Paraconductivity of pseudogapped superconductors

Abstract

We calculate Aslamazov-Larkin paraconductity $σ_{AL}(T)$ 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 $ε= (T-T_c)/T_c$. Upon decreasing $ε$, Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at $ε\leq ε_1 \ll 1 $. Characteristic scale $ε_1 $ is much larger than the width $ε_2$ of the thermodynamical critical region, that is determined via the Ginzburg criterion, $ε_2 \approx ε_1^d$. We argue that in the intermediate region $ε_2 \leq ε\leq ε_1$ 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 $ε\leq ε_2$; in particular, conductivity occurs to be strongly inhomogeneous in real space.