Hydrodynamics and Nonlocal Conductivities in Vortex States

TL;DR

This paper develops a hydrodynamical framework for vortex states in type II superconductors, analyzing nonlocal conductivities via the Kubo formula, revealing directional dependencies and effects of vortex lattice freezing.

Contribution

It introduces a hydrodynamical model based on the time-dependent Ginzburg-Landau equation for vortex states, and examines nonlocal conductivities considering anisotropy and vortex lattice effects.

Findings

Nonlocal conductivities deviate from vortex flow expressions.

DC Hall conductivity becomes zero in the vortex lattice.

Nonlocality varies with direction relative to the magnetic field.

Abstract

A hydrodynamical description for vortex states in type II superconductors with no pinning is presented based on the time-dependent GL equation, and the nonlocal conductivities are examined in terms of Kubo formula. Typically, the nonlocal conductivities deviate from the usual vortex flow expressions as the nonlocality parallel to the field becomes weaker than that perpendicular to the field associated with the freezing to the vortex lattice, and, for instance, the dc Hall conductivity nonlocal only in directions perpendicular to the field becomes zero in the vortex lattice due to its infinite shear viscosity. Various situations are discussed on the basis of the resulting expressions.