en>Mirko Raner: added a missing minus sign (the NIA is negative for the given example)

2009-03-14T04:59:19Z

added a missing minus sign (the NIA is negative for the given example)

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The term '''type-1.5 superconductor''' refers to a ''multicomponent'' [[superconductor]] characterized by two or more [[Superconducting coherence length|coherence lengths]] <math>\xi_{1,2}</math> related to the magnetic field [[London penetration depth|penetration length]] <math>\lambda</math> as follows: <math>\xi_1 < \sqrt{2} \lambda <\xi_2</math>.

Physically it means that it has two superconducting components, which densities vary on two different characteristic length scales. One of which is larger and another is smaller than the characteristic length scale of the variation of magnetic field.

As a consequence, it has behavior different from that of [[Type-I superconductor|type-I]], where <math>\sqrt{2} \lambda <\xi </math> and [[type-II superconductor]]s, where <math>\sqrt{2} \lambda >\xi </math>.

Type-1.5 superconductors should possess [[Quantum vortex|quantum vortices]]: magnetic flux carrying excitations which allow magnetic field to pass through superconductor due to a vortex-like circulation of superconducting particles. In contrast to type-II superconductors
these vortices have long-range attractive, short-range repulsive interaction. As a consequence type-1.5 superconductor
in magnetic field undergoes a macroscopic phase separation into domains of [[Meissner state]] (domains with expelled magnetic field) and clusters of quantum vortices which are bound together by attractive intervortex forces. The domains of Meissner state retain the two-component superconductivity, while in the vortex clusters one of the superconducting components is suppressed. Thus such materials should allow coexistence of various properties of type-I and type-II superconductors.

Animation from numerical calculations
of vortex cluster formation are
available at "{{Citation/make link|http://www.youtube.com/user/QuantumVortices/videos|Numerical simulations of vortex clusters formation in type-1.5 superconductors.}}"

==Detailed explanation==

[[Type-I superconductor]]s completely expel external magnetic fields if the strength of the
applied field is sufficiently low; This state is called the [[Meissner state]]. However at elevated magnetic field, when the magnetic field energy becomes comparable with the superconducting condensation energy, the [[superconductivity]] is destroyed by the formation of macroscopically large inclusions of non-superconducting phase.

[[Type-II superconductors]], besides the [[Meissner state]], possess another state: a sufficiently strong applied magnetic field can produce [[Quantum vortex|quantum vortices]] which can carry magnetic flux through the interior of the superconductor. These quantum vortices repel each other and thus tend to form uniform vortex lattices or liquids.<ref>Alexei A. Abrikosov [http://nobelprize.org/nobel_prizes/physics/laureates/2003/abrikosov-lecture.pdf Type II superconductors and the vortex lattice], Nobel Lecture, December 8, 2003</ref> Formally, vortex solutions exist also in models of type-I superconductivity, but the interaction between vortices is purely attractive, so a system of many vortices is unstable against a collapse onto a state of a single giant macroscopic vortex. More importantly, the vortices in type-I superconductor are energetically unfavorable. To produce them would require the application of a magnetic field stronger than what a superconducting condensate can sustain. Thus a type-I superconductor goes to non-superconducting states rather than forming vortices. In the usual [[Ginzburg–Landau theory]], only the quantum vortices with purely repulsive interaction are energetically cheap enough to be induced by applied magnetic field.

It was recently observed<ref name=babaev>{{cite journal| author = Egor Babaev and Martin J. Speight| title = Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors| journal = Physical Review B| volume = 72| issue = 18|page = 180502|year = 2005|doi = 10.1103/PhysRevB.72.180502|arxiv = cond-mat/0411681 |bibcode = 2005PhRvB..72r0502B }}</ref> that the type-I/type-II dichotomy could be broken in a two-component superconductor.

Examples of two-component superconductivity are multi-band superconductors [[magnesium diboride]]
and oxypnictides [[oxypnictide]]. There, one can distinguish two superconducting components associated with electrons belong to different bands [[band structure]].
A different example of two component systems is the projected superconducting states
of liquid [[metallic hydrogen]] or deuterium where mixtures of superconducting electrons and superconducting protons or deuterons were theoretically predicted.

