Ginzburg-Landau equations with consistent Langevin terms for nonuniform wires

TL;DR

This paper develops a statistically consistent Ginzburg-Landau model with Langevin terms for nonuniform superconducting wires, enabling accurate fluctuation analysis and application to paraconductivity and phase slip phenomena.

Contribution

It introduces a gauge-invariant, numerically stable method to incorporate thermal fluctuations into Ginzburg-Landau equations, consistent with statistical mechanics.

Findings

Method accurately reproduces fluctuation effects in superconducting wires.

Paraconductivity results align with Aslamazov-Larkin theory.

Constrictions influence phase slip behavior, but no thermally activated slips observed.

Abstract

Many analyses based on the time-dependent Ginzburg--Landau model are not consistent with statistical mechanics, because thermal fluctuations are not taken correctly into account. We use the fluctuation-dissipation theorem in order to establish the appropriate size of the Langevin terms, and thus ensure the required consistency. Fluctuations of the electromagnetic potential are essential, even when we evaluate quantities that do not depend directly on it. Our method can be cast in gauge-invariant form. We perform numerous tests, and all the results are in agreement with statistical mechanics. We apply our method to evaluate paraconductivity of a superconducting wire. The Aslamazov--Larkin result is recovered as a limiting situation. Our method is numerically stable and the nonlinear term is easily included. We attempt a comparison between our numerical results and the available experimental data. Within an appropriate range of currents, phase slips occur, but we found no evidence for thermally activated phase slips. We studied the behavior of a moderate constriction. A constriction pins and enhances the occurrence of phase slips.