intensive laser illumination, graphene could also possess a nonlinear phase shift due to the optical nonlinear [[Kerr effect]]. Based on a typical open and close aperture z-scan measurement, graphene possesses a giant non-linear Kerr coefficient of {{val|e=-7|u=cm<sup>2</sup>·W<sup>−1</sup>}}, almost nine orders of magnitude larger than that of bulk dielectrics.<ref name=ZHANGHAN>{{ Cite journal | author = Zhang, H. ''et al.'' | title = Z-scan measurement of the nonlinear refractive index of graphene | journal = Optics Letters | year = 2012 | volume = 37 | issue = 11 | pages = 1856–1858 | doi = 10.1364/OL.37.001856 | pmid = 22660052 | first2 = Stéphane | first3 = Qiaoliang | first4 = Loh | first5 = Serge | first6 = Nicolas | first7 = Pascal |bibcode = 2012OptL...37.1856Z }}</ref> This suggests that graphene may be a nonlinear Kerr medium, paving the way for graphene-based nonlinear Kerr photonics such as a [[soliton]].
 
===Excitonic===
 
First-principle calculations with quasiparticle corrections and many-body effects are performed to study the electronic and optical properties of graphene-based materials. The approach is described as three stages.<ref>{{cite journal |journal=Rev. Mod. Phys. |year=2002 |volume=74 |page=601 |doi=10.1103/RevModPhys.74.601 |bibcode=2002RvMP...74..601O |title=Electronic excitations: Density-functional versus many-body Green's-function approaches |last1=Onida |first1=Giovanni |last2=Rubio |first2=Angel |issue=2}}</ref> With GW calculation, the properties of graphene-based materials are accurately investigated, including graphene,<ref>{{cite journal |journal=Physical Review Letters |year=2009 |volume=103 |page=186802 |doi=10.1103/PhysRevLett.103.186802 |bibcode=2009PhRvL.103r6802Y |title=Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene |last1=Yang |first1=Li |last2=Deslippe |first2=Jack |last3=Park |first3=Cheol-Hwan |last4=Cohen |first4=Marvin |last5=Louie |first5=Steven |issue=18 |pmid=19905823|arxiv = 0906.0969 }}</ref> [[graphene nanoribbons]],<ref>{{cite journal |journal=Physical Review B |year=2008 |volume=77 |page=041404 |doi=10.1103/PhysRevB.77.041404 |title=Optical properties of graphene nanoribbons: The role of many-body effects |last1=Prezzi |first1=Deborah |last2=Varsano |first2=Daniele |last3=Ruini |first3=Alice |last4=Marini |first4=Andrea |last5=Molinari |first5=Elisa |issue=4|arxiv = 0706.0916 |bibcode = 2008PhRvB..77d1404P }}<br/>{{cite journal |journal=Nano Lett. |year=2007 |volume=7 |pages=3112–5 |doi=10.1021/nl0716404 |title=Excitonic Effects in the Optical Spectra of Graphene Nanoribbons |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=10 |pmid=17824720|arxiv = 0707.2983 |bibcode = 2007NanoL...7.3112Y }}<br/>{{cite journal |journal=Physical Review Letters |year=2008 |volume=101 |page=186401 |doi=10.1103/PhysRevLett.101.186401 |bibcode=2008PhRvL.101r6401Y |title=Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=18 |pmid=18999843}}</ref> edge and surface functionalized armchair graphene nanoribbons,<ref>{{cite journal |journal=J. Phys. Chem. C |year=2010 |volume=114 |page=17257 |doi=10.1021/jp102341b |title=Excitons of Edge and Surface Functionalized Graphene Nanoribbons |last1=Zhu |first1=Xi |last2=Su |first2=Haibin |issue=41}}</ref> hydrogen saturated armchair graphene nanoribbons,<ref>{{cite journal |journal=Nanoscale |year=2011 |volume=3 |pages=2324–8 |doi=10.1039/c1nr10095e |title=Excitonic properties of hydrogen saturation-edged armchair graphene nanoribbons |last1=Wang |first1=Min |last2=Li |first2=Chang Ming |issue=5 |pmid=21503364|bibcode = 2011Nanos...3.2324W }}</ref> [[Josephson effect]] in graphene SNS junctions with single localized defect<ref>{{Cite journal |author=Dima Bolmatov, Chung-Yu Mou |title=Josephson effect in graphene SNS junction with a single localized defect |journal=Physica B |volume=405 |page=2896 |year=2010 |doi=10.1016/j.physb.2010.04.015 |issue=13|arxiv = 1006.1391 |bibcode = 2010PhyB..405.2896B }}<br/>{{Cite journal |author=Dima Bolmatov, Chung-Yu Mou |title=Tunneling conductance of the graphene SNS junction with a single localized defect |journal=Journal of Experimental and Theoretical Physics (JETP) |volume=110 |page=613 |year=2010 |doi=10.1134/S1063776110040084 |issue=4|arxiv = 1006.1386 |bibcode = 2010JETP..110..613B }}</ref> and scaling properties in armchair graphene nanoribbons.<ref>{{cite journal |title=Scaling of Excitons in Graphene Nanoribbons with Armchair Shaped Edges |journal=Journal of Physical Chemistry A |year=2011 |volume=115 |issue=43 |pages=11998–12003 |doi=10.1021/jp202787h |last1=Zhu |first1=Xi |last2=Su |first2=Haibin}}</ref>
 
===Thermal===
 
====Stability====
[[Ab initio quantum chemistry methods|Ab initio calculations]] show that a graphene sheet is thermodynamically unstable if its size is less than about 20&nbsp;nm (“graphene is the least stable structure until about 6000 atoms”) and becomes the most stable [[fullerene]] (as within graphite) only for molecules larger than 24,000 atoms.<ref name=stability>{{Cite journal |author = O. B. Shenderova, V. V. Zhirnov, D. W. Brenner |year = 2002 |title = Carbon Nanostructures |journal = Critical Reviews in Solid State and Materials Sciences |volume = 27 |page = 227 |doi=10.1080/10408430208500497 |bibcode = 2002CRSSM..27..227S |issue = 3–4 }}</ref>
 
====Conductivity====
The near-room temperature [[thermal conductivity]] of graphene was measured to be between (4.84±0.44) × 10<sup>3</sup> to (5.30±0.48) × 10<sup>3</sup> W·m<sup>−1</sup>·K<sup>−1</sup>. These measurements, made by a non-contact optical technique, are in excess of those measured for carbon nanotubes or diamonds. The isotopic composition, the ratio of [[Carbon-12|<sup>12</sup>C]] to [[Carbon-13|<sup>13</sup>C]], has a significant impact on thermal conductivity, where isotopically pure <sup>12</sup>C graphene has higher conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.<ref name=chen2012natmat>{{Cite journal |first=Shanshan
|last=Chen |first2=Qingzhi |last2=Wu |first3=Columbia |last3=Mishra |first4=Junyong |last4=Kang |first5=Hengji |last5=Zhang
|first6=Kyeongjae |last6=Cho |first7=Weiwei |last7=Cai |first8=Alexander A. |last8=Balandin |first9=Rodney S. |last9=Ruoff
|publication-date=2012-01-10 |title=Thermal conductivity of isotopically modified graphene |journal=[[Nature Materials]]
|volume= 11 |issue= 3 |page= 203 |pmid= |doi=10.1038/nmat3207 |year=2012 |arxiv = 1112.5752 |bibcode = 2012NatMa..11..203C }}<br />''Lay summary'': {{Cite news |publication-date=2012-01-12 |title=Keeping Electronics Cool
|periodical=[[Scientific Computing (periodical)|Scientific Computing]] |at=scientificcomputing.com |accessdate=2012-01-15
|publisher=[[Advantage Business Media]]
|url=http://www.scientificcomputing.com/news-HPC-Keeping-Electronics-Cool-011212.aspx?et_cid=2422972&et_rid=220285420&linkid=http%3a%2f%2fwww.scientificcomputing.com%2fnews-HPC-Keeping-Electronics-Cool-011212.aspx |author1=Suzanne Tracy |date=2012-01-12 }}</ref>  It can be shown by using the [[Wiedemann–Franz law]], that the thermal conduction is [[phonon]]-dominated.<ref name="Balandin">{{Cite journal |author=Balandin, A. A. ''et al.'' |date=2008-02-20
|doi=10.1021/nl0731872 |title=Superior Thermal Conductivity of Single-Layer Graphene |journal=[[Nano Letters ASAP]]
|pmid=18284217 |volume=8 |issue=3 |pages=902–907 |bibcode=2008NanoL...8..902B |first2=Suchismita |first3=Wenzhong |first4=Irene |first5=Desalegne |first6=Feng |first7=Chun Ning
}}</ref> However, for a gated graphene strip, an applied gate bias causing a [[Fermi energy]] shift much larger than k<sub>B</sub>T can cause the electronic contribution to increase and dominate over the [[phonon]] contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.<ref name="Saito">{{Cite journal |journal=[[Physical Review B]]
|author=Saito, K., Nakamura, J., and Natori, A. |title=Ballistic thermal conductance of a graphene sheet
|volume=76 |page=115409 |year=2007 |doi=10.1103/PhysRevB.76.115409 |bibcode=2007PhRvB..76k5409S |issue=11
}}</ref><ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401">{{cite journal |author= Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. |year= 2011 |title= A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials |journal= ACS Nano |pmid= 21384860 |volume=5 |issue= 3 |pages= 2392–2401 |doi= 10.1021/nn200181e}}</ref>
 
Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has [[basal plane]][[thermal conductivity]] of over a {{val|1000|u=W·m<sup>−1</sup>·K<sup>−1</sup>}} (comparable to [[diamond]]). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger [[lattice spacing]].<ref>{{Cite book |url=http://books.google.com/?id=7p2pgNOWPbEC |title=Graphite and Precursors |author=Delhaes, P. |publisher=CRC Press |year=2001 |isbn=90-5699-228-7}}</ref> In addition, the ballistic thermal conductance of a graphene is shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon nanotubes.<ref name="mingo">{{Cite journal | author = Mingo N., Broido, D.A. |title = Carbon Nanotube Ballistic Thermal Conductance and Its Limits |doi=10.1103/PhysRevLett.95.096105 |journal = Physical Review Letters | volume = 95 | page = 096105 |year = 2005 | bibcode=2005PhRvL..95i6105M | issue = 9}}</ref>
 
Despite its 2-D nature, graphene has 3 [[acoustic phonon]] modes. The two in-plane modes (LA, TA) have a linear [[dispersion relation]], whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to this, the T<sup>2</sup> dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T<sup>1.5</sup> contribution of the out of plane mode.<ref name="mingo"/> Some graphene phonon bands display negative [[Grüneisen parameter]]s.<ref name="mounet">{{Cite journal |author = Mounet, N. and Marzari, N. |title = First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives |doi=10.1103/PhysRevB.71.205214 |journal = Physical Review B | volume = 71 | page = 205214 | year = 2005 |arxiv = cond-mat/0412643 |bibcode = 2005PhRvB..71t5214M |issue = 20 }}</ref> At low temperatures (where most optical modes with positive Grüneisen parameters are still not excited) the contribution from the negative Grüneisen parameters will be dominant and [[thermal expansion coefficient]] (which is directly proportional to Grüneisen parameters) negative. The lowest negative Grüneisen parameters correspond to the lowest transversal acoustic ZA modes. Phonon frequencies for such modes increase with the in-plane [[lattice parameter]] since atoms in the layer upon stretching will be less free to move in the z direction. This is similar to the behavior of a string, which, when it is stretched, will have vibrations of smaller amplitude and higher frequency. This phenomenon, named "membrane effect", was predicted by [[Ilya Mikhailovich Lifshitz|Lifshitz]] in 1952.<ref name="lifshitz">{{Cite journal |author = Lifshitz, I.M. |journal = Journal of Experimental and Theoretical Physics (in Russian) |volume = 22 | page = 475 | year = 1952}}</ref>
 
===Mechanical===
 
The flat graphene sheet is unstable with respect to scrolling i.e. bending into a cylindrical shape, which is its lower-energy state.<ref name=nmscrolling>{{Cite journal |author = S. Braga, V. R. Coluci, S. B. Legoas, R. Giro, D. S. Galvão, R. H. Baughman |year = 2004 |title = Structure and Dynamics of Carbon Nanoscrolls |journal = Nano Letters |volume = 4 |page = 881 |doi=10.1021/nl0497272 |bibcode = 2004NanoL...4..881B |issue = 5 }}</ref>
 
As of 2009, graphene appeared to be one of the strongest materials known with a [[breaking strength]] over 100 times greater than a hypothetical [[steel]] film of the same (thin) thickness,<ref name="nobelprize.org">[http://www.nobelprize.org/nobel_prizes/physics/laureates/2010/advanced-physicsprize2010.pdf 2010 Nobel Physics Laureates]. nobelprize.org.</ref> with a [[Young's modulus]]
(stiffness) of {{val|1|u=TPa}} ({{val|150000000|u=[[Pounds per square inch|psi]]}}).<ref name=lee>{{Cite journal |author = Lee, C. ''et al.'' |title = Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene |journal = Science |volume = 321 |year = 2008 |laysummary =http://web.archive.org/web/20110629131809/http://www.aip.org/isns/reports/2008/027.html |doi = 10.1126/science.1157996 |pmid = 18635798 |issue = 5887 |bibcode = 2008Sci...321..385L |pages = 385–8 |first2 = X. |first3 = J. W. |first4 = J. }}</ref> The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a {{val|4|u=kg}} cat but would weigh only as much as one of the cat's whiskers, at 0.77&nbsp;mg (about 0.001% of the weight of 1&nbsp;m<sup>2</sup> of paper).<ref name="nobelprize.org"/>
 
