The gravity dual of a p-wave superconductor

TL;DR

This paper constructs and analyzes black hole solutions in AdS_4 that model p-wave superconductors, revealing anisotropic conductivities, gap structures, and stability properties near the transition temperature.

Contribution

It introduces new holographic p-wave superconductor models with anisotropic conductivities and studies their stability and excitation spectra.

Findings

Conductivities are strongly anisotropic, indicating a nodal gap structure.

Normal state excitations have relaxation times increasing as temperature decreases.

P-wave backgrounds are stable near the transition, while p+ip configurations are unstable.

Abstract

We construct black hole solutions to the Yang-Mills equations in an AdS_4-Schwarzschild background which exhibit superconductivity. What makes these backgrounds p-wave superconductors is that the order parameter is a vector, and the conductivities are strongly anisotropic in a manner that is suggestive of a gap with nodes. The low-lying excitations of the normal state have a relaxation time which grows rapidly as the temperature decreases, consistent with the absence of impurity scattering. A numerical exploration of quasinormal modes close to the transition temperature suggests that p-wave backgrounds are stable against perturbations analogous to turning on a p+ip gap, whereas p+ip-wave configurations are unstable against turning into pure p-wave backgrounds.