Paraconductivity of pseudogapped superconductors

TL;DR

This paper calculates the paraconductivity in strongly disordered pseudogapped superconductors, revealing how fluctuations and inhomogeneities affect conductivity beyond classical models.

Contribution

It extends the Aslamazov-Larkin theory to disordered superconductors with large pseudogaps, identifying fluctuation regimes and their impact on conductivity.

Findings

Paraconductivity is twice the classical AL result in Gaussian approximation.

Local pairing fluctuations dominate at a certain scale, violating Gaussian approximation.

Conductivity becomes inhomogeneous at low temperatures due to strong fluctuations.

Abstract

We calculate Aslamazov-Larkin paraconductity $\sigma_{AL}(T)$ for a model of strongly disordered superconductors (dimensions $d=2,3$) with a large pseudogap whose magnitude strongly exceeds transition temperature $T_c$. We show that, within Gaussian approximation over Cooper-pair fluctuations, paraconductivity is just twice larger that the classical AL result at the same $\epsilon = (T-T_c)/T_c$. Upon decreasing $\epsilon$, Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at $\epsilon \leq \epsilon_1 \ll 1 $. Characteristic scale $\epsilon_1 $ is much larger than the width $\epsilon_2$ of the thermodynamical critical region, that is determined via the Ginzburg criterion, $\epsilon_2 \approx \epsilon_1^d$. We argue that in the intermediate region $\epsilon_2 \leq \epsilon \leq \epsilon_1$ paraconductivity follows the same AL power law, albeit with another (yet unknown) numerical prefactor. At further decrease of the temperature, all kinds of fluctuational corrections become strong at $\epsilon \leq \epsilon_2$; in particular, conductivity occurs to be strongly inhomogeneous in real space.