Type-1.5 superconductor: Difference between revisions

The term type-1.5 superconductor refers to a multicomponent superconductor with two coherence lengths $\xi _{1,2}$ related to the magnetic field penetration length $\lambda$ as follows: $\xi _{1}<{\sqrt {2}}\lambda <\xi _{2}$ . As a consequence, it has behavior different from that of type-I , where ${\sqrt {2}}\lambda <\xi$ and type-II superconductors, where ${\sqrt {2}}\lambda >\xi$ . Specifically, in type-1.5 superconductors quantum vortex excitations are thermodynamically stable but have long-range attractive interaction along with short-range repulsive interaction, and it allows the macroscopic phase separation into Meissner state (domains with expelled magnetic field) and clusters of quantum vortices. Animation from numerical calculations of vortex cluster formation are available at "Numerical simulations of vortex clusters formation in type-1.5 superconductors."

Summary of the properties of type-1.5 superconductor ^[1]
	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) ${\sqrt {2}}\lambda <\xi$	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) ${\sqrt {2}}\lambda >\xi$	Two characteristic length scales of condensate density variation $\xi _{1}$ , $\xi _{2}$ . 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 $\xi _{1}<{\sqrt {2}}\lambda <\xi _{2}$
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 N_c such that E(N)/N < E(N–1)/(N–1) for N<N_c and E(N)/N > E(N–1)/(N–1) for N>N_c, N-quanta vortex decays into vortex cluster

Type-I superconductors 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 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.^[2] 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. 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^[3] that the type-I/type-II dichotomy could be broken in a two-component superconductor.

An example of two-component superconductivity is the two-band superconductor magnesium diboride. There, one can distinguish two superconducting components associated with electrons belong to different bands. 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.

The minimal model of type-1.5 superconductor

For multicomponent superconductors with higher that U(1) symmetry the Ginzburg-Landau model reads:

$F=\sum _{i,j=1,2}{\frac {1}{2m}}|(\nabla -ieA)\psi _{i}|^{2}+\alpha _{i}|\psi _{i}|^{2}+\beta _{i}|\psi _{i}|^{4}+{\frac {1}{2}}(\nabla \times A)^{2}$

where $\psi _{i}=|\psi _{i}|e^{i\phi _{i}},i=1,2$ are two superconducting condensates. In case if the condensates are coupled only electromagnetically, i.e. by $A$ the model has three length scales: the London penetration length $\lambda ={\frac {1}{e{\sqrt {|\psi _{1}|^{2}+|\psi _{2}|^{2}}}}}$ and two coherence lengths $\xi _{1}={\frac {1}{\sqrt {2\alpha _{1}}}},\xi _{2}={\frac {1}{\sqrt {2\alpha _{2}}}}$ . The vortex excitations in that case have cores in both components which are co-centered because of electromagnetic coupling. The necessary but not sufficient condition for occurrence of type-1.5 regime is $\xi _{1}>\lambda >\xi _{2}$ .^[3] 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.^[3]^[1] ^[4] It was further 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 new superconducting phase in low magnetic fields dubbed "Semi-Meissner" state^[3]. 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.

Extended models

A two-band superconductor is described by the following Ginzburg-Landau model ^[5]

$F=\sum _{i,j=1,2}{\frac {1}{2m}}|(\nabla -ieA)\psi _{i}|^{2}+\alpha _{i}|\psi _{i}|^{2}+\beta _{i}|\psi _{i}|^{4}-\eta (\psi _{1}\psi _{2}^{*}+\psi _{1}^{*}\psi _{2})+\gamma [(\nabla -ieA)\psi _{1}\cdot (\nabla +ieA)\psi _{2}^{*}+(\nabla +ieA)\psi _{1}^{*}\cdot (\nabla -ieA)\psi _{2}]+\nu |\psi _{1}|^{2}|\psi _{2}|^{2}+{\frac {1}{2}}(\nabla \times A)^{2}$

where again $\psi _{i}=|\psi _{i}|e^{i\phi _{i}},i=1,2$ are two superconducting condensates. In multiband superconductors quite generically $\eta \neq 0,\gamma \neq 0$ . When $\eta \neq 0,\gamma \neq 0,\nu \neq 0$ three length scales of the problem are again the London penetration length and two coherence lengths. However in this case the coherence lengths ${\tilde {\xi }}_{1}(\alpha _{1},\beta _{1},\alpha _{2},\beta _{2},\eta ,\gamma ,\nu ),{\tilde {\xi }}_{2}(\alpha _{1},\beta _{1},\alpha _{2},\beta _{2},\eta ,\gamma ,\nu )$ are associated with "mixed" combinations of density fields.^[1]^[6]^[4]