However, the process of separating it from graphite, where it occurs naturally, requires technological development to be economical enough to be used in industrial processes.<ref name="nypost">{{cite news |url =http://www.nypost.com/seven/08252008/news/regionalnews/toughest_stuff__known_to_man_125993.htm |title = Toughest Stuff Known to Man: Discovery Opens Door to Space Elevator |first = Bill |last = Sanderson |publisher = nypost.com |date = 2008-08-25 |accessdate = 2008-10-09}}</ref><ref name="ScienceDaily">{{cite web |url =http://www.sciencedaily.com/releases/2010/01/100119111057.htm |title = Breakthrough in Developing Super-Material Graphene |publisher = ScienceDaily |date = 2010-01-20 |accessdate = 2010-02-21}}</ref>
 
The [[spring constant]] of suspended graphene sheets has been measured using an [[atomic force microscope]] (AFM). Graphene sheets, held together by van der Waals forces, were suspended over {{chem|SiO|2}} cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was {{val|0.5|u=TPa}}, which differs from that of bulk graphite. These high values make graphene very strong and rigid. These intrinsic properties could lead to using graphene for [[Nanoelectromechanical systems|NEMS]] applications such as pressure sensors and resonators.<ref>{{Cite journal |author = Frank, I. W., Tanenbaum, D. M., Van Der Zande, A.M., and McEuen, P. L. |title = Mechanical properties of suspended graphene sheets |doi=10.1116/1.2789446 |journal = J. Vac. Sci. Technol. B |volume = 25 |pages = 2558–2561 |year = 2007 |url =http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/JVSTB_Pushing_Graphene.pdf |bibcode = 2007JVSTB..25.2558F |issue = 6 }}</ref>
 
As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the [[Mermin-Wagner theorem]] shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,<ref name=Meyer07/> and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.{{sfn|Geim|Novoselov|2007}}<ref name="Carlsson"/><ref name="Fasolino"/><ref>{{Cite journal |author=Dima Bolmatov and Chung-Yu Mou |title = Graphene-based modulation-doped superlattice structures |journal = Journal of Experimental and Theoretical Physics (JETP) |volume = 112 |page = 102 |year=2011 |doi =10.1134/S1063776111010043|arxiv = 1011.2850 |bibcode = 2011JETP..112..102B }}<br/>{{Cite journal |author=Dima Bolmatov |title=Thermodynamic properties of tunneling quasiparticles in graphene-based structures |journal=Physica C |volume=471 |page=1651 |year=2011 |doi=10.1016/j.physc.2011.07.008 |issue=23–24|arxiv = 1106.6331 |bibcode = 2011PhyC..471.1651B }}</ref>
 
===Spin transport===
 
Graphene is claimed to be an ideal material for [[spintronics]] due to its small [[spin-orbit interaction]] and the near absence of [[nuclear magnetic moment]]s in carbon (as well as a weak [[hyperfine interaction]]). Electrical [[spin current]] injection and detection has been demonstrated up to room temperature.<ref name="Tombros">{{cite journal | title=Electronic spin transport and spin precession in single graphene layers at room temperature | bibcode=2007Natur.448..571T | last=Tombros | first=Nikolaos | coauthors=et al. | journal=Nature | year=2007 | format=PDF | volume=448 | issue=7153 | pages=571–575 | doi=10.1038/nature06037 | pmid=17632544|arxiv = 0706.1948 }}</ref><ref name="ChoSpin">
{{Cite journal |last = Cho |first = Sungjae |coauthors = Yung-Fu Chen, and Michael S. Fuhrer |year =2007 |volume = 91 |page = 123105 |title = Gate-tunable Graphene Spin Valve |journal = Applied Physics Letters |doi = 10.1063/1.2784934
| bibcode = 2007ApPhL..91l3105C |issue = 12 |arxiv = 0706.1597 }}</ref><ref name="Ohishi">{{Cite journal |last = Ohishi |first = Megumi |coauthors = et al. |year = 2007 |volume = 46 |pages = L605–L607 |title = Spin Injection into a Graphene Thin Film at Room Temperature |journal = Jpn J Appl Phys |doi = 10.1143/JJAP.46.L605 |bibcode = 2007JaJAP..46L.605O |arxiv = 0706.1451 }}</ref> Spin coherence length above 1 micrometre at room temperature was observed,<ref name="Tombros"/> and control of the spin current polarity with an electrical gate was observed at low temperature.<ref name="ChoSpin"/>
 
===Anomalous quantum Hall effect===
{{jargon|section|date=December 2013}}
 
The [[quantum Hall effect]] is relevant for accurate measuring of electrical quantities, and in 1985 [[Klaus von Klitzing]] received the [[Nobel prize]] for its discovery. The effect concerns the dependence of a transverse conductivity on a [[magnetic field]], which is perpendicular to a current-carrying stripe. Usually the phenomenon, the quantization of the so-called [[Hall effect|Hall conductivity]] <math>\sigma_{xy}</math> at integer multiples (the "[[Landau level]]") of the basic quantity <math>e^2/h</math> (where ''e'' is the elementary electric charge and ''h'' is [[Planck's constant]]) can be observed only in very clean [[silicon]] or [[gallium arsenide]] solids at very low temperatures around 3&nbsp;[[degrees Kelvin|K]] and very high magnetic fields.
 
In contrast graphene shows the quantum Hall effect just in the presence of a magnetic field and just with respect to conductivity-quantization: the effect is ''anomalous'' in that the sequence of stepsis shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is <math>\sigma_{xy} = \pm {4\cdot\left(N + 1/2 \right)e^2}/h </math>, where ''N'' is the Landau level and the double valley and double spin degeneracies give the factor of 4.{{sfn|Geim|Novoselov|2007}} Moreover, in graphene these anomalies are present at room temperature, i.e. at roughly {{val|20|u=°C}}.<ref name="2dgasDiracFermions"/> This anomalous behavior is a direct result of graphene's massless Dirac electrons. In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the [[Atiyah–Singer index theorem]] and is half-filled in neutral graphene,<ref name="Semenoff"/> leading to the "+1/2" in the Hall conductivity.<ref name="Gusynin">{{Cite journal |author =Gusynin, V. P. and Sharapov, S. G. |title = Unconventional Integer Quantum Hall Effect in Graphene |doi=10.1103/PhysRevLett.95.146801 |journal = Physical Review Letters |volume = 95 | page = 146801 |year =2005 |pmid=16241680 |bibcode=2005PhRvL..95n6801G |arxiv = cond-mat/0506575 |issue =14 }}</ref> Bilayer graphene also shows the quantum Hall effect, but with only one of the two anomalies (i.e. <math>\sigma_{xy} = \pm {4\cdot N\cdot e^2}/h </math>). In the second anomaly, the first plateau at ''N = 0'' is absent, indicating that bilayer graphene stays metallic at the neutrality point.{{sfn|Geim|Novoselov|2007}}
 
Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the [[Shubnikov–De Haas effect|Shubnikov–De Haas oscillations]], which show a phase shift of π, known as [[Geometric phase|Berry’s phase]].<ref name="2dgasDiracFermions"/><ref name="E-Phonon"/> Berry’s phase arises due to the zero effective carrier mass near the Dirac points.<ref name="Berry'sPhase">{{Cite journal | author = Zhang, Y., Tan, Y. W., Stormer, H. L., and Kim, P. |title = Experimental observation of the quantum Hall effect and Berry's phase in graphene |doi=10.1038/nature04235 |journal = Nature | volume = 438 | pages = 201–204 |year = 2005 | pmid = 16281031 | issue = 7065 |arxiv = cond-mat/0509355 |bibcode = 2005Natur.438..201Z }}</ref> Study of the temperature dependence of graphene's Shubnikov–de Haas oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass from the E–k relation.<ref name="2dgasDiracFermions"/>
 
Graphene samples prepared on nickel films, and on both the silicon face and carbon face of [[silicon carbide#Structure and properties|silicon carbide]], show the [[anomalous quantum Hall effect]] directly in electrical measurements.<ref name="ByungHeeHong"/><ref name="0908.1900"/><ref name="ShenAPL"/><ref name=0909.2903/><ref name=0909.1193/><ref name=phase1/> Graphitic layers on the carbon face of silicon carbide show a clear [[Dirac spectrum]] in[[ARPES|angle-resolved photoemission]] experiments, and the anomalous quantum Hall effect is observed in cyclotron resonance and tunneling experiments.<ref name="Fuhrer09">{{Cite journal |author = Michael S. Fuhrer |title = A physicist peels back the layers of excitement about graphene|doi=10.1038/4591037e |journal = Nature |volume = 459 |page = 1037 |year = 2009 |pmid = 19553953|issue = 7250 |bibcode = 2009Natur.459.1037F }}</ref>
 
====Strong magnetic fields====
 
Graphene's quantum Hall effect in magnetic fields above 10 [[Tesla (unit)|Tesla]]s or so reveals additional interesting features. Additional plateaus of the Hall conductivity at <math>\sigma_{xy} = \nu e^2/h</math> with <math>\nu = 0,\pm {1},\pm {4}</math> are observed.<ref name="nu-0-1-4">{{Cite journal | author = Zhang, Y. et al. |title = Landau-Level Splitting in Graphene in High Magnetic Fields |doi=10.1103/PhysRevLett.96.136806 |journal = Physical Review Letters | volume = 96 | page = 136806 |year = 2006 | bibcode=2006PhRvL..96m6806Z | issue = 13 | first2 = Z. | first3 = J. P. | first4 = M. S. | first5 = Y.-W. | first6 = M. | first7 = J. D. | first8 = J. A. | first9 = H. L. | first10 = P.|arxiv = cond-mat/0602649 }}</ref> Also, the observation of a plateau at <math>\nu = 3</math><ref name="nu-3">{{Cite journal | author = Du, X. et al. |title = Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene |doi=10.1038/nature08522 |journal = Nature | volume = 462 | pages = 192–195 |year = 2009 | issue=7270 | pmid = 19829294 | first2 = Ivan | first3 = Fabian | first4 = Adina | first5 = Eva Y.|arxiv = 0910.2532 |bibcode = 2009Natur.462..192D }}</ref> and the fractional quantum Hall effect at <math>\nu = 1/3</math> were reported.<ref name="nu-3"/><ref name="nu-one3rd">{{Cite journal | author = Bolotin, K. et al. |title = Observation of the fractional quantum Hall effect in graphene |doi=10.1038/nature08582 |journal = Nature | volume = 462 | pages = 196–199 |year = 2009 | issue=7270 | pmid=19881489 | first2 = Fereshte | first3 = Michael D. | first4 = Horst L. | first5 = Philip|arxiv = 0910.2763 |bibcode = 2009Natur.462..196B }}</ref>
 
These observations with <math>\nu = 0,\pm 1,\pm 3, \pm 4</math> indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis is that the [[magnetic catalysis]] of [[symmetry breaking]] is responsible for lifting the degeneracy.{{citation needed|date=December 2013}}
 
==Forms==
 
===Nanostripes===
 
[[Graphene nanoribbons]] ("nanostripes" in the "zig-zag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of [[spintronics]]. (In the "armchair" orientation, the edges behave like semiconductors.<ref name="Castro">{{Cite journal | author = A Castro Neto, ''et al.'' | title = The electronic properties of graphene | journal = Rev Mod Phys |volume = 81 |year = 2009 | page = 109 | url = http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |bibcode = 2009RvMP...81..109C |doi = 10.1103/RevModPhys.81.109 | first2 = N. M. R. | first3 = K. S. | first4 = A. K. |arxiv = 0709.1163 }}</ref>)
 
===Graphene oxide===
{{further2|[[Graphite oxide]]}}
Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called [[graphene oxide paper]] have a measured [[Tensile Modulus|tensile modulus]] of 32 [[GPa]].<ref>{{cite web | url = http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper | archiveurl = http://web.archive.org/web/20110720013914/http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper | archivedate = 2011-07-20 |title = Graphene Oxide Paper | publisher = Northwestern University | accessdate = 2011-02-28}}</ref> The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the polymerization pathway and similar chemical processes.<ref>{{cite journal |last1=Eftekhari |first1=Ali |last2=Yazdani |first2=Bahareh |title=Initiating electropolymerization on graphene sheets in graphite oxide structure |journal=Journal of Polymer Science Part A: Polymer Chemistry |volume=48 |page=2204 |year=2010 |doi=10.1002/pola.23990 |bibcode = 2010JPoSA..48.2204E |issue=10 }}</ref> Graphene oxide flakes in polymers display enhanced photo-conducting properties.<ref>{{cite journal |author=Nalla, Venkatram |last2=Polavarapu |first2=L |last3=Manga |first3=KK |last4=Goh |first4=BM |last5=Loh |first5=KP |last6=Xu |first6=QH |last7=Ji |first7=W |title=Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer–graphene oxide composite |journal=Nanotechnology |volume=21 |issue=41 |page=415203 |year=2010 |pmid=20852355 |doi=10.1088/0957-4484/21/41/415203 |bibcode = 2010Nanot..21O5203N }}</ref> Graphene-based membranes are impermeable to all gases and liquids (vacuum-tight). However, water evaporates through them as quickly as if the membrane was not present.<ref name="pmid22282806" />
 
===Chemical modification===
{{jargon|section|date=December 2013}}
[[File:slgo.jpg|left|350px|thumb|Photograph of single-layer graphene oxide undergoing high temperature chemical treatment, resulting in sheet folding and loss of carboxylic functionality, or through room temperature carbodiimide treatment, collapsing into star-like clusters.]] Soluble fragments of graphene can be prepared in the laboratory<ref>{{Cite journal | author =Sandip Niyogi, Elena Bekyarova, Mikhail E. Itkis, Jared L. McWilliams, Mark A. Hamon, and Robert C. Haddon |title = Solution Properties of Graphite and Graphene |journal = [[J. Am. Chem. Soc.]] | volume = 128 | pages = 7720–7721 |year = 2006 | doi = 10.1021/ja060680r | pmid =16771469 | issue =24}}</ref> through chemical modification of graphite. First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and [[nitric acid]]. A series of oxidation and exfoliation steps produce small graphene plates with [[carboxyl]] groups at their edges. These are converted to [[acid chloride]] groups by treatment with [[thionyl chloride]]; next, they are converted to the corresponding graphene [[amide]] via treatment with [[octadecylamine]]. The resulting material (circular graphene layers of 5.3 [[angstrom]] thickness) is soluble in [[tetrahydrofuran]], [[tetrachloromethane]] and [[1,2-Dichloroethane|dichloroethane]].
 