{| class="wikitable"
|+ Summary of the properties of type-1.5 superconductor <ref name=carlstrom />
!
! Type-I superconductor
! Type-II superconductor
! Type-1.5 superconductor
|-
! Characteristic length scales
| The characteristic magnetic field variation length scale ([[London penetration depth]]) is smaller than the characteristic length scale of condensate density variation ([[superconducting coherence length]]) <math>\sqrt{2}\lambda<\xi</math> || The characteristic magnetic field variation length scale (London penetration depth) is larger than the characteristic length scale of the condensate density variation (superconducting coherence length) <math>\sqrt{2}\lambda> \xi</math>|| Two characteristic length scales of condensate density variation <math>\xi_1</math>, <math>\xi_2</math>. Characteristic magnetic field variation length scale is smaller than one of the characteristic length scales of density variation and larger than another characteristic length scale of density variation <math>\xi_1<\sqrt{2}\lambda<\xi_2</math>
|-
! Intervortex interaction
| Attractive || Repulsive || Attractive at long range and repulsive at short range
|-
! Phases in magnetic field of a clean bulk superconductor
| (1) Meissner state at low fields; (2) Macroscopically large normal domains at larger fields. First-order phase transition between the states (1) and (2) || (1) Meissner state at low fields, (2) vortex lattices/liquids at larger fields. || (1) Meissner state at low fields (2) "Semi-Meissner state": vortex clusters coexisting with Meissner domains at intermediate fields (3) Vortex lattices/liquids at larger fields.
|-
! Phase transitions
|First-order phase transition between the states (1) and (2) || Second-order phase transition between the states (1) and (2) and second-order phase transition between from the state (2) to normal state || First-order phase transition between the states (1) and (2) and second-order phase transition between from the state (2) to normal state.
|-
! Energy of Superconducting/normal boundary
| Positive || Negative || Negative energy of superconductor/normal interface inside a vortex cluster, positive energy at the boundary of vortex cluster
|-
! Weakest magnetic field required to form a vortex
| Larger than thermodynamical critical magnetic field || Smaller than thermodynamical critical magnetic field || In some cases larger than critical magnetic field for single vortex but smaller than critical magnetic field for a vortex cluster
|-
! Energy E(N) of N-quanta axially symmetric vortex solutions
| E(N)/N < E(N–1)/(N–1) for all N, i.e. N-quanta vortex does not decay in 1-quanta vortices || E(N)/N > E(N–1)/(N–1) for all N, i.e. N-quanta vortex decays in 1-quanta vortices || There is a characteristic number of flux quanta Nc such that E(N)/N < E(N–1)/(N–1) for N<Nc and E(N)/N > E(N–1)/(N–1) for N>Nc, N-quanta vortex decays into vortex cluster
|}

== Type-1.5 superconductor in mixtures of independently conserved condensates==
For multicomponent superconductors with so called U(1)xU(1) symmetry the Ginzburg-Landau model
is a sum of two single-component Ginzburg-Landau model which are coupled by a vector potential
<math> A </math> :

<math> F=\sum_{i,j=1,2}\frac{1}{2m} |(\nabla - ie A) \psi_i|^2 + \alpha_i |\psi_i|^2 + \beta_i|\psi_i|^4 +\frac{1}{2}(\nabla \times A)^2 </math>

where <math> \psi_i = |\psi_i| e^{i \phi_i}, i=1,2 </math> are two superconducting condensates.
In case if the condensates are coupled only electromagnetically, i.e. by <math>A</math> the model has three length scales: the London penetration length
<math>\lambda = \frac{1}{e\sqrt{|\psi_1|^2 + |\psi_2|^2}}</math> and two coherence lengths <math>\xi_1=\frac{1}{\sqrt{2\alpha_1}},\xi_2=\frac{1}{\sqrt{2\alpha_2}}</math>.
The vortex excitations in that case have cores in both components which are co-centered because
of electromagnetic coupling mediated by the field <math> A </math>.
The necessary but not sufficient condition for occurrence of type-1.5 regime is <math>\xi_1 >\lambda>\xi_2</math>.<ref name="babaev" /> Additional condition of thermodynamic stability is satisfied for a range of parameters.
These vortices have a nonmonotonic interaction: they attract each other at large distances and repel each other at short distances.<ref name="babaev"/><ref name="carlstrom" /><ref name="silaev" />
It was shown that there is a range of parameters where these vortices are energetically favorable enough to be excitable by an external field, attractive interaction notwithstanding. This results in the formation of a special superconducting phase in low magnetic fields dubbed "Semi-Meissner" state.<ref name="babaev" /> The vortices, whose density is controlled by applied magnetic flux density, do not form a regular structure. Instead, they should have a tendency to form vortex "droplets" because of the long-range attractive interaction caused by condensate density suppression in the area around the vortex. Such vortex clusters should coexist with the areas of vortex-less two-component Meissner domains. Inside such vortex cluster the component with larger coherence length is suppressed: so that component has appreciable current only at the boundary of the cluster.