Microscopic models

Besides the Ginzburg-Landau models, type-1.5 superconductivity was also described at a microscopic level

^[4]

Current experimental research

In 2009, experimental results have been reported^[7]^[8]^[9] indicating 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 .^[10] 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 ^[6] and is robust in the presence of various inter-band couplings such as interband Josephson coupling.^[1]^[11]

Non-technical explanation

See ^[12]

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. It 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.

see description on ^[13]]

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.^[14]

References

^ ^a ^b ^c ^d Johan Carlstrom; Egor Babaev; Martin Speight (2010). "Type-1.5 superconductivity in multiband systems: the effects of interband couplings". arXiv:1009.2196 [cond-mat.supr-con].
^ Alexei A. Abrikosov Type II superconductors and the vortex lattice, Nobel Lecture, December 8, 2003
^ ^a ^b ^c ^d Egor Babaev and Martin J. Speight (2005). "Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors". Physical Review B. 72 (18): 180502. arXiv:cond-mat/0411681. Bibcode:2005PhRvB..72r0502B. doi:10.1103/PhysRevB.72.180502.
^ ^a ^b ^c Mihail Silaev, Egor Babaev (2011). "Microscopic theory of type-1.5 superconductivity in multiband systems". Phys. Rev. B. 84 (9): 094515. doi:10.1103/PhysRevB.84.094515.
^ A. Gurevich (2007). "Simits of the upper critical field in dirty two-gap superconductors". Physica C. 456: 160. arXiv:cond-mat/0701281. Bibcode:2007PhyC..456..160G. doi:10.1016/j.physc.2007.01.008.
^ ^a ^b Babaev, Egor; Carlström, Johan; Speight, Martin (2010). "Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors". Physical Review Letters. 105 (6): 067003. arXiv:0910.1607. Bibcode:2010PhRvL.105f7003B. doi:10.1103/PhysRevLett.105.067003. PMID 20868000.
^ V. V. Moshchalkov, M. Menghini, T. Nishio, Q.H. Chen, A.V. Silhanek, V.H. Dao, L.F. Chibotaru, N. D. Zhigadlo, J. Karpinsky (2009). "Type-1.5 Superconductors". Physical Review Letters. 102 (11): 117001. Bibcode:2009PhRvL.102k7001M. doi:10.1103/PhysRevLett.102.117001. PMID 19392228.{{cite journal}}: CS1 maint: multiple names: authors list (link)
^ New Type of Superconductivity Spotted, Science Now, 13 March 2009
^ Type-1.5 superconductor shows its stripes, physicsworld.com
^ Taichiro Nishio, Vu Hung Dao1, Qinghua Chen, Liviu F. Chibotaru, Kazuo Kadowaki, and Victor V. Moshchalkov (2010). "Scanning SQUID microscopy of vortex clusters in multiband superconductors". Physical Review B. 81 (2): 020506. Bibcode:2010PhRvB..81b0506N. doi:10.1103/PhysRevB.81.020506.{{cite journal}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
^ Dao; Chibotaru; Nishio; Moshchalkov (2010). "Giant vortices, vortex rings and reentrant behavior in type-1.5 superconductors". arXiv:1007.1849 [cond-mat.supr-con].
^ Physicists unveil a theory for a new kind of superconductivity, physorg.com]
^ Physicists unveil a theory for a new kind of superconductivity, physorg.com]
^ Johan Carlström, Julien Garaud and Egor Babaev Non-pairwise interaction forces in vortex cluster in multicomponent superconductors arXiv:1101.4599, Supplement material

[carlstrom-1] Johan Carlstrom; Egor Babaev; Martin Speight (2010). "Type-1.5 superconductivity in multiband systems: the effects of interband couplings". arXiv:1009.2196 [cond-mat.supr-con].