Refluxing single-layer graphene oxide (SLGO) in [[solvent]]s leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependant on their preparation methodology. When using thionyl chloride, [[acyl chloride]] groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%.
[[File:graphene chemistry.jpg|right|350px|thumb|Boehm titration results for various chemical reactions of single-layer graphene oxide, which reveal reactivity of the carboxylic groups and the resultant stability of the SLGO sheets after treatment.]]
 
[[Hydrazine]] reflux is commonly used for reducing SLGO to SLG(R), but [[titration]]s show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with HCl (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with [[carbodiimide]]s leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (ca. 3–5% conversion of the intermediate to the final amide).<ref>{{Cite journal | author = Raymond L.D. Whitby, Alina Korobeinyk, and Katya V. Glevatska |title = Morphological changes and covalent reactivity assessment of single-layer graphene oxides under carboxylic group-targeted chemistry |journal = [[Carbon]] |volume = 49 |issue = 2 |pages = 722–725 |year = 2011 | doi = 10.1016/j.carbon.2010.09.049}}</ref> It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reactions types have been explored. SLGO has also been grafted with [[polyallylamine]], cross-linked through [[epoxy]] groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.<ref>{{Cite journal | author = Sungjin Park, Dmitriy A. Dikin, SonBinh T. Nguyen, and Rodney S. Ruoff |title = Graphene Oxide Sheets Chemically Cross-Linked by Polyallylamine |journal = [[J. Phys. Chem. C]] | volume = 113 | pages = 15801–15804 |year = 2009 | doi = 10.1021/jp907613s | issue = 36}}</ref>
 
Full [[hydrogenation]] from both sides of graphene sheet results in [[graphane]], but partial hydrogenation leads to hydrogenated graphene.<ref>{{Cite journal | author= D. C. Elias ''et al.'' |title =Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane | journal = Science |year =2009 |volume = 323 | doi = 10.1126/science.1167130 | pmid= 19179524 | issue= 5914 |bibcode = 2009Sci...323..610E | pages= 610–3 | first2= R. R. | first3= T. M. G. | first4= S. V. | first5= P. | first6= M. P. | first7= A. C. | first8= D. W. | first9= M. I. | first10= A. K. | first11= K. S. |arxiv = 0810.4706 }}</ref> Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to [[fluorographene]] (graphene fluoride), while partial fluorination (generally halogenation) provides fluorinated (halogenated) graphene.
 
===Casimir effect and dispersion===
 
The [[Casimir effect]] is an interaction between any disjoint neutral bodies provoked by the fluctuations of the electrodynamical vacuum. Mathematically it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary (or matching) conditions on the surfaces of the interacting bodies. Since the interaction of graphene with an electromagnetic field is surprisingly strong for a one-atom-thick material, the Casimir effect is of growing interest.<ref name=BFGV>{{Cite journal | author = Bordag M., Fialkovsky I. V., Gitman D. M., Vassilevich D. V. | title = Casimir interaction between a perfect conductor and graphene described by the Dirac model |journal = Physical Review B |volume = 80 |year = 2009 | page = 245406 | doi = 10.1103/PhysRevB.80.245406 |bibcode = 2009PhRvB..80x5406B | issue = 24 |arxiv = 0907.3242 }}</ref><ref name=FMD>{{cite journal | author = Fialkovsky I. V., Marachevskiy V.N., Vassilevich D. V. | title = Finite temperature Casimir effect for graphene |year = 2011 | volume = 84 | issue = 35446 | journal = Physical Review B | arxiv = 1102.1757 | bibcode = 2011PhRvB..84c5446F | last2 = Marachevsky | last3 = Vassilevich | page = 35446 | doi = 10.1103/PhysRevB.84.035446}}</ref>
 
The related van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic, asymptotic power law in contrast to the usual inverse quartic.<ref name=DWR>{{Cite journal | author = Dobson J. F., White A., Rubio A. | title = Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals |journal = Physical Review Letters |volume = 96 |year = 2006 | page = 073201 | doi = 10.1103/PhysRevLett.96.073201 | issue = 7 | bibcode=2006PhRvL..96g3201D|arxiv = cond-mat/0502422 }}</ref>
 
===Bilayer graphene===
{{main|Bilayer graphene}}
Bilayer graphene displays the [[anomalous quantum Hall effect]], a tunable [[band gap]]<ref name="PRB75.155115">{{Cite journal |doi=10.1103/PhysRevB.75.155115 |title=Ab initio theory of gate induced gaps in graphene bilayers |year=2007 |last1=Min |first1=Hongki |last2=Sahu |first2=Bhagawan |last3=Banerjee |first3=Sanjay |last4=MacDonald |first4=A. |journal=Physical Review B |volume=75 |issue=15|arxiv = cond-mat/0612236 |bibcode = 2007PhRvB..75o5115M }}</ref> and potential for [[Exciton#Interaction|excitonic condensation]]<ref name="PRL104.096802">{{Cite journal |doi=10.1103/PhysRevLett.104.096802 |title=Anomalous Exciton Condensation in Graphene Bilayers |year=2010 |last1=Barlas |first1=Yafis |last2=Côté |first2=R. |last3=Lambert |first3=J. |last4=MacDonald |first4=A. H. |journal=Physical Review Letters |volume=104 |issue=9 |bibcode=2010PhRvL.104i6802B|arxiv = 0909.1502 }}</ref>&nbsp;–making them promising candidates for optoelectronic and nanoelectronic applications. Bilayer graphene typically can be found either in twisted configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other. Stacking order and orientation govern the optical and electronic properties of bilayer graphene.
 
One way to synthesize bilayer graphene is via [[chemical vapor deposition]], and can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.<ref name="nl204547v">{{Cite journal |doi=10.1021/nl204547v |title=Twinning and Twisting of Tri- and Bilayer Graphene |year=2012 |last1=Min |first1=Lola |last2=Hovden |first2=Robert |last3=Huang |journal=NanoLetters |volume=12 |issue=3 |first3=Pinshane |last4=Wojcik |first4=Michal |last5=Muller |first5=David A. |last6=Park |first6=Jiwoong |page=1609|bibcode = 2012NanoL..12.1609B }}</ref>
 
===3D graphene===
 
In 2013, a three-dimensional [[honeycomb]] of hexagonally arranged carbon was termed 3D graphene, although self-supporting 3D graphene has not yet been produced.<ref>{{Cite doi|10.1002/ange.201303497}}<br/>{{cite journal |url=http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells |title=3D graphene could replace expensive platinum in solar cells |publisher=KurzweilAI |date= |accessdate=2013-08-24 |last1=Wang |first1=Hui |last2=Sun |first2=Kai |last3=Tao |first3=Franklin |last4=Stacchiola |first4=Dario J. |last5=Hu |first5=Yun Hang |journal=Angewandte Chemie |volume=125 |issue=35 |page=9380}}</ref>
 
==Production techniques==
True isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle. However, other routes to 2d materials exist:
{{quote|Fundamental forces place seemingly insurmountable barriers in the way of creating [2D crystals]... The nascent 2D crystallites try to minimize their surface energy and inevitably morph into one of the rich variety of stable 3D structures that occur in soot.
 
But there is a way around the problem. Interactions with 3D structures stabilize 2D crystals during growth. So one can make 2D crystals sandwiched between or placed on top of the atomic planes of a bulk crystal. In that respect, graphene already exists within graphite... One can then hope to fool Nature and extract single-atom-thick crystallites at a low enough temperature that they remain in the quenched state prescribed by the original higher-temperature 3D growth.<ref name="PhysTod"/>}}
 
Graphene planes become better separated in [[Intercalation (chemistry)|intercalated]] graphite compounds.
 
Graphene fragments are produced (along with other debris) whenever graphite is abraded, such as when drawing with a pencil.<ref name=SciAm>
{{Cite news
|last1=Geim |first1=A. K.
|last2=Kim |first2=P.
|date=April 2008
|title=Carbon Wonderland
|url=http://www.scientificamerican.com/article.cfm?id=carbon-wonderland
|work=[[Scientific American]]
|accessdate=2009-05-05
|quote=... bits of graphene are undoubtedly present in every pencil mark
}}</ref>
 
In 2011 the Institute of Electronic Materials Technology and Department of Physics at [[Warsaw University]] announced Sicilicon-based epitaxy technology for producing large pieces of graphene with the best quality to date.<ref>
{{cite web
|date=22 April 2011
|title=Polish scientists hope to patent graphene mass-production technology
|url=http://www.wbj.pl/article-54247-polish-scientists-to-patent-graphene-mass-production-technology.html
|work=[[Warsaw Business Journal]]
}}<br/>
{{cite web
|last=Waszak |first1=S.
|date=April 2011
|title=Polish team claims leap for wonder material graphene
|url=http://www.physorg.com/news/2011-04-team-material-graphene.html
|work=[[Phys.org]]
}}</ref>
 
===Mechanical exfoliation===
This involves splitting single layers of graphene from multi-layered graphite. Achieving single layers typically requires multiple exfoliation steps, each producing a slice with fewer layers, until only one remains. Geim and Novosolev used adhesive tape to split the layers.
 
After exfoliation the flakes are deposited on a silicon wafer using "dry deposition". Individual atomic planes can be viewed with an optical microscope. Crystallites larger than 1&nbsp;mm and visible to the naked eye can be obtained with the technique. It is often referred to as a "[[scotch tape]]" or "drawing" method. The latter name appeared because the dry deposition resembles drawing with a piece of graphite.<ref name="PhysTod">{{Cite journal |author =Geim, A. K. & MacDonald, A. H. |title =Graphene: Exploring carbon flatland | url=http://scitation.aip.org/content/aip/magazine/physicstoday/article/60/8/10.1063/1.2774096 |journal = Physics Today | volume = 60 | pages = 35–41 | year = 2007 |doi =10.1063/1.2774096 |bibcode = 2007PhT....60h..35G |issue =8 }}</ref>
 
===Epitaxy===
[[Epitaxy]] refers to the deposition of a crystalline overlayer on a crystalline substrate, where there is registry between the two. In some cases epitaxial graphene layers are coupled to surfaces weakly enough (by [[Van der Waals force]]s) to retain the two dimensional [[electronic band structure]] of isolated graphene.<ref name=Gall1>
{{cite journal
|last1=Gall |first1=N. R.
|last2=Rut'Kov |first2=E. V.
|last3=Tontegode |first3=A. Ya.
|year=1997
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|journal=[[International Journal of Modern Physics B]]
|volume=11 |issue=16 |page=1865
|bibcode=1997IJMPB..11.1865G
|doi=10.1142/S0217979297000976
}}</ref><ref name=Gall2>
{{cite journal
|last1=Gall |first1=N. R.
|last2=Rut'Kov |first2=E. V.
|last3=Tontegode |first3=A. Ya.
|year=1995
|title=Influence of surface carbon on the formation of silicon-refractory metal interfaces
|journal=[[Thin Solid Films]]
|volume=266 |issue=2 |page=229
|bibcode=1995TSF...266..229G
|doi=10.1016/0040-6090(95)06572-5
}}</ref> An example of weakly coupled epitaxial graphene is the one grown on SiC.<ref name="Nov 04">
{{cite journal
|last1=Novoselov |first1=K. S.
|last2=Geim |first2=A. K.
|last3=Morozov |first3=S. V.
|last4=Jiang |first4=D.
|last5=Zhang |first5=Y.
|last6=Dubonos |first6=S. V.
|last7=Grigorieva |first7=I. V.
|last8=Firsov |first8=A. A.
|year=2004
|title=Electric Field Effect in Atomically Thin Carbon Films
|url=http://onnes.ph.man.ac.uk/nano/Publications/Science_2004.pdf
|journal=[[Science (journal)|Science]]
|volume=306 |issue=5696 |pages=666–669
|arxiv=cond-mat/0410550
|bibcode=2004Sci...306..666N
|doi=10.1126/science.1102896
|pmid=15499015
}}</ref>
 
Graphene monolayers grown on SiC and Ir are weakly coupled to these substrates (how weakly remains debated) and the graphene–substrate interaction can be further passivated.<ref name=SiCplusH2/>
 
====Silicon carbide====
{{Main|Tunable nanoporous carbon|l1=Carbide-derived Carbon}}
 
Heating [[silicon carbide]] (SiC) to high temperatures (>{{val|1100|u=°C}}) under low pressures (~10<sup>−6</sup> torr) reduces it to graphene.<ref>{{Cite journal | author = Sutter, P. |title = Epitaxial graphene: How silicon leaves the scene |journal = Nature Materials |volume = 8 |year = 2009 | pmid = 19229263 | doi = 10.1038/nmat2392 | issue = 3 |bibcode = 2009NatMa...8..171S | pages = 171–2 }}</ref> This process produces epitaxial graphene with dimensions dependent upon the size of the wafer. The face of the SiC used for graphene formation, silicon- or carbon-terminated, highly influences the thickness, mobility and carrier density of the resulting graphene.
 
