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| The '''quantum Hall effect''' (or '''integer quantum Hall effect''') is a [[quantum mechanics|quantum-mechanical]] version of the [[Hall effect]], observed in [[2DEG|two-dimensional electron systems]] subjected to low [[temperature]]s and strong [[magnetic field]]s, in which the Hall [[Electrical conductivity|conductivity]] σ undergoes certain [[quantum Hall transitions]] to take on the quantized values
| | == Occhiali Da Sole Ray Ban veloce sinterizzato 9900 Base == |
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| :<math> \sigma = \frac{I_\text{channel}}{V_\text{Hall}} = \nu \; \frac{e^2}{h}, </math>
| | Prendiamo ad esempio il loro guardaroba. Hanno intricati disegni ed esotiche, i materiali sono altamente durevoli ed i disegni sono semplicemente incutere timore. Essi prestano un designer di toccare per la camera e può alterare completamente il modo di una semplice stanza sembra.. <br><br>Il termine è stato prorogato per i genitori di bambini gravemente o affetti da malattie croniche, specialmente quelli in cure palliative, per ottenere le loro lettere (no e-mail) per me la richiesta dei biglietti gratuiti per il viaggio in treno Cuyahoga Valley Scenic Railroad Polar Express 14 dicembre. Il viaggio è anche per i figli dei soldati attualmente dispiegati o recentemente tornati da Afghanistan e clienti a Hattie Larlham, un centro di assistenza residenziale per persone con disabilità dello sviluppo. Guardiani devono rispettare il nuovo termine del 20 novembre.. <br><br>Vassell ha detto sostenitori l'alterco [http://www.mutuisi.it/area_riservata/gestione_news/editor.asp Occhiali Da Sole Ray Ban] è iniziato quando ha notato i due uomini fuori dalla sua finestra al piano terra, Thelwell detto, aggiungendo che i testimoni hanno confermato il racconto di Vassell. Gli uomini cominciarono a schernire Vassell e rotto la finestra. Vassell, sentendosi minacciato, ha chiamato un amico da un dormitorio vicina per chiedere aiuto. <br><br>Gnu freestyle Magne Traction Rider Choice Snowboards è di nuova concezione per il 2008 e le frontiere professionali come Zach Leach, Kyle Clancy e Dennis Bonjourno hanno già dato un giro di prova su diversi concorsi. Tavole Rider Choice hanno una costruzione a sandwich, sciancratura direzionale, nuova forma smussata punta / coda del 2008, veloce sinterizzato 9900 Base, UHMW Sidewalls e leggero della piuma Mervin [http://www.comandulli.it/webOLD/class.asp Occhiali Da Sole Oakley] AG1 Core. Per coronare il tutto questa scheda [http://www.gardailmelograno.com/web_ted/bottom.asp Pandora Bracciali] viene fornito con Magne Traction geometria per l'ultimo spettacolo di freestyle di fascia alta. <br><br>Fosse Federer potuto continuare con l'aiuto di antidolorifici, probabilmente non avrebbe detto una parola sul pregiudizio. Come è stato, una volta ha ottenuto l'Australian Open, è stato molto positivo circa la sua condizione. Anche se ha confessato di non essere in grado di arrivare fino a piena [http://www.landa.it/web_fra/config.asp Air Max] velocità in pratica fino a un paio di giorni prima dell'inizio del torneo, lui era ottimista circa la sua capacità di giocare. <br><br>Ci siamo seduti uno accanto all'altro, il suo braccio intorno alle spalle. Posai la testa sulla sua spalla. Mi chiedo cosa la gente avrebbe pensato se ci vedevano come questo. Le società non fanno le leggi. I partiti politici non fanno le leggi. Membri del Congresso fanno leggi. |