[2] Alexei A. Abrikosov Type II superconductors and the vortex lattice, Nobel Lecture, December 8, 2003

[babaev-3] Egor Babaev and Martin J. Speight (2005). "Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors". Physical Review B. 72 (18): 180502. arXiv:cond-mat/0411681. Bibcode:2005PhRvB..72r0502B. doi:10.1103/PhysRevB.72.180502.

[silaev-4] Mihail Silaev, Egor Babaev (2011). "Microscopic theory of type-1.5 superconductivity in multiband systems". Phys. Rev. B. 84 (9): 094515. doi:10.1103/PhysRevB.84.094515.

[gurevich-5] A. Gurevich (2007). "Simits of the upper critical field in dirty two-gap superconductors". Physica C. 456: 160. arXiv:cond-mat/0701281. Bibcode:2007PhyC..456..160G. doi:10.1016/j.physc.2007.01.008.

[babaev2-6] Babaev, Egor; Carlström, Johan; Speight, Martin (2010). "Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors". Physical Review Letters. 105 (6): 067003. arXiv:0910.1607. Bibcode:2010PhRvL.105f7003B. doi:10.1103/PhysRevLett.105.067003. PMID 20868000.

[7] V. V. Moshchalkov, M. Menghini, T. Nishio, Q.H. Chen, A.V. Silhanek, V.H. Dao, L.F. Chibotaru, N. D. Zhigadlo, J. Karpinsky (2009). "Type-1.5 Superconductors". Physical Review Letters. 102 (11): 117001. Bibcode:2009PhRvL.102k7001M. doi:10.1103/PhysRevLett.102.117001. PMID 19392228.{{cite journal}}: CS1 maint: multiple names: authors list (link)

[8] New Type of Superconductivity Spotted, Science Now, 13 March 2009

[9] Type-1.5 superconductor shows its stripes, physicsworld.com

[10] Taichiro Nishio, Vu Hung Dao1, Qinghua Chen, Liviu F. Chibotaru, Kazuo Kadowaki, and Victor V. Moshchalkov (2010). "Scanning SQUID microscopy of vortex clusters in multiband superconductors". Physical Review B. 81 (2): 020506. Bibcode:2010PhRvB..81b0506N. doi:10.1103/PhysRevB.81.020506.{{cite journal}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)

[11] Dao; Chibotaru; Nishio; Moshchalkov (2010). "Giant vortices, vortex rings and reentrant behavior in type-1.5 superconductors". arXiv:1007.1849 [cond-mat.supr-con].

[12] Physicists unveil a theory for a new kind of superconductivity, physorg.com]

[13] Physicists unveil a theory for a new kind of superconductivity, physorg.com]

[14] Johan Carlström, Julien Garaud and Egor Babaev Non-pairwise interaction forces in vortex cluster in multicomponent superconductors arXiv:1101.4599, Supplement material

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@@ Line 1: / Line 1: @@
 {{technical|date=October 2011}}
-The term '''type-1.5 superconductor''' refers to a ''multicomponent'' [[superconductor]] with two [[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>. 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>. Specifically, in type-1.5 superconductors quantum vortex excitations are thermodynamically stable but have long-range attractive interaction along with short-range repulsive interaction, and it allows the macroscopic phase separation into [[Meissner state]] (domains with expelled magnetic field) and clusters of quantum vortices.
+The term '''type-1.5 superconductor''' refers to a ''multicomponent'' [[superconductor]] with two [[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>. 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>. Specifically, in type-1.5 superconductors quantum vortex excitations are thermodynamically stable but have long-range attractive interaction along with short-range repulsive interaction, and it allows the macroscopic phase separation into [[Meissner state]] (domains with expelled magnetic field) and clusters of quantum vortices. 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.}}"
 {| class="wikitable"
 |+ Summary of the properties of type-1.5 superconductor <ref name=carlstrom />

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