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

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 $\ensuremath{\kappa}$. The model was generalized by Ginzburg for anisotropic materials in 1952. In this paper we expand the above length-scale analysis to anisotropic multicomponent superconductors that can have multiple coherence lengths as well as multiple magnetic-field penetration lengths, leading to unconventional length-scale hierarchies. We demonstrate that the anisotropies in multiband superconductors lead 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, whereas the penetration lengths are larger in the other direction. Focusing on a model of a clean anisotropic multiband $s$-wave supercocoductors we show exampes of a new regime where vortex cores overlap in one direction, resulting in attractive core-core interaction, while in the orthogonal direction the magnetic-field penetration length exceeds the coherence lengths, leading to dominance of repulsive current-current interaction, resulting in an unconventional magnetic response.