The Holographic Disorder-Driven Superconductor-Metal Transition

TL;DR

This paper investigates how disorder affects a holographic superconductor, revealing a transition to a metal with unique conductivity features and a non-mean-field order parameter behavior near the critical point.

Contribution

It introduces a model of disorder in holographic superconductors and uncovers novel disorder-driven transition characteristics and spectral signatures.

Findings

Disorder induces island formation and a transition to metallic behavior.

Conductivity features are explained via hydrodynamic quasi-normal modes.

Order parameter exhibits non-mean-field behavior near the transition.

Abstract

We implement the effects of disorder on a holographic superconductor by introducing a random chemical potential on the boundary. We demonstrate explicitly that increasing disorder leads to the formation of islands where the superconducting order is enhanced and subsequently to the transition to a metal. We study the behavior of the superfluid density and of the conductivity as a function of the strength of disorder. We find explanations for various marked features in the conductivities in terms of hydrodynamic quasi-normal modes of the holographic superconductors. These identifications plus a particular disorder-dependent spectral weight shift in the conductivity point to a signature of the Higgs mode in the context of disordered holographic superconductors. We observe that the behavior of the order parameter close to the transition is not mean-field type as in the clean case, rather we find robust agreement with $\exp(- A\, |T-T_c|^{-\nu})$, with $\nu =1.03\pm 0.02 $ for this disorder-driven smeared transition.