The electronic band-structure (so-called Dirac cone structure) was first visualized in this material.<ref name=ohta1>{{Cite journal |author = Ohta, T. ''et al.'' |year = 2007 |title = Interlayer Interaction and Electronic Screening in Multilayer Graphene Investigated with Angle-Resolved Photoemission Spectroscopy |journal = Physical Review Letters |volume = 98 |page = 206802 |doi = 10.1103/PhysRevLett.98.206802 |pmid=17677726 |bibcode=2007PhRvL..98t6802O |issue = 20 |first2 = Aaron |first3 = J. |first4 = Thomas |first5 = Karsten |first6 = Eli}}</ref><ref name=ohta2>{{Cite journal |author = Bostwick, A. ''et al.'' |year = 2007 |title = Symmetry breaking in few layer graphene films |journal = New Journal of Physics |volume = 9 |page = 385 |doi = 10.1088/1367-2630/9/10/385 |bibcode = 2007NJPh....9..385B |issue = 10 |first2 = Taisuke |first3 = Jessica L |first4 = Konstantin V |first5 = Thomas |first6 = Karsten |first7 = Eli |arxiv = 0705.3705 }}</ref><ref name="Lanzara06">{{Cite journal |last1=Zhou |first1=S.Y. |title = First direct observation of Dirac fermions in graphite |doi = 10.1038/nphys393 |journal = Nature Physics |volume = 2 |pages = 595–599 |year = 2006 |arxiv = cond-mat/0608069 |bibcode = 2006NatPh...2..595Z |issue=9 |first2 =G.-H. |first3 =J. |first4 =A. V. |first5 =C. D. |first6 =R. D. |first7 =Y. |first8 =D.-H. |first9 =Steven G. |first10 =A.}}</ref> Weak anti-localization is observed in this material, but not in exfoliated graphene produced by the pencil-trace method.<ref name=exf>{{Cite journal |author = Morozov, S.V. ''et al.'' |title = Strong Suppression of Weak Localization in Graphene |doi = 10.1103/PhysRevLett.97.016801 |journal = Physical Review Letters |volume = 97 |page = 016801 |year = 2006 |pmid = 16907394 |issue = 1 |bibcode=2006PhRvL..97a6801M |arxiv = cond-mat/0603826 |first2 = K. S. |first3 = M. I. |first4 = F. |first5 = L. A. |first6 = D. |first7 = A. K. }}</ref> Large, temperature-independent mobilities have been observed, approaching those in exfoliated graphene placed on silicon oxide, but lower than mobilities in suspended graphene produced by the drawing method. Even without transfer, graphene on SiC exhibits massless Dirac fermions.<ref name="ByungHeeHong"/><ref name="0908.1900">{{cite journal |author = Johannes Jobst, Daniel Waldmann, Florian Speck, Roland Hirner, Duncan K. Maude, Thomas Seyller, Heiko B. Weber |title = How Graphene-like is Epitaxial Graphene? Quantum Oscillations and Quantum Hall Effect |year = 2009 |doi = 10.1103/PhysRevB.81.195434 |journal = Physical Review B |volume = 81 |issue = 19 |arxiv =0908.1900|bibcode = 2010PhRvB..81s5434J }}</ref><ref name="ShenAPL">{{Cite journal |author = T. Shen, J.J. Gu, M. Xu, Y.Q. Wu, M.L. Bolen, M.A. Capano, L.W. Engel, P.D. Ye |title = Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001) |doi=10.1063/1.3254329 |journal = Applied Physics Letters |bibcode = 2009ApPhL..95q2105S |year = 2009 |volume = 95 |issue = 17 |page = 172105 |arxiv = 0908.3822 }}</ref><ref name=0909.2903>{{cite journal |author = Xiaosong Wu, Yike Hu, Ming Ruan, Nerasoa K Madiomanana, John Hankinson, Mike Sprinkle, Claire Berger, Walt A. de Heer |year = 2009 |title = Half integer quantum Hall effect in high mobility single layer epitaxial graphene |doi = 10.1063/1.3266524 |journal = Applied Physics Letters |volume = 95 |issue = 22 |page = 223108 |arxiv = 0909.2903|bibcode = 2009ApPhL..95v3108W }}</ref><ref name=0909.1193>{{cite journal |author = Samuel Lara-Avila, Alexei Kalaboukhov, Sara Paolillo, Mikael Syväjärvi, Rositza Yakimova, Vladimir Fal'ko, Alexander Tzalenchuk, Sergey Kubatkin |year = 2009 |title = SiC Graphene Suitable For Quantum Hall Resistance Metrology |doi = 10.1038/nnano.2009.474 |journal = Nature Nanotechnology |volume = 5 |issue = 3 |pages = 186–9 |pmid = 20081845 |arxiv=0909.1193|bibcode = 2010NatNa...5..186T }}</ref><ref name=phase1>{{cite journal |author = J.A. Alexander-Webber, A.M.R. Baker, T.J.B.M. Janssen, A. Tzalenchuk, S. Lara-Avila, S. Kubatkin, R. Yakimova, B. A. Piot, D. K. Maude, and R.J. Nicholas |year = 2013 |title = Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene |doi = 10.1103/PhysRevLett.111.096601 |journal = Physical Review Letters |volume = 111 |issue = 9 |page = 096601 |pmid = 24033057 |arxiv=1304.4897|bibcode = 2013PhRvL.111i6601A }}</ref>
 
The weak van der Waals force that provides the cohesion of multilayer graphene stacks does not always affect the electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of certain multilayered epitaxial graphenes are identical to that of a single layer,<ref name="Hass1">{{Cite journal |author = Hass, J. ''et al.'' |year = 2008 |title = Why multilayer graphene on 4H-SiC(000(1)over-bar) behaves like a single sheet of graphene |journal = Physical Review Letters |volume = 100 |page = 125504 |doi = 10.1103/PhysRevLett.100.125504 |bibcode=2008PhRvL.100l5504H |issue = 12 |first2 = F. |first3 = J. |first4 = M. |first5 = N. |first6 = W. |first7 = C. |first8 = P. |first9 = L. |first10 = E.}}</ref> in other cases the properties are affected,<ref name=ohta1/><ref name=ohta2/> as they are in bulk graphite. This effect is well understood theoretically and is related to the symmetry of the interlayer interactions.<ref name="Hass1"/>
 
Epitaxial graphene on SiC can be patterned using standard microelectronics methods. The band gap can be tuned by laser irradiation.<ref>{{cite journal |doi=10.1021/nn201757j |title=Laser Patterning of Epitaxial Graphene for Schottky Junction Photodetectors |year=2011 |last1=Singh |first1=Ram Sevak |last2=Nalla |first2=Venkatram |last3=Chen |first3=Wei |last4=Wee |first4=Andrew Thye Shen |last5=Ji |first5=Wei |journal=ACS Nano |volume=5 |issue=7 |pages=5969–75 |pmid=21702443}}</ref>
 
====Metal substrates====
The atomic structure of a metal substrate can seed the growth of graphene. Graphene grown on [[ruthenium]] does not typically produce uniform layer thickness. Bonding between the bottom graphene layer and the substrate may affect layer properties.<ref name = "PhysOrg.com">{{Cite news | title =A smarter way to grow graphene | url = http://www.physorg.com/news129980833.html |publisher = PhysOrg.com |date=May 2008}}</ref>
 
Graphene grown on [[iridium]] is very weakly bonded, uniform in thickness and can be highly ordered. As on many other substrates, graphene on iridium is slightly rippled. Due to the long-range order of these ripples, minigaps in the electronic band-structure (Dirac cone) become visible.<ref name="grIr111">{{Cite journal |author =Pletikosić, I. ''et al.'' | year = 2009 |title = Dirac Cones and Minigaps for Graphene on Ir(111) |journal = Physical Review Letters |volume = 102 |page = 056808 |doi = 10.1103/PhysRevLett.102.056808 |bibcode=2009PhRvL.102e6808P |issue =5 |first2 =M. |first3 =P. |first4 =R. |first5 =J. |first6 =A. |first7 =C. |first8 =T.|arxiv = 0807.2770 }}</ref>
High-quality sheets of few-layer graphene exceeding {{convert|1|cm2|abbr=on|sigfig=1}} in area have been synthesized via [[chemical vapor deposition]] on thin [[nickel]] films with [[methane]] as a carbon source. These sheets have been successfully transferred to various substrates.<ref name="ByungHeeHong">{{Cite journal |last = Kim |first = Kuen Soo |coauthors = ''et al.'' |title = Large-scale pattern growth of graphene films for stretchable transparent electrodes |year=2009 |doi = 10.1038/nature07719 |journal = Nature |volume=457 |pmid = 19145232 |issue = 7230 |bibcode = 2009Natur.457..706K |pages = 706–10 }}</ref><ref name = hongR/><ref>J. Rafiee, X. Mi, H. Gullapalli, A.V. Thomas, F. Yavari, Y. Shi, P.M. Ajayan, N.A. Koratkar, Wetting transparency of graphene, Nature Materials, 11 (2012) 217-222.</ref>
 
An improvement of this technique employs [[copper]] foil; at very low pressure, the growth of graphene automatically stops after a single graphene layer forms. Arbitrarily large films can be created.<ref name = hongR/><ref name="CopperGraphene">{{Cite journal |last = Li |first = Xuesong |coauthors = ''et al.'' |title = Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils |year=2009 |pmid = 19423775 |doi = 10.1126/science.1171245 |journal = Science |volume=324 |issue = 5932 |bibcode = 2009Sci...324.1312L |pages = 1312–4 |arxiv = 0905.1712 }}</ref> The single layer growth is also due to low concentration of carbon in methane. Larger [[hydrocarbon]]s such as [[ethane]] and [[propane]] produce bilayer graphene.<ref>{{cite journal |last=Wassei |first=Jonathan K. |coauthors=Mecklenburg, Matthew; Torres, Jaime A.; Fowler, Jesse D.; Regan, B. C.; Kaner, Richard B.; Weiller, Bruce H. |title=Chemical Vapor Deposition of Graphene on Copper from Methane, Ethane and Propane: Evidence for Bilayer Selectivity |journal=Small |date=12 May 2012 |volume=8 |issue=9 |pages=1415–1422 |doi=10.1002/smll.201102276 |url=http://onlinelibrary.wiley.com/doi/10.1002/smll.201102276/abstract |pmid=22351509}}</ref> Atmospheric pressure CVD growth produces multilayer graphene on copper (similar to that grown on nickel films).<ref name=lenski>{{cite journal |last1=Lenski |first1=Daniel R. |last2=Fuhrer |first2=Michael S. |title=Raman and optical characterization of multilayer turbostratic graphene grown via chemical vapor deposition |year=2011 |doi=10.1063/1.3605545 |journal=Journal of Applied Physics |volume=110 |page=013720|arxiv = 1011.1683 |bibcode = 2011JAP...110a3720L }}</ref> Graphene has been demonstrated at temperatures compatible with conventional [[CMOS]] processing, using a nickel-based alloy with gold as catalyst.<ref name="cmosgraphene">{{Cite journal |author =Weatherup, R.S. ''et al.'' | year = 2011 |title = In Situ Characterization of Alloy Catalysts for Low-Temperature Graphene Growth |journal = Nano Letters |doi = 10.1021/nl202036y |volume =11 |issue =10 |pages =4154–60 |pmid =21905732 |first2 =Bernhard C. |first3 =Raoul |first4 =Caterina |first5 =Carsten |first6 =Robert |first7 =Stephan|bibcode = 2011NanoL..11.4154W }}</ref>
 
===Reduction of Graphite Oxide===
[[Graphite oxide]] reduction was probably the first method of graphene synthesis. P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962.<ref name="Boehm">[http://graphenetimes.com/2009/12/boehms-1961-isolation-of-graphene/ Boehm’s 1961 isolation of graphene]. Graphene Times (2009-12-07). Retrieved on 2010-12-10.</ref> Geim acknowledged Boehm's contribution.<ref>[http://www.aps.org/publications/apsnews/201001/letters.cfm Letters to the Editor. Many Pioneers in Graphene Discovery]. Aps.org. January 2010.</ref> Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes. Reduction of graphite oxide monolayer films, e.g. by [[hydrazine]], [[annealing (metallurgy)|annealing]] in [[argon]]/[[hydrogen]], was reported to yield graphene films. However, the quality is lower compared to scotch-tape graphene, due to incomplete removal of functional groups. Furthermore, the [[oxidation]] protocol introduces permanent defects due to over-oxidation. Recently, the oxidation protocol was enhanced to yield [[graphene oxide]] with an almost intact carbon framework that allows highly efficient removal of functional groups. The measured [[charge carrier]] mobility exceeded {{convert|1000|cm|2}}/Vs.<ref name="Eigler2013">{{cite journal |author= S. Eigler, M. Enzelberger-Heim, S. Grimm, P. Hofmann, W. Kroener, A. Geworski, C. Dotzer, M. Röckert, J. Xiao, C. Papp, O. Lytken, H.-P. Steinrück, P. Müller, A. Hirsch |title= Wet Chemical Synthesis of Graphene | journal = Advanced Materials |volume=25 |issue=26 |year=2013 |pages=3583–3587 | doi=10.1002/adma.201300155 |pmid= 23703794}}</ref> [[Spectroscopic]] analysis of reduced graphene oxide has been conducted.<ref>{{cite doi|10.1039/C2CP40790F}}</ref><ref name="Yamada">{{cite doi|10.1007/s10853-013-7630-0}}</ref>
 
Applying a layer of graphite oxide film to a [[DVD]] and burning it in a DVD writer produced a thin graphene film with high electrical conductivity (1738 siemens per meter) and specific surface area (1520 square meters per gram), and was highly resistant and malleable.<ref>{{cite web |url=http://www.sciencemag.org/content/335/6074/1326 |title=Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors |publisher=Sciencemag.org |date=2012-03-16 |accessdate=2013-05-02}}<br/>{{cite web |last=Marcus |first=Jennifer |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |title=Researchers develop graphene supercapacitor holding promise for portable electronics / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=2012-03-15 |accessdate=2013-05-02}}</ref>
 
