AC Conductivity Crossover in Localized Superconductors

TL;DR

This paper investigates the low-frequency AC conductivity in localized superconductors, revealing that the conductivity exponent can exceed 2 and exhibits temperature-dependent crossover, providing new insights into localization phenomena in superconducting systems.

Contribution

It introduces the study of AC conductivity in localized superconductors, showing the exponent can surpass 2 and identifying temperature-dependent crossover behavior.

Findings

AC conductivity exponent can be greater than 2 in certain symmetry classes.

Temperature influences the scaling form of AC conductivity.

Provides a potential experimental signature for localized superconductors.

Abstract

An important experimental signature of localization is the low-frequency AC conductivity, which typically vanishes as $\omega^{\phi}$. The exponent $\phi = 2$ for Anderson insulators, whereas for many body localized insulators $\phi$ is a continuously varying exponent $1 \le \phi \le 2$. In this work, we study the low-frequency AC conductivity of localized superconductors, in which disorder is strong enough to localize all quasiparticles, while remaining weak enough to leave superconductivity intact. We find that while the ac conductivity still follows the general form $\sigma(\omega) \sim \omega^{\phi}$, the exponent $\phi$ can be markedly different from the characteristic value for localized insulators. In particular, in certain symmetry classes at zero temperature, we obtain $\phi > 2$. We further identify an interesting temperature dependent crossover in the scaling form of the AC conductivity, which could be useful for the experimental characterization of localized superconductors.