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| where <math>I_\text{channel}</math> is the channel [[electric current|current]], <math>V_\text{Hall}</math> is the [[Hall voltage]], ''e'' is the [[elementary charge]] and ''h'' is [[Planck's constant]]. The prefactor ν is known as the "filling factor", and can take on either integer (ν = 1, 2, 3, .. ) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5 ...) values. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively. The integer quantum Hall effect is very well understood, and can be simply explained in terms of single-particle orbitals of an electron in a magnetic field (see [[Landau quantization]]). The [[fractional quantum Hall effect]] is more complicated, as its existence relies fundamentally on electron–electron interactions. It is also very well understood as an integer quantum Hall effect, not of electrons but of charge-flux composites known as [[composite fermions]]. In 1988, it was proposed that there was quantum Hall effect without Landau levels. This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the [[quantum spin Hall effect]] which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents.<ref> {{cite book | first=Zyun F. | last=Ezawa | title=Quantum Hall Effects: Recent Theoretical and Experimental Developments | edition=3rd | publisher=World Scientific | year=2013 | isbn=978-981-4360-75-3}}</ref>
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| ==Applications==
| | <li>[http://www.philatelie-france-russie.fr/spip.php?article51/ http://www.philatelie-france-russie.fr/spip.php?article51/]</li> |
| The quantization of the Hall conductance has the important property of being incredibly precise. Actual measurements of the Hall conductance have been found to be integer or fractional multiples of ''e<sup>2</sup>/h'' to nearly one part in a billion. This phenomenon, referred to as "exact quantization", has been shown to be a subtle manifestation of the principle of [[gauge invariance]].<ref>{{cite journal|last=Laughlin|first=R.|title=Quantized Hall conductivity in two dimensions|journal=Physical Review B|year=1981|volume=23|issue=10|pages=5632–5633|doi=10.1103/PhysRevB.23.5632|url=http://prb.aps.org/abstract/PRB/v23/i10/p5632_1|accessdate=8 May 2012|bibcode = 1981PhRvB..23.5632L }}</ref> It has allowed for the definition of a new practical [[physical unit|standard]] for [[electrical resistance]], based on the resistance quantum given by the von Klitzing constant ''R''<sub>K</sub> = ''h/e<sup>2</sup>'' = 25812.807557(18) [[Ohm (unit)|Ω]].<ref>{{cite journal|year = 2010|title = Towards a quantum resistance standard based on epitaxial graphene|journal = [[Nature Nanotechnology]]|volume = 5|issue = 3|pages = 186–189|doi = 10.1038/nnano.2009.474 | url=http://www.nature.com/nnano/journal/v5/n3/abs/nnano.2009.474.html|pmid = 20081845|bibcode = 2010NatNa...5..186T|last1 = Tzalenchuk|first1 = Alexander|last2 = Lara-Avila|first2 = Samuel|last3 = Kalaboukhov|first3 = Alexei|last4 = Paolillo|first4 = Sara|last5 = Syväjärvi|first5 = Mikael|last6 = Yakimova|first6 = Rositza|last7 = Kazakova|first7 = Olga|last8 = Janssen|first8 = T. J. B. M.|last9 = Fal'ko|first9 = Vladimir |first10=Sergey |last10=Kubatkin| arxiv = 0909.1220 }}</ref> This is named after [[Klaus von Klitzing]], the discoverer of exact quantization. Since 1990, a fixed [[conventional electrical unit|conventional value]] ''R''<sub>K-90</sub> is used in resistance calibrations worldwide.<ref>{{cite web|url=http://physics.nist.gov/cgi-bin/cuu/Value?rk90|title= conventional value of von Klitzing constant|work= NIST}}</ref> The quantum Hall effect also provides an extremely precise independent determination of the [[fine structure constant]], a quantity of fundamental importance in [[quantum electrodynamics]].