===Metal-carbon melts===
This process dissolves carbon atoms inside a [[transition metal]] melt at a certain temperature and then precipitates the dissolved carbon at lower temperatures as single layer graphene (SLG).<ref name="shaahin">{{Cite journal |author=Shaahin Amini, Javier Garay, Guanxiong Liu, Alexander A. Balandin, Reza Abbaschian |title=Growth of Large-Area Graphene Films from Metal-Carbon Melts |journal=Journal of Applied Physics |volume=108 |issue=9 |page=094321 |year=2010 |doi=10.1063/1.3498815 |bibcode = 2010JAP...108i4321A |arxiv = 1011.4081 }}</ref>
 
The metal is first melted in contact with a carbon source, possibly a graphite crucible inside which the melt is carried out or graphite powder or chunks that are placed in the melt. Keeping the melt in contact with the carbon at a specific temperature dissolves the carbon atoms, saturating the melt based on the [[binary phase diagram]] of metal-carbon. Upon lowering the temperature, carbon's solubility decreases and the excess carbon precipitates atop the melt. The floating layer can be either skimmed or frozen for later removal. Using different morphology, including thick graphite, few layer graphene (FLG) and SLG were observed on metal substrate. [[Raman spectroscopy]] proved that SLG had grown on [[nickel]] substrate. The SLG Raman spectrum featured no D and D′ band, indicating its pristine nature. Among transition metals, nickel provides the best substrate for growing SLG. Since nickel is not Raman active, direct Raman spectroscopy of graphene layers on top of the nickel is achievable.<ref name="shaahin"/>
 
===Sodium ethoxide pyrolysis===
Gram-quantities of graphene were produced by the reduction of [[ethanol]] by [[sodium]] metal, followed by [[pyrolysis]] of the [[ethoxide]] product and washing with water to remove sodium salts.<ref>{{Cite journal |doi = 10.1038/nnano.2008.365 |title = Gram-scale production of graphene based on solvothermal synthesis and sonication |year = 2008 |author = Choucair, M. |journal = Nature Nanotechnology |pmid = 19119279 |volume = 4 |issue = 1 |pages = 30–3 |last2 = Thordarson |first2 = P |last3 = Stride |first3 = JA |bibcode = 2009NatNa...4...30C }}</ref>
 
===Nanotube slicing===
Graphene can be created by cutting open [[carbon nanotube]]s.<ref>{{cite journal | title = Nanotubes cut to ribbons New techniques open up carbon tubes to create ribbons | author = Brumfiel, G. |journal = Nature |year = 2009 |doi = 10.1038/news.2009.367}}</ref> In one such method [[MWNT|multi-walled carbon nanotubes]] are cut open in solution by action of [[potassium permanganate]] and [[sulfuric acid]].<ref>{{Cite journal | title = Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons | author = Kosynkin, D. V. ''et al.'' | journal = Nature |volume = 458 | year =2009 |doi =10.1038/nature07872 | pmid = 19370030 | issue = 7240 |bibcode = 2009Natur.458..872K | pages = 872–6 | first2 = Amanda L. | first3 = Alexander | first4 = Jay R. | first5 = Ayrat | first6 = B. Katherine | first7 = James M. }}</ref> In another method graphene nanoribbons were produced by [[plasma etching]] of nanotubes partly embedded in a [[polymer]] film.<ref>{{Cite journal | title = Narrow graphene nanoribbons from carbon nanotubes | author = Liying Jiao, Li Zhang, Xinran Wang, Georgi Diankov & [[Hongjie Dai]] |journal = Nature |volume = 458 | year = 2009 |doi = 10.1038/nature07919 | pmid = 19370031 | issue = 7240 |bibcode = 2009Natur.458..877J | pages = 877–80 }}</ref>
 
===Solvent exfoliation===
Dispersing graphite in a proper liquid medium can produce graphene by [[sonication]]. Non-exfoliated graphite is separated from graphene by [[centrifugation]],<ref>{{cite doi|10.1038/nnano.2008.215}}</ref> producing graphene concentrations initially up to {{val|0.01|u=mg/ml}} in [[N-methylpyrrolidone]] (NMP) and later to {{val|2.1|u=mg/ml}} in NMP,.<ref>{{cite doi|10.1039/C1JM11076D}}</ref> Using a suitable [[ionic liquid]] as the dispersing liquid medium for graphite exfoliation<ref>{{cite doi|10.1039/C0JM02461A}}</ref> produced concentrations of {{val|5.33|u=mg/ml}}.  The concentration of graphene sheets produced by this method is very low because there is nothing preventing the sheets from restacking due to the van der Waals forces pulling them back together.  the maximum concentrations achieved are the points at which the van der Waals forces overcome the interactive forces between the graphene sheets and the solvent molecules.
 
===Surfactant-aided exfoliation===
Similar to solvent exfoliation, graphite is sonicated in a suitable solvent.  In this case, however, surfactant molecules are added which prevent the restacking of the graphene sheets by adsorbing to the surface of the graphene.  The concentration of graphene achieved by this method is higher than solvent exfoliation, but the removal of the surfactant molecules is often necessary and usually requires chemical treatments.
 
===Interface trapping===
Macro-scale graphene films can be created by sonicating graphite while at the interface of two immiscible liquids, most notably heptane and water.  The graphene sheets are exfoliated because of the sonication and then adsorbed to the high energy interface between the heptane and the water, where they are kept from restacking.  The force holding the graphene at the interface is very strong, withstanding forces in excess of 300,000 g.  The solvents may then be evaporated, leaving behind the graphene film.  Films created using the interface trapping method are very transparent (up to ~95 %T) and conductive.<ref>Woltornist, S. J., Oyer, A. J., Carrillo, J.-M. Y., Dobrynin, A. V, & Adamson, D. H. (2013). Conductive thin films of pristine graphene by solvent interface trapping. ACS nano, 7(8), 7062–6. doi:10.1021/nn402371c</ref>
 
===Carbon dioxide reduction===
A highly exothermic reaction combusts [[magnesium]] in an oxidation-reduction reaction with carbon dioxide, producing a variety of carbon nanoparticles including graphene and [[fullerene]]s. The carbon dioxide reactant may be either solid (dry-ice) or gaseous. The products of this reaction are carbon and [[magnesium oxide]]. {{cite patent|US|8377408|status=patent}} was issued for this process.<ref>{{cite doi|10.1039/C1JM11227A}}</ref>
 
==Potential applications==
Potential applications include lightweight, thin, flexible, yet durable display screens, electric circuits, and solar cells, as well as various medical, chemical and industrial processes enhanced or enabled by the use of new graphene materials.<ref>{{cite web |last=Monie |first=Sanjay |title=Developments in Conductive Inks |url=http://industrial-printing.net/content/developments-conductive-inks?page=0%2C3#.URemb1pU6-E |publisher=Industrial & Specialty Printing |accessdate=26 April 2010}}</ref>
 
In 2008, graphene produced by exfoliation was one of the most expensive materials on Earth, with a sample with the area of the cross section of a human hair costing more than $1,000 as of April 2008 (about $100,000,000/cm<sup>2</sup>).<ref name = SciAm/> Since then, exfoliation procedures have been scaled up, and now companies sell graphene in large quantities.<ref>
{{cite journal
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|year=2009
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|journal=[[Nature Nanotechnology]]
|volume=4 |issue=10 |pages=612–4
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|doi=10.1038/nnano.2009.279
|pmid=19809441
}}</ref> The price of epitaxial graphene on SiC is dominated by the substrate price, which was approximately $100/cm<sup>2</sup> as of 2009.{{update|date=December 2013}} Hong and his team in South Korea pioneered the synthesis of large-scale graphene films using [[chemical vapour deposition]] (CVD) on thin [[nickel]] layers, which triggered research on practical applications,<ref>
{{cite web
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|title=Bigger, Stretchier Graphene
|url=http://www.technologyreview.com/news/411654/bigger-stretchier-graphene/
|work=[[MIT Technology Review]]
}}</ref> with wafer sizes up to {{convert|30|in}} reported.<ref name=hongR>
{{cite journal
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|last11=Kim |first11=Y.-J.
|last12=Kim |first12=K. S.
|last13=Ozyilmaz |first13=B.
|last14=Ahn |first14=J.-H.
|last15=Hong |first15=B. H.
|last16=Iijima |first16=S.
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|title=Roll-to-roll production of 30-inch graphene films for transparent electrodes
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}}</ref>
 
In 2013, the European Union made a €1 billion grant to be used for research into potential graphene applications.<ref>{{cite web |url=http://europa.eu/rapid/press-release_IP-13-54_en.htm |title=EUROPA - PRESS RELEASES - Press Release - Graphene and Human Brain Project win largest research excellence award in history, as battle for sustained science funding continues |publisher=Europa.eu |date=2013-01-28 |accessdate=2013-05-02}}</ref> In 2013 the Graphene Flagship consortium formed, including [[Chalmers University of Technology]] and seven other European universities and research centers, along with [[Nokia]].<ref>{{cite web |last=Thomson |first=Iain |title=Nokia shares $1.35bn EU graphene research grant |url=http://www.theregister.co.uk/2013/02/01/nokia_eu_graphene_grant/ |publisher=The Register}}<br/>{{cite web |url=http://www.graphene-flagship.eu/GF/consortium.php |title=FET Graphene Flagship |publisher=Graphene-flagship.eu |date= |accessdate=2013-08-24}}</ref> [[Nokia]] has also been working on graphene technology for several years.<ref>{{cite web |last=Sherriff |first=Lucy |url=http://www.zdnet.com/nokia-dials-into-graphene-in-photo-sensor-patent-move-7000003759/ |title=Nokia dials into graphene in photo-sensor patent move |publisher=ZDNet |date=2012-09-05 |accessdate=2013-08-24}}</ref>
 
===Medicine===
Graphene is reported to have enhanced [[PCR]] by increasing the yield of [[DNA]] product.<ref>{{cite doi|10.1088/0957-4484/23/45/455106}}</ref> Experiments revealed that graphene's [[thermal conductivity]] could be the main factor behind this result. Graphene yields DNA product equivalent to positive control with up to 65% reduction in PCR cycles.
 
===Integrated circuits===
For [[integrated circuits]], graphene has a high [[carrier mobility]], as well as low noise, allowing it to be used as the channel in a [[field-effect transistor]]. Single sheets of graphene are hard to produce and even harder to make on an appropriate substrate.<ref>{{Cite journal |author =Chen, J., Ishigami, M., Jang, C., Hines, D. R., Fuhrer, M. S., and Williams, E. D. | title = Printed graphene circuits |journal = Advanced Materials | volume = 19 | pages = 3623–3627 |year = 2007 |doi =10.1002/adma.200701059 |issue =21}}</ref>
 
In 2008, the smallest transistor so far, one atom thick, 10 atoms wide was made of graphene.<ref name="Ponomarenko, L. A. et al. 2008 356"/> IBM announced in December 2008 that they had fabricated and characterized graphene transistors operating at GHz frequencies.<ref>{{cite web |url=http://arxivblog.com/?p=755 |title=Graphene transistors clocked at 26 GHz Arxiv article |publisher=Arxivblog.com |date=2008-12-11 |accessdate=2009-08-15}}</ref> In May 2009, an n-type transistor was announced meaning that both n and p-type graphene transistors had been created.<ref>{{Cite journal |laysummary = http://news.ufl.edu/2009/05/07/graphene/ |author = Wang, X.; Li, X.; Zhang, L.; Yoon, Y.; Weber, P. K.; Wang, H.; Guo, J.; [[Hongjie Dai|Dai, H.]] |journal = Science |volume = 324 |issue = 5928 |year = 2009 |pmid = 19423822 | doi = 10.1126/science.1170335 |title = N-Doping of Graphene Through Electrothermal Reactions with Ammonia |bibcode = 2009Sci...324..768W |pages = 768–71 }}</ref><ref name="americanelements">{{cite web |title=Nanotechnology Information Center: Properties, Applications, Research, and Safety Guidelines |url=http://www.americanelements.com/nanotech.htm |publisher=[[American Elements]]}}</ref> A functional graphene integrated circuit was demonstrated&nbsp;– a complementary [[Inverter (logic gate)|inverter]] consisting of one p- and one n-type graphene transistor.<ref>{{Cite journal |laysummary = http://physicsworld.com/cws/article/news/38924 |author = Traversi, F.; Russo, V.; Sordan, R. |journal = Appl. Phys. Lett. | volume = 94 | page = 223312 |year = 2009 | doi = 10.1063/1.3148342 |title = Integrated complementary graphene inverter |bibcode = 2009ApPhL..94v3312T |issue = 22 |arxiv = 0904.2745 }}</ref> However, this inverter suffered from a very low voltage gain.
 
According to a January 2010 report,<ref name="UK's NPL">{{cite web |url = http://www.npl.co.uk/news/european-collaboration-breakthrough-in-developing-graphene |title = European collaboration breakthrough in developing graphene |publisher = NPL |date = 2010-01-19 |accessdate = 2010-02-21}}</ref> graphene was epitaxially grown on SiC in a quantity and with quality suitable for mass production of integrated circuits. At high temperatures, the quantum Hall effect could be measured in these samples. IBM built 'processors' using 100&nbsp;GHz transistors on {{convert|2|in|mm|adj=on}} graphene sheets.<ref name="LinDimitrakopoulos2010">{{cite journal |last1=Lin |first1=Y.-M. |last2=Dimitrakopoulos |first2=C. |last3=Jenkins |first3=K. A. |last4=Farmer |first4=D. B. |last5=Chiu |first5=H.-Y. |last6=Grill |first6=A. |last7=Avouris |first7=Ph. |title=100-GHz Transistors from Wafer-Scale Epitaxial Graphene |journal=Science |volume=327 |issue=5966 |year=2010 |pages=662–662 |issn=0036-8075 |doi=10.1126/science.1184289 |pmid=20133565|arxiv = 1002.3845 |bibcode = 2010Sci...327..662L }}</ref>
 
In June 2011, IBM researchers announced that they had succeeded in creating the first graphene-based integrated circuit, a broadband radio mixer.<ref name="LinValdes-Garcia2011">{{cite journal |last1=Lin |first1=Y.-M. |last2=Valdes-Garcia |first2=A. |last3=Han |first3=S.-J. |last4=Farmer |first4=D. B. |last5=Meric |first5=I. |last6=Sun |first6=Y. |last7=Wu |first7=Y. |last8=Dimitrakopoulos |first8=C. |last9=Grill |first9=A. |last10=Avouris |first10=P. |last11=Jenkins |first11=K. A. |title=Wafer-Scale Graphene Integrated Circuit |journal=Science |volume=332 |issue=6035 |year=2011 |pages=1294–1297 |issn=0036-8075 |doi=10.1126/science.1204428 |pmid=21659599|bibcode = 2011Sci...332.1294L }}</ref> The circuit handled frequencies up to 10&nbsp;GHz. Its performance was unaffected by temperatures up to 127 C.
 
