Mismatch of conductivity anisotropy in the mixed and normal states of type-II superconductors

TL;DR

This paper investigates the vortex viscosity in anisotropic superconductors with mismatched normal and superconducting anisotropies using TDGL theory, deriving asymptotics and a variational method, and showing temperature dependence of anisotropy.

Contribution

It introduces a variational approach for calculating vortex viscosity in anisotropic superconductors with arbitrary characteristic ratios, extending previous models.

Findings

Derived asymptotics for small and large electric field penetration depths.

Proposed a variational procedure for arbitrary ratios of coherence length to penetration depth.

Showed that viscosity and flux-flow conductivity anisotropy depend on temperature.

Abstract

We have calculated the Bardeen-Stephen contribution to the vortex viscosity for uniaxial anisotropic superconductors within the time-dependent Ginzburg-Landau (TDGL) theory. We focus our attention on superconductors with a mismatch of anisotropy of normal and superconducting characteristics. Exact asymptotics for the Bardeen-Stephen contribution have been derived in two limits: the cases of small and large electric field penetration depth (as compared to the coherence length). Also we suggest a variational procedure which allows us to calculate the vortex viscosity for superconductors with arbitrary ratio of the coherence lenght to the electric field penetration depth. The approximate analytical result is compared with numerical calculations. Finally, using a generalized TDGL theory, we prove that the viscosity anisotropy and, thus, the flux-flow conductivity anisotropy may depend on temperature.