Keldysh Ginzburg-Landau action of fluctuating superconductors

TL;DR

This paper derives a comprehensive Ginzburg-Landau action for fluctuating superconductors using the Keldysh nonlinear sigma-model, revealing nonlocal effects, gauge invariance, and potential for calculating current fluctuation moments.

Contribution

It introduces a systematic derivation of the Ginzburg-Landau functional incorporating nonlocal and anomalous couplings within the Keldysh framework for disordered superconductors.

Findings

Includes nonlocal $ riangle$-dependent diffusion constant effects.

Reveals anomalous Gor'kov-Eliashberg coupling.

Ensures gauge invariance and fluctuation dissipation compliance.

Abstract

We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $\Delta$-dependent contribution to the diffusion constant, which leads, for example, to Maki-Thompson corrections. It also exhibits an anomalous Gor'kov-Eliashberg coupling between $\Delta$ and the scalar potential, as well as a peculiar nonlocal nonlinear term. The action is gauge invariant and satisfies the fluctuation dissipation theorem. It may be employed e.g. for calculation of higher moments of the current fluctuations.