A Dirty Holographic Superconductor

TL;DR

This paper investigates how disorder introduced via a random chemical potential affects a holographic superconductor, revealing that disorder can enhance critical temperature and follows universal spectral renormalization laws.

Contribution

It demonstrates that disorder can increase the critical temperature in holographic superconductors and uncovers a universal power-law renormalization of spectral exponents.

Findings

Critical temperature is enhanced by disorder.

Spectra of condensate and charge density follow universal power-laws.

Spectral exponents are linearly related to disorder spectrum parameter.

Abstract

We study the effects of disorder on a holographic superconductor by introducing a random chemical potential on the boundary. We consider various realizations of disorder and find that the critical temperature for superconductivity is enhanced. We also present evidence for a precise form of renormalization in this system. Namely, when the random chemical potential is characterized by a Fourier spectrum of the form $k^{-2\alpha}$ we find that the spectra of the condensate and the charge density are again power-laws, whose exponents are accurately and universally governed by linear functions of $\alpha$.