Type 1.5 superconductor

Detailed explanation

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. 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 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 oxypnictide 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 states of 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 and s + i s or between U ( 1 ) and U ( 1 ) × U ( 1 ) should rather generically fall into type-1.5 state near that transition due to divergence of one of the coherence lengths.

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 A  :

F = ∑ i , j = 1 , 2 1 2 m | ( ∇ − i e A ) ψ i | 2 + α i | ψ i | 2 + β i | ψ i | 4 + 1 2 ( ∇ × A ) 2

where ψ i = | ψ i | e i ϕ 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 λ = 1 e | ψ 1 | 2 + | ψ 2 | 2 and two coherence lengths ξ 1 = 1 2 α 1 , ξ 2 = 1 2 α 2 . The vortex excitations in that case have cores in both components which are co-centered because of electromagnetic coupling mediated by the field A . The necessary but not sufficient condition for occurrence of type-1.5 regime is ξ 1 > λ > ξ 2 . 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. 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. 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

F = ∑ i , j = 1 , 2 1 2 m | ( ∇ − i e A ) ψ i | 2 + α i | ψ i | 2 + β i | ψ i | 4 − η ( ψ 1 ψ 2 ∗ + ψ 1 ∗ ψ 2 ) + γ [ ( ∇ − i e A ) ψ 1 ⋅ ( ∇ + i e A ) ψ 2 ∗ + ( ∇ + i e A ) ψ 1 ∗ ⋅ ( ∇ − i e A ) ψ 2 ] + ν | ψ 1 | 2 | ψ 2 | 2 + 1 2 ( ∇ × A ) 2

where again ψ i = | ψ i | e i ϕ i , i = 1 , 2 are two superconducting condensates. In multiband superconductors quite generically η ≠ 0 , γ ≠ 0 . When η ≠ 0 , γ ≠ 0 , ν ≠ 0 three length scales of the problem are again the London penetration length and two coherence lengths. However, in this case the coherence lengths ξ ~ 1 ( α 1 , β 1 , α 2 , β 2 , η , γ , ν ) , ξ ~ 2 ( α 1 , β 1 , α 2 , β 2 , η , γ , ν ) are associated with "mixed" combinations of density fields.

Microscopic models

A microscopic theory of type-1.5 superconductivity has been reported.

Current experimental research

In 2009, experimental results have been reported 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 . 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 and is robust in the presence of various inter-band couplings such as interband Josephson coupling. In 2014 experimental study suggested that Sr2RuO4 is type-1.5 superconductor

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 at least 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.

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.