Superconducting fluctuations at arbitrary disorder strength

TL;DR

This paper derives a comprehensive expression for superconducting fluctuation corrections to conductivity across all disorder regimes, clarifying the interplay of different diagrammatic contributions and their behavior near and far from the transition.

Contribution

It provides a unified diagrammatic analysis of superconducting fluctuations applicable at arbitrary disorder levels, extending previous results and clarifying the cancellation of diagrammatic contributions.

Findings

In the diffusive limit, results match recent Keldysh calculations.

Near the transition, no divergent $(T\tau)^2$ term appears in the ballistic limit.

Far above the transition, conductivity correction scales roughly as $T\tau$.

Abstract

We study the effect of superconducting fluctuations on the conductivity of metals at arbitrary temperatures $T$ and impurity scattering rates $\tau^{-1}$. Using the standard diagrammatic technique but in the Keldysh representation, we derive the general expression for the fluctuation correction to the dc conductivity applicable for any space dimensionality and analyze it the case of the film geometry. We observe that the usual classification in terms of the Aslamazov-Larkin, Maki-Thompson and density-of-states diagrams is to some extent artificial since these contributions produce similar terms, which partially cancel each other. In the diffusive limit, our results fully coincide with recent calculations in the Keldysh technique. In the ballistic limit near the transition, we demonstrate the absence of a divergent term $(T\tau)^2$ attributed previously to the density-of-states contribution. In the ballistic limit far above the transition, the temperature-dependent part of the conductivity correction is shown to scale roughly as $T\tau$.