Perturbative studies of the conductivity in the vortex-liquid regime

TL;DR

This paper computes the Aslamazov-Larkin conductivity correction in a vortex-liquid under magnetic field using perturbative methods, exploring local and nonlocal responses, and effects of weak disorder.

Contribution

It introduces two approaches to calculate conductivity perturbatively, including a flux-flow formula valid to all orders and analysis of nonlocal effects and disorder impacts.

Findings

Flux-flow formula holds to all orders of perturbation.

Nonlocal conductivities show cancellations and precursors to viscous length scales.

Weak disorder effects are analyzed on conductivity responses.

Abstract

We calculate the Aslamazov-Larkin term of the conductivity in the presence of a magnetic field applied along the c-axis from the time-dependent Ginzburg-Landau equation perturbatively using two approaches. In the first a uniform electric field is explicitly applied; in the second the Kubo formula is used to extract the linear response. The former yields a version of the flux-flow formula for the uniform ab-plane conductivity, sigma_{xx}(k=0), that holds to all orders of perturbation theory. Obtaining the same result from the Kubo formula requires considerable cancellation of terms. We also use the Kubo calculation to examine the nonlocal ab-plane conductivity, sigma_{xx}( k \neq 0) (where the cancellations no longer occur), as well as the nonlocal c-axis conductivity sigma_{zz}( k \neq 0), and look for the perturbative precursors of the growing viscous length scales. In addition, we consider the effects of weak disorder -- both uncorrelated (point defects) and correlated (columnar and planar defects).