Hierarchies of length-scale based typology in anisotropic U(1)s -wave multiband superconductors

Abstract

Since Ginzburg and Landau's seminal work in 1950 superconducting states have been classified by the hierarchy of the fundamental length scales of the theory; the magnetic field penetration lengths and coherence lengths. In the simplest single-component case they form a dimensionless ratio \kappa. As pointed out by Ginzburg in 1952, in general the ratio depends on the direction of the applied magnetic field due to material anisotropies. Single component materials can therefore display type-1 superconductivity when the field is applied in one direction and type-2 when the field is applied in a different direction. In this paper we expand the above length scale analysis to anisotropic multi-component superconductors, that can have multiple coherence lengths as well as multiple magnetic field penetration lengths, leading to unconvential length scale hierarchies. We demonstrate that the anisotropies in multi-band superconductors cannot in general be rescaled, leading to new regimes with various mixed hierarchies in different directions. For example, a regime is possible, where for a field applied in a certain direction coherence lengths are smaller than the magnetic field penetration lengths in one of the perpendicular directions, where as the penetration lengths are lager in the another direction. We demonstrate a new regime, where vortices form stripes in the direction where coherence lengths exceed the magnetic field penetration length and vortex cores overlap, while the vortex stripes repel each other in the orthogonal direction where the magnetic field penetration length exceeds the coherence lengths.