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

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.