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| | | <li>[http://bbs.0714.cn/forum.php?mod=viewthread&tid=4080880&fromuid=780822 http://bbs.0714.cn/forum.php?mod=viewthread&tid=4080880&fromuid=780822]</li> |
| ==History==
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| The integer quantization of the Hall conductance was originally predicted by Ando, Matsumoto, and Uemura in 1975, on the basis of an approximate calculation which they themselves did not believe to be true. Several workers subsequently observed the effect in experiments carried out on the inversion layer of [[MOSFET]]s. It was only in 1980 that [[Klaus von Klitzing]], working with samples developed by [[Michael Pepper]] and Gerhard Dorda, made the unexpected discovery that the Hall conductivity was ''exactly'' quantized. For this finding, von Klitzing was awarded the 1985 [[Nobel Prize in Physics]]. The link between exact quantization and gauge invariance was subsequently found by [[Robert B. Laughlin|Robert Laughlin]]. Most integer quantum Hall experiments are now performed on [[gallium arsenide]] [[heterostructure]]s, although many other semiconductor materials can be used. In 2007, the integer quantum Hall effect was reported in [[graphene]] at temperatures as high as room temperature,<ref>{{cite journal|year = 2007|title = Room-Temperature Quantum Hall Effect in Graphene|journal = [[Science (journal)|Science]]|volume = 315|issue = 5817|pages = 1379|doi = 10.1126/science.1137201| pmid = 17303717|arxiv=cond-mat/0702408|bibcode = 2007Sci...315.1379N|last1 = Novoselov|first1 = K. S.|last2 = Jiang|first2 = Z.|last3 = Zhang|first3 = Y.|last4 = Morozov|first4 = S. V.|last5 = Stormer|first5 = H. L.|last6 = Zeitler|first6 = U.|last7 = Maan|first7 = J. C.|last8 = Boebinger|first8 = G. S.|last9 = Kim|first9 = P.|last10=Geim|first10=A. K. }}</ref> and in the oxide ZnO-Mg<sub>x</sub>Zn<sub>1-x</sub>O.<ref>{{Cite journal| doi=10.1126/science.1137430| title=Quantum Hall Effect in Polar Oxide Heterostructures| year=2007| last1=Tsukazaki| first1=A.| last2=Ohtomo| first2=A.| last3=Kita| first3=T.| last4=Ohno| first4=Y.| last5=Ohno| first5=H.| last6=Kawasaki| first6=M.| journal=Science| volume=315| issue=5817| pages=1388–91| pmid=17255474|bibcode = 2007Sci...315.1388T }}</ref>
| | <li>[http://cs1.bn50.com/forum.php?mod=viewthread&tid=398367&fromuid=12430 http://cs1.bn50.com/forum.php?mod=viewthread&tid=398367&fromuid=12430]</li> |
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| ==Integer quantum Hall effect – Landau levels==
| | <li>[http://matchsouls.com/tweet/?module=awwmrhch http://matchsouls.com/tweet/?module=awwmrhch]</li> |
| [[File:QuantumHallEffectExplanationWithLandauLevels.ogv|360px|alt=Animated graph showing filling of landau levels as B changes and the corresponding position on a graph of hall coefficient and magnetic field|Illustrative only. The Landau Levels spread out with increasing field. Between the levels the quantum hall effect is seen.]]
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| In two dimensions, when classical electrons are subjected to a magnetic field they follow circular cyclotron orbits. When the system is treated quantum mechanically, these orbits are quantized. The energy levels of these quantized orbitals take on discrete values: <math>E_n = \hbar \omega_c (n+1/2)</math>, where ''ω<sub>c</sub> = eB/m'' is the cyclotron frequency. These orbitals are known as [[Landau quantization|Landau levels]], and at weak magnetic fields, their existence gives rise to many interesting "quantum oscillations" such as the [[Shubnikov–de Haas effect|Shubnikov–de Haas oscillations]] and the [[de Haas–van Alphen effect]] (which is often used to map the Fermi surface of metals).
| | <li>[http://www.osvaldocarretta.it/node/68#comment-6274631 http://www.osvaldocarretta.it/node/68#comment-6274631]</li> |
| For strong magnetic fields, each Landau level is highly degenerate (i.e. there are many single particle states which have the same energy ''E<sub>n</sub>''). Specifically, for a sample of area A, in magnetic field B, the degeneracy of each Landau level is <math>N = g_s BA/\phi_0</math> (where g<sub>s</sub> represents a factor of 2 for spin degeneracy, and <math>\phi_0</math> is the magnetic flux quantum). For sufficiently strong B-fields, each Landau level may have so many states that all of the free electrons in the system sit in only a few Landau levels; it is in this regime where one observes the quantum Hall effect.
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| | | </ul> |
| ==Mathematics== | |
| [[Image:Hofstadter's butterfly.png|thumb|[[Hofstadter's butterfly]]]]
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| The integers that appear in the Hall effect are examples of [[topological quantum number]]s. They are known in mathematics as the first [[Chern_class#Chern_numbers|Chern numbers]] and are closely related to [[Geometric phase|Berry's phase]]. A striking model of much interest in this context is the Azbel-Harper-Hofstadter model whose quantum phase diagram is the [[Hofstadter butterfly]] shown in the figure. The vertical axis is the strength of the [[magnetic field]] and the horizontal axis is the [[chemical potential]], which fixes the electron density. The colors represent the integer Hall conductances. Warm colors represent positive integers and cold colors negative integers. The phase diagram is fractal and has structure on all scales. In the figure there is an obvious [[self-similarity]].
