Relaxed superconductors

TL;DR

This paper investigates holographic models with momentum relaxation to understand superconductivity, revealing how finite DC conductivity transitions to superfluid behavior and how low-frequency optical conductivity can be modeled by a two-fluid system.

Contribution

It introduces and analyzes two holographic models with momentum relaxation, demonstrating their thermodynamic relevance and detailed conductivity behavior in the superconducting phase.

Findings

Normal phase exhibits finite DC conductivity.

Broken phase shows a superfluid pole replacing DC conductivity.

Low-frequency optical conductivity can be modeled by a two-fluid system.

Abstract

Momentum relaxation can be built into many holographic models without sacrificing homogeneity of the bulk solution. In this paper we study two such models: one in which translational invariance is broken in the dual theory by spatially-dependent sources for massless scalar fields and another that features an additional neutral scalar field. We turn on a charged scalar field in order to explore the condensation of a charged scalar operator in the dual theories. After demonstrating that the relaxed superconductors we construct are thermodynamically relevant, we find that the finite DC electrical conductivity of the normal phase is replaced by a superfluid pole in the broken phase. Moreover, when the normal phase possesses a Drude behaviour at low frequencies, the optical conductivity of the broken phase at low frequencies can be described by a two-fluid model that is a sum of a Drude peak and a superfluid pole, as was found recently for inhomogeneous holographic superconductors. We also study cases in which this low-frequency behavior does not hold. We find that the Drude description is accurate when the retarded current-current correlator has a purely-dissipative pole that is well-separated from the rest of the excitations.