In June 2013 an 8 transistor 1.28&nbsp;GHz ring oscillator circuit was described.<ref>{{cite web |url=http://physicsworld.com/cws/article/news/2013/jun/17/graphene-circuit-breaks-the-gigahertz-barrier |title=Graphene circuit breaks the gigahertz barrier |year=2013 }}</ref>
 
====Transistors====
 
Graphene exhibits a pronounced response to perpendicular external electric fields, potentially forming [[field-effect transistor]]s (FET). A 2004 paper documented FETs with an on-off ratio of ~30 at room temperature.{{citation needed|date=May 2013}} A 2006 paper announced an all-graphene planar FET with side gates.<ref>[http://gtresearchnews.gatech.edu/newsrelease/graphene.htmCarbon-Based Electronics: Researchers Develop Foundation for Circuitry and Devices Based on Graphite] March 14, 2006</ref> Their devices showed changes of 2% at cryogenic temperatures. The first top-gated FET (on–off ratio of <2) was demonstrated in 2007.<ref>{{Cite journal |author = Lemme, M. C. '' et al. '' |title = A graphene field-effect device |journal = IEEE Electron Device Letters | volume = 28 | page = 282 |year = 2007 |doi = 10.1109/LED.2007.891668 |arxiv = cond-mat/0703208 |bibcode = 2007IEDL...28..282L |issue = 4 }}</ref> Graphene nanoribbons may prove generally capable of replacing silicon as a semiconductor.<ref name="MIT1">{{Cite news
| author = Bullis, K. |title = Graphene Transistors |publisher = [[Massachusetts Institute of Technology|MIT]] Technology Review, Inc |location = Cambridge |date = 2008-01-28 |url = http://www.technologyreview.com/Nanotech/20119/ |accessdate = 2008-02-18}}</ref>
 
{{cite patent|US|7015142|status=patent}} for graphene-based electronics was issued in 2006. In 2008, researchers at [[MIT Lincoln Lab]] produced hundreds of transistors on a single chip<ref name="Kedzierski">{{Cite journal |author = Kedzierski, J. ''et al.'' |title = Epitaxial Graphene Transistors on SiC Substrates |doi = 10.1109/TED.2008.926593 |journal = IEEE Transactions on Electron Devices |volume = 55 |pages = 2078–2085 |year = 2008 |bibcode = 2008ITED...55.2078K |issue = 8 |first2 = Pei-Lan |first3 = Paul |first4 = Peter W. |first5 = Craig L. |first6 = Mike |first7 = Claire |first8 = Walt A. |arxiv = 0801.2744 }}</ref> and in 2009, very high frequency transistors were produced at [[Hughes Research Laboratories]].<ref name="HRL">{{Cite journal |author =Moon, J.S. ''et al.'' |title = Epitaxial-Graphene RF Field-Effect Transistors on Si-Face 6H-SiC Substrates |doi = 10.1109/LED.2009.2020699 |journal = IEEE Electron Device Letters |volume = 30 |pages = 650–652 |year = 2009 |bibcode = 2009IEDL...30..650M |issue =6 |first2 =D. |first3 =M. |first4 =D. |first5 =C. |first6 =P.M. |first7 =G. |first8 =J.L. |first9 =B. |first10 =R. |first11 =C. |first12 =D.K. }}</ref>
 
A 2008 paper demonstrated a switching effect based on a reversible chemical modification of the graphene layer that gives an on–off ratio of greater than six orders of magnitude. These reversible switches could potentially be employed in nonvolatile memories.<ref>{{Cite journal |author = Echtermeyer, Tim. J. '' et al. '' |journal = IEEE Electron Device Letters | volume = 29 |page = 952 |year = 2008 | doi = 10.1109/LED.2008.2001179 |title = Nonvolatile Switching in Graphene Field-Effect Devices |bibcode = 2008IEDL...29..952E |issue = 8 |arxiv = 0805.4095 }}</ref>
 
In 2009, researchers demonstrated four different types of [[logic gates]], each composed of a single graphene transistor.<ref>{{Cite journal |author = Sordan, R.; Traversi, F.; Russo, V. |journal = Appl. Phys. Lett. | volume = 94 | page = 073305 |year = 2009 | doi = 10.1063/1.3079663 |title = Logic gates with a single graphene transistor |bibcode = 2009ApPhL..94g3305S |issue = 7 }}</ref>
 
Practical uses for these circuits are limited by the very small [[voltage gain]] they exhibit. Typically, the amplitude of the output signal is about 40 times less than that of the input signal. Moreover, none of these circuits operated at frequencies higher than 25&nbsp;kHz.
 
In the same year, tight-binding numerical simulations<ref name = "fiori2">Fiori G., Iannaccone G., "On the possibility of tunable-gap bilayer graphene FET", IEEE Electr. Dev. Lett., 30, 261 (2009)</ref> demonstrated that the band-gap induced in graphene bilayer field effect transistors is not sufficiently large for high-performance transistors for digital applications, but can be sufficient for ultra-low voltage applications, when exploiting a tunnel-FET architecture.<ref name = "fiori3">Fiori G., Iannaccone G., "Ultralow-Voltage Bilayer graphene tunnel FET", IEEE Electr. Dev. Lett., 30, 1096 (2009)</ref>
 
In February 2010, researchers announced transistors with an on/off rate of 100 gigahertz, far exceeding the rates of previous attempts, and exceeding the speed of silicon transistors with an equal gate length. The {{val|240|u=nm}} devices were made with conventional silicon-manufacturing equipment.<ref name=Bourzac2010>{{Cite news
| last = Bourzac |first = Katherine |title = Graphene Transistors that Can Work at Blistering Speeds |work = MIT Technology Review |date = 2010-02-05 |url = http://www.technologyreview.com/computing/24482/?a=f}}</ref><ref name=TW2010>[http://news.techworld.com/personal-tech/3212175/ibm-shows-off-100ghz-graphene-transistor/ IBM shows off 100GHz graphene transistor – Techworld.com]. News.techworld.com. Retrieved on 2010-12-10.</ref><ref>{{Cite journal |journal=Science |title=100-GHz Transistors from Wafer-Scale Epitaxial Graphene |first7=P |last7=Avouris |first6=A |last6=Grill |first5=HY |last5=Chiu |first4=DB |last4=Farmer |first3=KA |last3=Jenkins |first2=C |last2=Dimitrakopoulos |volume=327 |author=Lin et al. |issue=5966 |year=2010 |page=662 |pmid=20133565 |publisher=Science |doi=10.1126/science.1184289 |bibcode = 2010Sci...327..662L |arxiv = 1002.3845 }}</ref>
 
In November 2011, researchers used 3d printing ([[additive manufacturing]]) as a method for fabricating graphene devices.<ref>[http://arxiv.org/abs/1111.4970 Ink-Jet Printed Graphene Electronics]. Cornell University Library. Retrieved on 2011-29-11.</ref>
 
In 2013, researchers demonstrated graphene's high mobility in a detector that allows broad band frequency selectivity ranging from the THz to IR region (0.76-33THz)<ref>{{cite journal |last=Kawano |first=Yukio |title=Wide-band frequency-tunable terahertz and infrared detection with graphene |journal=Nanotechnology |year=2013 |volume=24 |issue=21 |doi=10.1088/0957-4484/24/21/214004|page=214004 |pmid=23618878|bibcode = 2013Nanot..24u4004K }}</ref> A separate group created a terahertz-speed transistor with bistable characteristics, which means that the device can spontaneously switch between two electronic states. The device consists of two layers of graphene separated by an insulating layer of [[boron nitride]] a few atomic layers thick. Electrons move through this barrier by [[quantum tunneling]]. These new transistors exhibit “negative differential conductance,” whereby the same electrical current flows at two different applied voltages.<ref>{{cite journal |url=http://www.kurzweilai.net/radical-new-graphene-design-operates-at-terahertz-speed |title=Radical new graphene design operates at terahertz speed |doi=10.1038/ncomms2817 |publisher=KurzweilAI |date= |accessdate=2013-05-02|arxiv = 1303.6864 |bibcode = 2013NatCo...4E1794B |last1=Britnell |first1=L. |last2=Gorbachev |first2=R. V. |last3=Geim |first3=A. K. |last4=Ponomarenko |first4=L. A. |last5=Mishchenko |first5=A. |last6=Greenaway |first6=M. T. |last7=Fromhold |first7=T. M. |last8=Novoselov |first8=K. S. |last9=Eaves |first9=L. |journal=Nature Communications |volume=4 |pages=1794– |pmid=23653206 |pmc=3644101 }}<br/>{{cite DOI|10.1038/ncomms2817}}</ref>
 
Graphene does not have an energy band-gap, which presents a hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. The negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gap-less graphene. The negative differential resistance&nbsp;— observed under certain biasing schemes&nbsp;— is an intrinsic property of graphene resulting from its symmetric band structure. The results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.<ref>{{cite journal|author1=Guanxiong Liu|author2=Sonia Ahsan|last3=Khitun|first3=Alexander G.|last4=Lake|first4=Roger K.|last5=Balandin|first5=Alexander A.|title=Graphene-Based Non-Boolean Logic Circuits|year=2013|volume=114|issue=10|journal=Journal of Applied Physics, ,  (2013)|arxiv=1308.2931|bibcode=2013JAP...114o4310L|page=4310|doi=10.1063/1.4824828}}</ref>
 
In 2013 researchers reported the creation of transistors printed on flexible plastic that operate at 25-gigahertz, sufficient for communications circuits and that can be fabricated at scale. The researchers first fabricate the non-graphene-containing structures—the electrodes and gates—on plastic sheets. Separately, they grow large graphene sheets on metal, then peel it off and transfer it to the plastic. Finally, they top the sheet with a waterproof layer. The devices work after being soaked in water, and are flexible enough to be folded.<ref>{{cite web |last=Bourzac |first=Katherine |url=http://www.technologyreview.com/news/518606/printed-graphene-transistors-promise-a-flexible-electronic-future/ |title=Superfast, Bendable Electronic Switches Made from Graphene &#124; MIT Technology Review |publisher=Technologyreview.com |date= |accessdate=2013-08-24}}</ref>
 
===Redox===
[[Graphene oxide]] can be reversibly reduced and oxidized using electrical stimulus. Controlled reduction and oxidation in two-terminal devices containing multilayer graphene oxide films are shown to result in switching between partially reduced graphene oxide and graphene, a process that modifies the electronic and optical properties. Oxidation and reduction are related to resistive switching.<ref>{{Cite journal |author =Ekiz, O.O., et al. |title = Reversible Electrical Reduction and Oxidation of Graphene Oxide | journal = ACS Nano |year = 2011 |doi=10.1021/nn1014215 |volume = 5 |issue = 4 |pages = 2475–2482 |pmid = 21391707}}<br/>{{Cite journal |author =Ekiz, O.O., et al. |title = Supporting information for Reversible Electrical Reduction and Oxidation of Graphene Oxide |journal = ACS Nano |year = 2011 |doi = 10.1021/nn1014215 |volume =5 |issue =4 |pages =2475–2482 |pmid =21391707}}</ref>
 
===Transparent conducting electrodes===
Graphene's high electrical conductivity and high optical transparency make it a candidate for transparent conducting electrodes, required for such applications as [[touchscreen]]s, [[liquid crystal display]]s, [[solar cell|organic photovoltaic cells]], and [[organic light-emitting diode]]s. In particular, graphene's mechanical strength and flexibility are advantageous compared to [[indium tin oxide]], which is brittle. Graphene films may be deposited from solution over large areas.<ref name="MPI">{{Cite journal
|last = Wang
|first = X.
|coauthors = et al.
|year = 2007
|title = Transparent, Conductive Graphene Electrodes for Dye-Sensitized Solar Cells
|journal = Nano Letters
|doi = 10.1021/nl072838r
|volume = 8
|pmid = 18069877
|issue = 1 |bibcode = 2008NanoL...8..323W
|pages = 323–7 }}</ref><ref name="Eda">{{Cite journal |author=Eda G, Fanchini G, Chhowalla M |title=Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material |journal=Nat Nanotechnol |volume=3 |issue=5 |pages=270–4 |year=2008 |pmid=18654522 |doi=10.1038/nnano.2008.83}}</ref>
 
Large-area, continuous, transparent and highly conducting few-layered graphene films were produced by chemical vapor deposition and used as [[anode]]s for application in [[photovoltaic]] devices. A power conversion efficiency (PCE) up to 1.71% was demonstrated, which is 55.2% of the PCE of a control device based on indium tin oxide.<ref>{{Cite journal |title=Large area, continuous, few-layered graphene as anodes in organic photovoltaic devices |journal=Applied Physics Letters |volume=95 |page=063302 |year=2009 |doi=10.1063/1.3204698 |author=Wang, Yu ''et al.'' |bibcode = 2009ApPhL..95f3302W |issue=6 |first2=Xiaohong |first3=Yulin |first4=Furong |first5=Kian Ping }}</ref>
 
[[Organic light-emitting diode]]s (OLEDs) with graphene anodes have been demonstrated.<ref>{{Cite journal
|last = Wu
|first = J.B.
|coauthors = et al.
|year = 2010
|title = Organic Light-Emitting Diodes on Solution-Processed Graphene Transparent Electrodes
|journal = ACS Nano
|volume = 4
|page = 43
|doi= 10.1021/nn900728d
}}</ref> The electronic and optical performance of graphene-based devices are similar to devices made with indium tin oxide.
 