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| Concerning physical mechanisms, impurities and/or particular states (e.g., edge currents) are important for both the 'integer' and 'fractional' effects. In addition, Coulomb interaction is also essential in the [[fractional quantum Hall effect]]. The observed strong similarity between integer and fractional quantum Hall effects is explained by the tendency of electrons to form bound states with an even number of magnetic flux quanta, called ''[[composite fermions]]''.
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| ==See also==
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| *[[quantum Hall transitions]]
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| *[[Fractional quantum Hall effect]]
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| *[[Composite fermions]]
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| *[[Hall effect]]
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| *[[Hall probe]]
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| *[[Graphene]]
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| *[[Quantum spin Hall effect]]
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| *[[Static forces and virtual-particle exchange#Coulomb potential between two current loops embedded in a magnetic field|Coulomb potential between two current loops embedded in a magnetic field]]
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| ==References==
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| {{reflist}}
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| ==Further reading==
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| *{{cite journal|year = 1975|title = Theory of Hall Effect in a Two-Dimensional Electron System|journal = [[Journal of the Physical Society of Japan|J. Phys. Soc. Jpn.]]|volume = 39|pages = 279–288|doi = 10.1143/JPSJ.39.279|bibcode = 1975JPSJ...39..279A|issue = 2|last1 = Ando|first1 = Tsuneya|last2 = Matsumoto|first2 = Yukio|last3 = Uemura|first3 = Yasutada }}
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| *{{cite journal|year = 1980|title = New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance|journal = [[Physical Review Letters|Phys. Rev. Lett.]]|volume = 45|issue = 6|pages = 494–497|doi = 10.1103/PhysRevLett.45.494|bibcode=1980PhRvL..45..494K|last1 = Klitzing|first1 = K.|last2 = Dorda|first2 = G.|last3 = Pepper|first3 = M.}}
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| *{{cite journal|last = Laughlin|first = R. B.|year = 1981|title = Quantized Hall conductivity in two dimensions|journal = Phys. Rev. B.|volume = 23|issue = 10|pages = 5632–5633|doi = 10.1103/PhysRevB.23.5632|bibcode = 1981PhRvB..23.5632L }}
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| *{{cite journal|last = Yennie|first = D. R.|year = 1987|title = Integral quantum Hall effect for nonspecialists|journal = Rev. Mod. Phys.|volume = 59|issue = 3|pages = 781–824|doi = 10.1103/RevModPhys.59.781|bibcode=1987RvMP...59..781Y}}
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| *{{cite journal|year = 2008|title = A topological Dirac insulator in a quantum spin Hall phase|journal = [[Nature (journal)|Nature]]|volume = 452|issue = 7190|pages = 970–974|doi = 10.1038/nature06843|pmid = 18432240|bibcode = 2008Natur.452..970H|last1 = Hsieh|first1 = D.|last2 = Qian|first2 = D.|last3 = Wray|first3 = L.|last4 = Xia|first4 = Y.|last5 = Hor|first5 = Y. S.|last6 = Cava|first6 = R. J.|last7 = Hasan|first7 = M. Z. |arxiv = 0902.1356 }}
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| *''25 years of Quantum Hall Effect'', K. von Klitzing, Poincaré Seminar (Paris-2004). [http://parthe.lpthe.jussieu.fr/poincare/textes/novembre2004.html Postscript]. [http://hrma.physics.sjtu.edu.cn/PhysicsHorizon/25yearsQHE-lecture.pdf Pdf].