==Type-1.5 superconductivity in multiband systems==
In a [[two-band superconductor]] the electrons in different bands do not independently conserved thus the definition of two superconducting components is different.
A two-band superconductor is described by the following Ginzburg-Landau model
<ref name=gurevich>{{cite journal| author = A. Gurevich| title = Simits of the upper critical field in dirty two-gap superconductors| journal = Physica C| volume = 456|page = 160|year = 2007|arxiv = cond-mat/0701281 |bibcode = 2007PhyC..456..160G |doi = 10.1016/j.physc.2007.01.008 }}</ref>

<math> F=\sum_{i,j=1,2}\frac{1}{2m} |(\nabla - ie A) \psi_i|^2 + \alpha_i |\psi_i|^2 + \beta_i|\psi_i|^4 - \eta( \psi_1\psi_2^* + \psi_1^*\psi_2)
+ \gamma [(\nabla - ie A) \psi_1 \cdot (\nabla + ie A) \psi_2^* + (\nabla + ie A) \psi_1^* \cdot (\nabla - ie A) \psi_2] + \nu |\psi_1|^2|\psi_2|^2 +\frac{1}{2}(\nabla \times A)^2 </math>

where again <math> \psi_i = |\psi_i| e^{i \phi_i}, i=1,2 </math> are two superconducting condensates.
In multiband superconductors quite generically <math>\eta\ne 0, \gamma \ne 0</math>.
When <math>\eta\ne 0, \gamma \ne 0, \nu \ne 0</math> three length scales of the problem are again the London penetration length
and two coherence lengths. However in this case the coherence lengths <math>\tilde{\xi}_1(\alpha_1,\beta_1,\alpha_2,\beta_2,\eta,\gamma,\nu),\tilde{\xi}_2(\alpha_1,\beta_1,\alpha_2,\beta_2,\eta,\gamma,\nu)</math> are associated with "mixed" combinations of density fields.<ref name="carlstrom" /><ref name="silaev" /><ref name="babaev2" />

==Microscopic models==
A microscopic theory of type-1.5 superconductivity has been reported.<ref name=silaev>{{cite journal |author=Mihail Silaev, Egor Babaev |title=Microscopic theory of type-1.5 superconductivity in multiband systems |journal=Phys. Rev. B |volume=84 |issue=9 |pages=094515 |year=2011 |pmid= |pmc= |doi=10.1103/PhysRevB.84.094515 |url= |arxiv = 1102.5734 |bibcode = 2011PhRvB..84i4515S }}</ref>