A carbon-based device called a [[light-emitting electrochemical cell]] (LEC) was demonstrated with chemically-derived graphene as the [[cathode]] and the [[conductive polymer]] [[PEDOT]] as the anode.<ref>{{Cite journal
|last = Matyba
|first = P.
|coauthors = et al.
|year = 2010
|title = Graphene and Mobile Ions: The Key to All-Plastic, Solution-Processed Light-Emitting Devices
|journal = ACS Nano
|volume = 4
|doi = 10.1021/nn9018569
|pmid=20131906
|issue = 2
|pages = 637–42
}}</ref> Unlike its predecessors, this device contains only carbon-based electrodes, with no metal.
 
===Ethanol distillation===
Graphene oxide membranes allow water vapor to pass through, but are impermeable to other liquids and gases.<ref name="pmid22282806">{{cite journal |title=Unimpeded permeation of water through helium-leak-tight graphene-based membranes |doi=10.1126/science.1211694 |year=2012 |journal=Science |volume=335 |issue=6067 |pages=442–4 |pmid=22282806 |arxiv=1112.3488 |last2=Wu |last3=Jayaram |last4=Grigorieva |last5=Geim |last1=Nair |first1=R. R. |first2=H. A. |first3=P. N. |first4=I. V. |first5=A. K.|bibcode = 2012Sci...335..442N }}</ref> This phenomenon has been used for further distilling of [[vodka]] to higher alcohol concentrations, in a room-temperature laboratory, without the application of heat or vacuum as used in traditional [[distillation]] methods.<ref>{{cite news | url=http://www.dailymail.co.uk/sciencetech/article-2092321/Hi-tech-wonder-material-graphene-unexpected-use--distill-vodka-room-temperature.html | location=London | work=Daily Mail | first=Rob | last=Waugh | title=Hi-tech 'wonder material' graphene has an unexpected use&nbsp;– it can distill vodka at room temperature}}</ref> Further development and commercialization of such membranes could revolutionize the economics of [[biofuel]] production and the [[alcoholic beverage]] industry.
 
===Desalination===
Research suggests that graphene filters could outperform other techniques of [[desalination]] by a significant margin.<ref name="Cohen-TanugiGrossman2012">{{cite journal |last1=Cohen-Tanugi |first1=David |last2=Grossman |first2=Jeffrey C. |title=Water Desalination across Nanoporous Graphene |journal=Nano Letters |volume=12 |issue=7 |year=2012 |pages=3602–3608 |issn=1530-6984 |doi=10.1021/nl3012853 |pmid=22668008|bibcode = 2012NanoL..12.3602C }}</ref>
 
===Solar cells===
 
Graphene has a unique combination of high electrical conductivity and optical transparency, which make it a candidate for use in solar cells. A single sheet of graphene is a zero-bandgap semiconductor whose charge carriers are delocalized over large areas, implying that carrier scattering does not occur. Because this material only absorbs 2.3% of visible light, it is a candidate for applications requiring a transparent conductor. Graphene can be assembled into a film electrode with low roughness. However, graphene films produced via solution processing contain lattice defects and grain boundaries that act as recombination centers and decrease the material's electrical conductivity. Thus, these films must be made thicker than one atomic layer to obtain useful sheet resistances. This added resistance can be combatted by incorporating conductive filler materials, such as a [[silica]] matrix. Reduced graphene film's electrical conductivity can be improved by attaching large [[aromatcicity|aromatic molecules]] such as [[pyrene]]-1-sulfonic acid sodium salt (PyS) and the disodium salt of 3,4,9,10-perylenetetracarboxylic diimide bisbenzenesulfonic acid (PDI).  These molecules, under high temperatures, facilitate better π-conjugation of the graphene basal plane. Graphene films have high transparency in the visible and near-[[infrared]] regions and are chemically and thermally stable.<ref name="Mukhopadhyay 2013 202-213">{{cite book |last=Mukhopadhyay|first=Prithu |title=Graphite, Graphene and their Polymer Nanocomposites |year=2013 |publisher=Taylor & Francis Group |location=Boca Raton, Florida |isbn=978-1-4398-2779-6 |pages=202–213}}</ref>
 
For graphene to be used in commercial solar cells, large-scale production are required. However, no scalable process for producing  graphene is available, including the peeling of pyrolytic graphene or thermal decomposition of silicon carbide.<ref name="Mukhopadhyay 2013 202-213"/>
 
Graphene's high charge mobilities recommend it for use as a charge collector and transporter in [[photovoltaic]]s (PV). Using graphene as a photoactive material requires its bandgap to be 1.4-1.9eV. In 2010, single cell efficiencies of nanostructured graphene-based PVs of over 12% were achieved.  According to P. Mukhopadhyay and R. K. Gupta [[organic photovoltaics]] could be "devices in which semiconducting graphene is used as the photoactive material and metallic graphene is used as the conductive electrodes".<ref name="Mukhopadhyay 2013 202-213"/> In 2013 In 2012, researchers from the University of Florida reported efficiency of 8.6% for a prototype cell consisting of a wafer of silicon coated with a layer of graphene doped with trifluoromethanesulfonyl-amide (TFSA). In 2013 another team  claimed to have reached 15.6% percent using a combination of [[titanium oxid]]e and graphene as a charge collector and [[perovskite]] as a sunlight absorber. The device is manufacturable at temperatures under {{convert|150|C|F}} using solution-based deposition. This lowers production costs and offers the potential using flexible plastics.<ref>{{cite web|url=http://www.gizmag.com/graphene-solar-cell-record-efficiency/30466 |title=Graphene-based solar cell hits record 15.6 percent efficiency |publisher=Gizmag.com |date= |accessdate=2014-01-23}}</ref><ref>{{cite doi|10.1021/nl403997a}}</ref>
 
Large scale production of highly transparent graphene films by [[chemical vapor deposition]] was achieved in 2008. In this process, ultra-thin graphene sheets are created by first depositing carbon atoms in the form of graphene films on a nickel plate from [[methane]] gas. A protective layer of [[thermoplastic]] is laid over the graphene layer and the nickel underneath is dissolved in an acid bath. The final step is to attach the plastic-protected graphene to a flexible [[polymer]] sheet, which can then be incorporated into an OPV cell. Graphene/polymer sheets range in size up to 150 square centimeters and can be used to create dense arrays of flexible OPV cells. It may eventually be possible to run printing presses covering extensive areas with inexpensive solar cells, much like newspaper presses print newspapers ([[roll-to-roll]]).<ref>{{Cite news |url=http://www.sciencedaily.com/releases/2010/07/100723095430.htm |title=Graphene organic photovoltaics: Flexible material only a few atoms thick may offer cheap solar power |work=ScienceDaily |date=July 24, 2010}}<br/>Walker, Sohia. (2010-08-04) [http://www.comptalks.com/use-of-graphene-photovoltaics-as-alternate-source-of-energy/ Use of graphene photovoltaics as alternate source of energy|Computer Talks]. Comptalks.com. Retrieved on 2010-12-10.</ref>
 
Silicon generates only one current-driving electron for each photon it absorbs, while graphene can produce multiple electrons. Solar cells made with graphene could offer 60% conversion efficiency&nbsp;– double the widely-accepted maximum efficiency of silicon cells.<ref>inhabitat.com cooperating with ICFO (Institute of Photonic Sciences)[http://inhabitat.com/graphene-based-solar-cells-could-yield-60-efficiency/ (2013-04-03]</ref>
 
===Single-molecule gas detection===
Theoretically graphene makes an excellent sensor due to its 2D structure. The fact that its entire volume is exposed to its surrounding makes it very efficient to detect [[adsorption|adsorbed]] molecules. However, similar to carbon nanotubes, graphene has no dangling bonds on its surface. Gaseous molecules cannot be readily adsorbed onto graphene surfaces, so intrinsically graphene is insensitive.<ref>{{cite journal |last=Dan |first=Yaping |title=Intrinsic Response of Graphene Vapor Sensors |journal=Nano Letters |year=2009 |month=4 |volume=9 |issue=4 |pages=1472–1475 |doi=10.1021/nl8033637 |last2=Lu |first2=Ye |last3=Kybert |first3=Nicholas J. |last4=Luo |first4=Zhengtang |last5=Johnson |first5=A. T. Charlie |pmid=19267449|arxiv = 0811.3091 |bibcode = 2009NanoL...9.1472D }}</ref> The sensitivity of graphene chemical gas sensors can be dramatically enhanced by functionalization, for example, coating the film with a thin layer of certain polymers. The thin polymer layer acts like a concentrator that absorbs gaseous molecules. The molecule absorption introduces a local change in [[electrical resistance]] of graphene sensors. While this effect occurs in other materials, graphene is superior due to its high electrical conductivity (even when few carriers are present) and low noise, which makes this change in resistance detectable.<ref name=ChemDoping/>
 
===Quantum dots===
Graphene [[quantum dot]]s (GQDs) keep all dimensions less than 10&nbsp;nm. Their size and edge [[crystallography]] govern their electrical, magnetic, optical and chemical properties. GQDs can be produced via graphite nanotomy<ref name = "GQD">{{Cite journal |author = Nihar Mohanty, David Moore, Zhiping Xu, T. S. Sreeprasad, Ashvin Nagaraja, Alfredo A. Rodriguez and Vikas Berry |title = Nanotomy Based Production of Transferrable and Dispersible Graphene-Nanostructures of Controlled Shape and Size |doi= 10.1038/ncomms1834 |journal = Nature Communications | volume = 3 | page = 844 |year = 2012 |issue=5|bibcode = 2012NatCo...3E.844M }}</ref> or via bottom-up, solution-based routes ([[Diels-Alder reaction|Diels-Alder, cyclotrimerization and/or cyclodehydrogenation reactions]]).<ref name = "GQD1">{{Cite journal |author = Jinming Cai, Pascal Ruffieux, Rached Jaafar, Marco Bieri, Thomas Braun, Stephan Blankenburg, Matthias Muoth, Ari P. Seitsonen, Moussa Saleh, Xinliang Feng, Klaus Müllen & Roman Fasel |title = Atomically precise bottom-up fabrication of graphene nanoribbons |doi= 10.1038/nature09211 |journal = Nature | volume = 466 | page = 470 |year = 2010 |issue = 7305|bibcode = 2010Natur.466..470C }}</ref> GQDs with controlled structure can be incorporated into applications in electronics, optoelectronics and electromagnetics. [[Quantum confinement]] can be created by changing the width of GNRs{{clarify|date=December 2013}} at select points along the ribbon.<ref name="Ponomarenko, L. A. et al. 2008 356">{{Cite journal | laysummary =http://news.bbc.co.uk/2/hi/technology/7352464.stm |author = Ponomarenko, L. A. ''et al.'' |title = Chaotic Dirac Billiard in Graphene Quantum Dots | journal = Science | volume = 320 |year = 2008 | doi =10.1126/science.1154663 | pmid = 18420930 | issue = 5874 |bibcode = 2008Sci...320..356P | pages = 356–8| first2 = F. | first3 = M. I. | first4 = R. | first5 = E. W. | first6 = K. S. | first7 = A. K. |arxiv = 0801.0160 }}</ref><ref>{{Cite journal |author =Wang, Z. F., Shi, Q. W., Li, Q., Wang, X., Hou, J. G., Zheng, H., et al. |title = Z-shaped graphene nanoribbon quantum dot device |doi=10.1063/1.2761266 |journal = Applied Physics Letters | volume = 91 | page = 053109 |year = 2007 |bibcode = 2007ApPhL..91e3109W |issue =5 |arxiv = 0705.0023 }}</ref>
 
===Frequency multiplier===
 
In 2009, researchers built experimental graphene [[frequency multiplier]]s that take an incoming signal of a certain frequency and output a signal at a multiple of that frequency.<ref>{{Cite journal |laysummary = http://www.physorg.com/news156698836.html |author = Wang, H.; Nezich, D.; Kong, J.; Palacios, T. |journal = IEEE Electr. Device. L. | volume = 30 | page = 547 |year = 2009 | doi = 10.1109/LED.2009.2016443 |title = Graphene Frequency Multipliers |issue = 5}}<br/>{{Cite journal |author =D. Cricchio, P. P. Corso, E. Fiordilino, G. Orlando, and F. Persico |journal = J. Phys. B |year=2009 |volume=42 |page=085404 |doi =10.1088/0953-4075/42/8/085404 |title =A paradigm of fullerene |issue =8|bibcode = 2009JPhB...42h5404C }}</ref>
 
===Optical modulator===
When the [[Fermi level]] of graphene is tuned, its optical absorption can be changed. In 2011, researchers reported the first graphene-based optical modulator. Operating at {{val|1.2|u=GHz}} without a temperature controller, this modulator has a broad bandwidth (from 1.3 to 1.6 μm) and small footprint (~{{val|25|u=μm<sup>2</sup>}}).<ref>{{cite journal |last=Liu |first=Ming |coauthors=Yin, Xiaobo, Ulin-Avila, Erick, Geng, Baisong, Zentgraf, Thomas, Ju, Long, Wang, Feng, Zhang, Xiang |title=A graphene-based broadband optical modulator |journal=Nature |date=8 May 2011 |volume=474 |issue=7349 |pages=64–67 |doi=10.1038/nature10067 |pmid=21552277|bibcode = 2011Natur.474...64L }}</ref>
 
