Suppression of superconductivity due to non-perturbative saddle points in the nonlinear $\sigma$-model

TL;DR

This paper investigates how non-perturbative saddle point fluctuations in the nonlinear sigma-model lead to superconductivity suppression and finite resistivity in disordered wires, revealing effects beyond traditional Ginzburg-Landau theory.

Contribution

It identifies a new type of thermal fluctuation, described by saddle points in the nonlinear sigma-model, that causes resistivity in superconducting wires beyond phase slips.

Findings

Fluctuations described by saddle points cause finite resistivity.

The contribution to resistivity is evaluated with exponential accuracy.

Magnetoresistance due to these fluctuations is negative.

Abstract

We study superconductivity suppression due to thermal fluctuations in disordered wires using the replica nonlinear $\sigma$-model ($NL\sigma M$). We show that in addition to the thermal phase slips there is another type of fluctuations that result in a finite resistivity. These fluctuations are described by saddle points in $NL\sigma M$ and cannot be treated within the Ginzburg-Landau approach. The contribution of such fluctuations to the wire resistivity is evaluated with exponential accuracy. The magnetoresistance associated with this contribution is negative.