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| * Magnet Lab Press Release [http://www.magnet.fsu.edu/mediacenter/news/pressreleases/2007february15.html Quantum Hall Effect Observed at Room Temperature]
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| *{{cite journal|last=Avron|first=Joseph E.|coauthors=Osadchy, Daniel, Seiler, Ruedi|title=A Topological Look at the Quantum Hall Effect|journal=Physics Today|year=2003|volume=56|issue=8|pages=38|doi=10.1063/1.1611351|url=http://www.physicstoday.org/resource/1/phtoad/v56/i8/p38_s1|accessdate=8 May 2012|bibcode = 2003PhT....56h..38A }}
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| *Zyun F. Ezawa: ''Quantum Hall Effects - Field Theoretical Approach and Related Topics.'' World Scientific, Singapore 2008, ISBN 978-981-270-032-2
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| *Sankar D. Sarma, Aron Pinczuk: ''Perspectives in Quantum Hall Effects.'' Wiley-VCH, Weinheim 2004, ISBN 978-0-471-11216-7
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| * {{Cite journal|doi=10.1103/PhysRevB.76.085316|title=Quantum Hall effect transition in scanning gate experiments|year=2007|last1=Baumgartner|first1=A.|last2=Ihn|first2=T.|last3=Ensslin|first3=K.|last4=Maranowski|first4=K.|last5=Gossard|first5=A.|journal=Physical Review B|volume=76|issue=8|bibcode = 2007PhRvB..76h5316B }}
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| * E. I. Rashba and V. B. Timofeev, Quantum Hall Effect, Sov. Phys. - Semiconductors v. 20, pp. 617-647 (1986).
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| {{DEFAULTSORT:Quantum Hall Effect}}
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| [[Category:Hall effect]]
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| [[Category:Condensed matter physics]]
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| [[Category:Quantum electronics]]
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| [[Category:Spintronics]]
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| [[Category:Quantum phases]]
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| [[Category:Mesoscopic physics]]
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Occhiali Da Sole Ray Ban veloce sinterizzato 9900 Base
Prendiamo ad esempio il loro guardaroba. Hanno intricati disegni ed esotiche, i materiali sono altamente durevoli ed i disegni sono semplicemente incutere timore. Essi prestano un designer di toccare per la camera e può alterare completamente il modo di una semplice stanza sembra..
Il termine è stato prorogato per i genitori di bambini gravemente o affetti da malattie croniche, specialmente quelli in cure palliative, per ottenere le loro lettere (no e-mail) per me la richiesta dei biglietti gratuiti per il viaggio in treno Cuyahoga Valley Scenic Railroad Polar Express 14 dicembre. Il viaggio è anche per i figli dei soldati attualmente dispiegati o recentemente tornati da Afghanistan e clienti a Hattie Larlham, un centro di assistenza residenziale per persone con disabilità dello sviluppo. Guardiani devono rispettare il nuovo termine del 20 novembre..
Vassell ha detto sostenitori l'alterco Occhiali Da Sole Ray Ban è iniziato quando ha notato i due uomini fuori dalla sua finestra al piano terra, Thelwell detto, aggiungendo che i testimoni hanno confermato il racconto di Vassell. Gli uomini cominciarono a schernire Vassell e rotto la finestra. Vassell, sentendosi minacciato, ha chiamato un amico da un dormitorio vicina per chiedere aiuto.
Gnu freestyle Magne Traction Rider Choice Snowboards è di nuova concezione per il 2008 e le frontiere professionali come Zach Leach, Kyle Clancy e Dennis Bonjourno hanno già dato un giro di prova su diversi concorsi. Tavole Rider Choice hanno una costruzione a sandwich, sciancratura direzionale, nuova forma smussata punta / coda del 2008, veloce sinterizzato 9900 Base, UHMW Sidewalls e leggero della piuma Mervin Occhiali Da Sole Oakley AG1 Core. Per coronare il tutto questa scheda Pandora Bracciali viene fornito con Magne Traction geometria per l'ultimo spettacolo di freestyle di fascia alta.
Fosse Federer potuto continuare con l'aiuto di antidolorifici, probabilmente non avrebbe detto una parola sul pregiudizio. Come è stato, una volta ha ottenuto l'Australian Open, è stato molto positivo circa la sua condizione. Anche se ha confessato di non essere in grado di arrivare fino a piena Air Max velocità in pratica fino a un paio di giorni prima dell'inizio del torneo, lui era ottimista circa la sua capacità di giocare.
Ci siamo seduti uno accanto all'altro, il suo braccio intorno alle spalle. Posai la testa sulla sua spalla. Mi chiedo cosa la gente avrebbe pensato se ci vedevano come questo. Le società non fanno le leggi. I partiti politici non fanno le leggi. Membri del Congresso fanno leggi.
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