Hydrodynamics of Holographic Superconductors

TL;DR

This paper investigates the spectral properties and collective excitations of a holographic superconductor, revealing the emergence of second sound, a pseudo diffusion mode, and analyzing their behavior across the phase transition.

Contribution

It provides a detailed analysis of quasinormal modes and Green functions in a holographic superconductor, including the calculation of second sound and diffusion modes, and explains methods for operators mixing under RG flow.

Findings

Identification of a second sound mode in the broken phase.

Calculation of second sound speed and attenuation length as functions of temperature.

Discovery of a pseudo diffusion mode with a gap that closes at the critical temperature.

Abstract

We study the poles of the retarded Green functions of a holographic superconductor. The model shows a second order phase transition where a charged scalar operator condenses and a U(1) symmetry is spontaneously broken. The poles of the holographic Green functions are the quasinormal modes in an AdS black hole background. We study the spectrum of quasinormal frequencies in the broken phase, where we establish the appearance of a massless or hydrodynamic mode at the critical temperature as expected for a second order phase transition. In the broken phase we find the pole representing second sound. We compute the speed of second sound and its attenuation length as function of the temperature. In addition we find a pseudo diffusion mode, whose frequencies are purely imaginary but with a non-zero gap at zero momentum. This gap goes to zero at the critical temperature. As a technical side result we explain how to calculate holographic Green functions and their quasinormal modes for a set of operators that mix under the RG flow.