===Coolant additive===
Graphene's high thermal conductivity suggests that it could be used as an additive in coolants. Preliminary research work showed that 5% graphene by volume can enhance the thermal conductivity of a base fluid by 86%.<ref>{{cite doi|10.1016/j.physleta.2011.01.040}}</ref> Another application due to graphene's enhanced thermal conductivity was found in PCR.<ref>{{cite doi|10.1088/0957-4484/23/45/455106}}</ref>
 
===Reference material===
Graphene's properties suggest it as a [[Certified reference materials|reference material]] for characterizing electroconductive and transparent materials. One layer of graphene absorbs 2.3% of white light.<ref>{{Cite journal |author=R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, A. K. Geim | year = 2008 |title = Fine Structure Constant Defines Visual Transparency of Graphene |journal = Science |pmid=18388259 |volume = 320 |issue=5881 |page = 1308 |doi = 10.1126/science.1156965 |bibcode = 2008Sci...320.1308N }}</ref>
 
This property was used to define the ''[[conductivity of transparency]]'' that combines [[sheet resistance]] and [[Transparency and translucency|transparency]]. This parameter was used to compare materials without the use of two independent parameters.<ref>{{Cite journal |author = S. Eigler |year = 2009 |title = A new parameter based on graphene for characterizing transparent, conductive materials |journal = Carbon |volume = 47 |pages =2936–2939 |doi = 10.1016/j.carbon.2009.06.047 |issue = 12}}</ref>
 
===Thermal management===
In 2011, researchers reported that a three-dimensional, vertically aligned, functionalized multilayer graphene architecture can be an approach for graphene-based [[thermal interfacial materials]] ([[TIMs]]) with superior thermal conductivity and ultra-low [[interfacial thermal resistance]] between graphene and metal.<ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401"/>
 
Graphene-metal composites can be utilized in thermal interface materials.<ref name="shaahin"/>
 
===Energy storage===
 
====Supercapacitor====
Due to graphene's high surface area to mass ratio, one potential application is in the conductive plates of [[supercapacitor]]s.<ref name="Stoller">
{{Cite journal |last = Stoller |first = Meryl D. |coauthors = Sungjin Park, Yanwu Zhu, Jinho An, and Rodney S. Ruoff |year=2008 |url = http://bucky-central.me.utexas.edu/RuoffsPDFs/179.pdf |format=PDF |doi=10.1021/nl802558y |title = Graphene-Based Ultracapacitors |journal=Nano Lett |volume=8 |pmid = 18788793 |issue = 10 |bibcode = 2008NanoL...8.3498S |pages = 3498–502 }}</ref>
 
In February 2013 researchers announced a novel technique to produce graphene [[supercapacitor]]s based on the DVD burner reduction approach.<ref>{{cite web |last=Malasarn |first=Davin |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-technique-243553.aspx |title=UCLA researchers develop new technique to scale up production of graphene micro-supercapacitors / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=2013-02-19 |accessdate=2013-05-02}}</ref>
 
====Electrode for Li-ion batteries====
Stable [[Li-ion]] cycling has recently been demonstrated in bi- and few layer graphene films grown on [[nickel]] [[substrate]]s,<ref>{{cite doi|10.1021/am301782h}}<br/>{{cite web |url=http://jes.ecsdl.org/content/159/6/A752.abstract |title=Fabrication and Electrochemical Characterization of Single and Multi-Layer Graphene Anodes for Lithium-Ion Batteries |publisher=Jes.ecsdl.org |date= |accessdate=2013-06-24}}</ref>  while single layer graphene films have been demonstrated as a protective layer against corrosion in battery components such as the battery case.<ref>{{cite doi|10.1021/ja301586m}}</ref> This creates possibilities for flexible electrodes for microscale Li-ion batteries where the anode acts as the active material as well as the current collector.<ref>{{cite web |last=Johnson |first=Dexter |url=http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/faster-and-cheaper-process-for-graphene-in-liion-batteries |title=Faster and Cheaper Process for Graphene in Li-ion Batteries - IEEE Spectrum |publisher=Spectrum.ieee.org |date=2013-01-17 |accessdate=2013-06-24}}</ref>
 
There are also [[Nanowire battery|silicon-graphene anode]] Li-ion batteries<ref>http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/graphenesilicon-anodes-for-liion-batteries-go-commercial</ref><ref>http://phys.org/news/2013-04-xgs-silicon-graphene-anode-materials-lithium-ion.html</ref>.
 
===Engineered piezoelectricity===
[[Density functional theory]] simulations predict that depositing certain [[adatom]]s on graphene can render it [[Piezoelectricity|piezoelectrically]] responsive to an electric field applied in the out-of-plane direction. This type of locally engineered piezoelectricity is similar in magnitude to that of bulk piezoelectric materials and makes graphene a candidate for control and sensing in nanoscale devices.<ref>{{cite web |title=Straintronics: Stanford engineers create piezoelectric graphene |url=http://news.stanford.edu/news/2012/april/straintronics-piezoelectric-graphene-040312.html |publisher=Stanford University |accessdate=16 April 2012}}<br/>{{cite journal |last=Ong |first=M. |coauthors=Reed, E.J. |title=Engineered Piezoelectricity in Graphene |journal=ACS Nano |year=2012 |doi=10.1021/nn204198g |volume=6 |issue=2 |pages=1387–94 |pmid=22196055}}</ref>
 
===Biodevice===
Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly gatable structure make antibody-functionalized graphene sheets excellent candidates for mammalian and microbial detection and diagnosis devices.<ref name="Berry">
{{Cite journal
|first = Nihar
|last = Mohanty
|coauthors = Vikas Berry
|year = 2008
|doi=10.1021/nl802412n |title = Graphene-based Single-Bacterium Resolution Biodevice and DNA-Transistor&nbsp;– Interfacing Graphene-Derivatives with Nano and Micro Scale Biocomponents
|journal = Nano Letters
|volume = 8 |pages = 4469–76 |pmid = 18983201 |bibcode = 2008NanoL...8.4469M
|issue = 12 }}</ref>
 
[[File:GrapheneE2.png|thumb|Energy of the electrons with wavenumber '''k''' in graphene, calculated in the [[Tight Binding]]-approximation. The unoccupied (occupied) states, colored in blue–red (yellow–green), touch each other without [[energy gap]] exactly at the above-mentioned six k-vectors.]]
 
The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA sequencing. Integration of graphene (thickness of {{val|0.34|u=nm}}) layers as nanoelectrodes into a nanopore<ref>{{Cite journal
|last1 = Xu
|first = M. S. Xu
|coauthors = D. Fujita and N. Hanagata
|year = 2009
|pmid = 19904762
|doi=10.1002/smll.200900976 |title = Perspectives and Challenges of Emerging Single-Molecule DNA Sequencing Technologies
|journal = Small
|volume = 5
|issue = 23 |pages =2638–49}}</ref> can solve a bottleneck for nanopore-based single-molecule DNA sequencing.
 
On November 20, 2013 the [[Bill & Melinda Gates Foundation]] awarded $100,000 to 'to develop new elastic composite materials for condoms containing nanomaterials like graphene'.<ref>{{cite news |title=Bill Gates condom challenge 'to be met' by graphene scientists |url=http://www.bbc.co.uk/news/uk-england-manchester-25016994 |accessdate=21 November 2013 |newspaper=BBC News |date=20 November 2013}}</ref>
 
==Pseudo-relativistic theory{{anchor|pseudorel|reason=linked from [[#Anomalous quantum Hall effect]]}}==
Graphene's electrical properties can be described by a conventional [[tight-binding]] model; in this model the energy of the electrons with wave vector '''k''' is<ref name="Semenoff" /><ref name="Wallace">{{Cite journal |author =Wallace, P. R. | title = The Band Theory of Graphite |doi=10.1103/PhysRev.71.622 |journal=Physical Review |volume = 71 | year =1947 | page=622 |bibcode = 1947PhRv...71..622W |issue =9 }}</ref>
 
:<math>E=\pm\sqrt{\gamma_0^2\left(1+4\cos^2{\frac{k_ya}{2}}+4\cos{\frac{k_ya}{2}} \cdot \cos{\frac{k_x\sqrt{3}a}{2}}\right)}</math>
 
with the nearest-neighbor hopping energy γ<sub>0</sub> ≈ {{val|2.8|u=eV}} and the [[lattice constant]] a ≈ {{val|2.46|u=Å}}. The [[conduction band|conduction]] and [[valence band]], respectively, correspond to the different signs in the above [[dispersion relation]]; they touch each other at six points, the "K-values". However, only two of these six points are independent, while the rest are equivalent by symmetry. In the vicinity of the K-points the energy depends ''linearly'' on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the [[wave function]] even has an effective [[Spinor|2-spinor structure]].
 
As a consequence, at low energies, even neglecting the true spin, the electrons can be described by an equation that is formally equivalent to the massless [[Dirac equation]]. This pseudo-relativistic description is restricted to the [[Chirality (chemistry)|chiral limit]], i.e., to vanishing rest mass ''M''<sub>0</sub>, which leads to interesting additional features:<ref name="Semenoff"/><ref name=cabra2>{{cite journal |last=Lamas |first=C.A. |coauthors=D. C. Cabra, and N. Grandi |title=Generalized Pomeranchuk instabilities in graphene |journal=Physical Review B |year=2009 |volume=80 |issue=7 |doi=10.1103/PhysRevB.80.075108 |arxiv=0812.4406|bibcode = 2009PhRvB..80g5108L }}</ref>
 
:<math>v_F\, \vec \sigma \cdot \nabla \psi(\mathbf{r})\,=\,E\psi(\mathbf{r}).</math>
 
Here ''v<sub>F</sub>'' ~ {{val|e=6}} is the [[Fermi distribution|Fermi velocity]] in graphene, which replaces the velocity of light in the Dirac theory; <math>\vec{\sigma}</math> is the vector of the [[Pauli matrices]], <math>\psi(\mathbf{r})</math> is the two-component wave function of the electrons, and ''E'' is their energy.<ref name="Castro"/>
 
==See also==
{{columns-list|3|
 
* [[Exfoliated graphite nano-platelets]]
* [[Graphane]]
* [[Graphyne]]
* [[Two-dimensional polymers (2DP)|Two-dimensional polymers]]
* [[Silicene]]
* [[Stanene]]
* [[Bismuth#Bismuthine and bismuthides|Bismuthide]]
}}
 
==References==
{{Reflist|colwidth=30em}}
 
==Sources==
* {{cite journal
|last1=Geim |first1=A. K.
|last2=Novoselov |first2=K. S.
|year=2007
|title=The rise of graphene
|journal=[[Nature Materials]]
|volume=6 |issue=3 |pages=183–91
|bibcode=2007NatMa...6..183G
|doi=10.1038/nmat1849
|pmid=17330084 |ref=harv
}}
 
==External links==
{{commons category|Graphene}}
* [http://www.periodicvideos.com/videos/mv_graphene.htm Graphene] at ''[[The Periodic Table of Videos]]'' (University of Nottingham)
* [http://www.onnes.ph.man.ac.uk/nano/Publications.html#Graphene Most of graphene papers published by Andre Geim's group are downloadable here]
* [http://www.nsf.gov/news/news_summ.jsp?cntn_id=111341&org=NSF&from=news Is Graphene the New Silicon?] National Science Foundation, March 27, 2008
* {{cite web |url=http://www.nanohub.org/resource_files/2005/12/00723/2004.10.20-l21-ece453.pdf |title=Band structure of graphene |format=PDF |accessdate=2009-08-15}}
* [http://www.graphene-info.com/ Graphene portal with daily news and resources]
* {{cite web |url=http://physics.aps.org/articles/v2/30 |title=Pauling's dreams for graphene |author=Antonio H. Castro Neto |date=12 May 2009}}
* {{Cite journal |author=N M R Peres and R M Ribeiro | year = 2009 |title = Focus on Graphene |journal = [[New Journal of Physics]] |volume = 11 |page = 095002 | doi = 10.1088/1367-2630/11/9/095002 |bibcode = 2009NJPh...11i5002P |issue=9 }}
* [http://www.nanohub.org/resources/7180 Online short course: Colloquium on Graphene Physics and Devices]
* [http://www.xstructure.inr.ac.ru/x-bin/auththeme3.py?level=2&index1=181648&skip=0 List of Authority Articles on Graphene Theme]
* [http://www.vega.org.uk/video/programme/326 Short video explanation 'What is Graphene?']
* [http://www.vega.org.uk/video/programme/325 Short video 'Graphene and the Carbon Revolution']
* [http://www.sciencedaily.com/releases/2011/06/110620161308.htm 'Scientists Find Simple Way to Produce Graphene']
* [http://www.bbc.co.uk/news/technology-13886438 'Graphene technology moves closer']
* [http://www.bbc.co.uk/news/science-environment-20975580 Graphene: Patent surge reveals global race]
* [http://www.eetimes.com/discussion/other/4211323/What-Graphene-Offers-for-Future-Electronic-Devices 'What Graphene offers for future Electronic Devices by Linda Rae']
* [http://www.tmworld.com/article/509963-Graphene_shows_promise.php 'Graphene Shows Promise: Researchers are Looking for New Materials that can take over where Silicon will Leave Off']
* [http://www.nanotechweb.org/cws/article/tech/39191 'Defects Improve Graphene Conductivity']
* [http://www.iopscience.iop.org/page/graphene 'IOP Science Graphene Articles]
* [http://www.cdc.gov/niosh/surveyreports/pdfs/356-12a.pdf 'Engineering Controls for Nano-scale Graphene Platelets During Manufacturing and Handling Processes']
 
{{Allotropes of carbon}}
{{Emerging technologies}}
 
[[Category:Aromatic compounds]]
[[Category:Nanomaterials]]
[[Category:Carbon forms]]
[[Category:Quantum Lattice models]]
[[Category:Quantum phases]]
[[Category:Superhard materials]]
[[Category:Semiconductor materials]]
[[Category:Emerging technologies]]
 
{{Link FA|ru}}

Revision as of 21:34, 28 February 2014

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