λ
\xi
\xi>λ
\xi<λ
21/2
\xi>\sqrt{2}λ
\xi<\sqrt{2}λ
Type-I superconductors completely expel external magnetic fields if the strength of the applied field is sufficiently low. Also the supercurrent can flow only on the surface of such a superconductor but not in its interior. 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 currents in the interior of superconductor due to formation of quantum vortices. The vortices also 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.[1] 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 normal domain with supercurrent flowing on its surface. 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 proposed[2] that the type-I/type-II dichotomy could be broken in a multi-component superconductors, which possess multiple coherence lengths.
Examples of multi-component superconductivity are multi-band superconductors magnesium diboride and oxypnictides and exotic superconductors with nontrivial Cooper-pairing. There, one can distinguish two or more superconducting components associated, for example with electrons belong to different bands band structure. A different example of two component systems is the projected superconducting statesof liquid metallic hydrogen or deuterium where mixtures of superconducting electrons and superconducting protons or deuterons were theoretically predicted.
It was also pointed out that systems which have phase transitions between different superconducting states such as between
s
s+is
U(1)
U(1) x U(1)
| 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}λ<\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}λ>\xi | Two characteristic length scales of condensate density variation \xi1 \xi2 \xi1<\sqrt{2}λ<\xi2 | |
|---|---|---|---|---|
| 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 |
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
A
F=\sumi,j=1,2
| 1 | |
| 2m |
|(\nabla-ieA)
| 2 | |
| \psi | |
| i| |
+\alphai
| 2 | |
| |\psi | |
| i| |
+\betai|\psi
| 4 | ||
| + | ||
| i| |
| 1 | |
| 2 |
(\nabla x A)2
where
\psii=|\psii|
| i\phii | |
| e |
,i=1,2
A
λ=
| 1 | |||||||||||||||
|
| \xi | ||||
|
A
\xi1>λ>\xi2
In a two-band superconductor the electrons in different bands are not independently conserved thus the definition of two superconducting components is different. A two-band superconductor is described by the following Ginzburg-Landau model.[3]
F=\sumi,j=1,2
| 1 | |
| 2m |
|(\nabla-ieA)
| 2 | |
| \psi | |
| i| |
+\alphai
| 2 | |
| |\psi | |
| i| |
+\betai|\psi
| 4 | |
| i| |
-η(\psi1\psi
| * | |
| 2 |
+
| *\psi | |
| \psi | |
| 2) + |
\gamma[(\nabla-ieA)\psi1 ⋅ (\nabla+ieA)
| * | |
| \psi | |
| 2 |
+(\nabla+ieA)
| * | |
| \psi | |
| 1 |
⋅ (\nabla-ieA)\psi2]+\nu
| 2 | ||
| |\psi | + | |
| 2| |
| 1 | |
| 2 |
(\nabla x A)2
where again
\psii=|\psii|
| i\phii | |
| e |
,i=1,2
η\ne0,\gamma\ne0
η\ne0,\gamma\ne0,\nu\ne0
\tilde{\xi}1(\alpha1,\beta1,\alpha2,\beta2,η,\gamma,\nu),\tilde{\xi}2(\alpha1,\beta1,\alpha2,\beta2,η,\gamma,\nu)
A microscopic theory of type-1.5 superconductivity has been reported.[4]
In 2009, experimental results have been reported[5] [6] [7] 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.[8] 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[9] and is robust in the presence of various inter-band couplings such as interband Josephson coupling.[10] [11] In 2014, experimental study suggested that Sr2RuO4 is type-1.5 superconductor.[12]
Type-I and type-II superconductors feature dramatically different charge flow patterns. Type-I superconductors have two state-defining properties: The lack of electric resistance and the fact that they do not allow an external magnetic field to pass through them. 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 to cancel the interior magnetic field, similar to how typical conductors cancel interior electric fields with surface charge distributions. An externally applied magnetic field of sufficiently low strength is cancelled in the interior of a type-I superconductor by the field produced by the surface current. In type-II superconducting materials, however, a complicated flow of superconducting electrons can form deep in the interior of the material. In a type-II material, magnetic fields can penetrate into the interior, carried inside by vortices that form an Abrikosov vortex lattice.
In type-1.5 superconductors, there are at least two superconducting components. In such materials, 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.[13]
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]
Animations from numerical calculations of vortex cluster formation are available at ""