==Current experimental research==
In 2009, experimental results have been reported<ref>{{ cite journal| author = V. V. Moshchalkov, M. Menghini, T. Nishio, Q.H. Chen, A.V. Silhanek, V.H. Dao, L.F. Chibotaru, N. D. Zhigadlo, J. Karpinsky|title = Type-1.5 Superconductors| journal = Physical Review Letters| volume = 102| issue = 11| page = 117001|year =2009| doi = 10.1103/PhysRevLett.102.117001| pmid=19392228| bibcode=2009PhRvL.102k7001M|arxiv = 0902.0997 }}</ref><ref>[http://sciencenow.sciencemag.org/cgi/content/full/2009/313/1 New Type of Superconductivity Spotted], Science Now, 13 March 2009</ref><ref>[http://physicsworld.com/cws/article/news/37806 Type-1.5 superconductor shows its stripes], physicsworld.com</ref>
claiming that  [[magnesium diboride]] may fall into this new class of superconductivity. The term type-1.5 superconductor was coined for this state. Further experimental data backing this conclusion was reported in
.<ref>{{ cite journal| author = Taichiro Nishio, Vu Hung Dao1, Qinghua Chen, Liviu F. Chibotaru, Kazuo Kadowaki, and Victor V. Moshchalkov|title = Scanning SQUID microscopy of vortex clusters in multiband superconductors| journal = Physical Review B| volume = 81| issue = 2| page = 020506|year =2010| doi = 10.1103/PhysRevB.81.020506|bibcode = 2010PhRvB..81b0506N |arxiv = 1001.2199 }}</ref> More recent theoretical works show that the type-1.5 may be more general phenomenon because it does not require a material with two truly superconducting bands, but can also happen as a result of even very small interband proximity effect
<ref name= "babaev2">{{cite journal|last1=Babaev|first1=Egor|last2=Carlström|first2=Johan|last3=Speight|first3=Martin|title=Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors|arxiv=0910.1607|journal=Physical Review Letters|volume=105|issue=6|pages=067003|year=2010|pmid=20868000|doi=10.1103/PhysRevLett.105.067003|bibcode=2010PhRvL.105f7003B}}</ref> and is robust in the presence of various inter-band couplings such as interband Josephson coupling.<ref name="carlstrom">{{cite arxiv |eprint=1009.2196 |author1=Johan Carlstrom |author2=Egor Babaev |author3=Martin Speight |title=Type-1.5 superconductivity in multiband systems: the effects of interband couplings |class=cond-mat.supr-con |year=2010}}</ref><ref>{{cite arxiv|eprint=1007.1849|author1=Dao|author2=Chibotaru|author3=Nishio|author4=Moshchalkov|title=Giant vortices, vortex rings and reentrant behavior in type-1.5 superconductors|class=cond-mat.supr-con|year=2010}}</ref>

==Non-technical explanation==
In Type-I and Type-II superconductors charge flow patterns are dramatically different. Type I has two state-defining properties: Lack of electric resistance and the fact that it does not allow an external magnetic field to pass through it. When a magnetic field is applied to these materials, superconducting electrons produce a strong current on the surface which in turn produces a magnetic field in the opposite direction. Inside this type of superconductor, the external magnetic field and the field created by the surface flow of electrons add up to zero. That is, they cancel each other out.
In Type II superconducting materials where a complicated flow of superconducting electrons can happen deep in the interior. In Type II material, a magnetic field can penetrate, carried inside by vortices which form Abrikosov vortex lattice. In type-1.5 superconductor there are two superconducting components. There the external magnetic field can produce clusters of tightly packed vortex droplets because in such materials vortices should attract each other at large distances and repel at short length scales. Since the attraction originates in vortex core's overlaps in one of the superconducting components, this component will be depleted in the vortex cluster. Thus
a vortex cluster will represent two competing types of superflow. One component will form vortices bunched together while the second component will produce supercurrent flowing on the surface of vortex clusters in a way similar to how electrons flow on the exterior of Type I superconductors. These vortex clusters are separated by "voids," with no vortices, no currents and no magnetic field.<ref>[http://www.physorg.com/news/2011-10-physicists-unveil-theory-kind-superconductivity.html6 Physicists unveil a theory for a new kind of superconductivity], physorg.com</ref>

[[File:Type15.png]]

==Animations of type-1.5 superconducting behavior==
Movies from numerical simulations of the Semi-Meissner state where Meissner domains
coexist with clusters where vortex droplets form in one superconducting components and macroscopic normal domains in the other.<ref>Johan Carlström, Julien Garaud and Egor Babaev [http://people.umass.edu/garaud/NonPairwise.html Non-pairwise interaction forces in vortex cluster in multicomponent superconductors arXiv:1101.4599], Supplement material</ref>

==See also==
{{colbegin|3}}
*[[Type I superconductor]]
*[[Type-II superconductor]]
*[[Conventional superconductor]]
*[[Covalent superconductors]]
*[[High-temperature superconductivity]]
*[[List of superconductors]]
*[[Room temperature superconductor]]
*[[Superconductivity]]
*[[Superconductor classification]]
*[[Technological applications of superconductivity]]
*[[Timeline of low-temperature technology]]
*[[Unconventional superconductor]]
{{colend}}

==References==
{{reflist|2}}

[[Category:Superconductivity]]

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en>Mirko Raner: added a missing minus sign (the NIA is negative for the given example)