The Rich Structure of Gauss-Bonnet Holographic Superconductors

TL;DR

This paper investigates Gauss-Bonnet holographic superconductors in five dimensions, analyzing how backreaction, scalar mass, and coupling constant influence critical temperature, zero-temperature solutions, and conductivity properties.

Contribution

It provides a comprehensive analysis of backreaction effects, scalar mass dependence, and the zero-temperature limit in Gauss-Bonnet holographic superconductors, including new constraints and behaviors.

Findings

Backreaction increases critical temperature near the BF bound when $\alpha ightarrow L^2/4$.

Reducing $\alpha$ below zero raises the critical temperature and diminishes backreaction effects.

Zero temperature solutions are constrained; regular solutions with tachyonic scalars are not permitted.

Abstract

We study fully backreacting, Gauss-Bonnet (GB) holographic superconductors in 5 bulk spacetime dimensions. We explore the system's dependence on the scalar mass for both positive and negative GB coupling, $\alpha$. We find that when the mass approaches the Breitenlohner-Freedman (BF) bound and $\alpha\rightarrow L^2/4$ the effect of backreaction is to increase the critical temperature, $T_c$, of the system: the opposite of its effect in the rest of parameter space. We also find that reducing $\alpha$ below zero increases $T_c$ and that the effect of backreaction is diminished. We study the zero temperature limit, proving that this system does not permit regular solutions for a non-trivial, tachyonic scalar field and constrain possible solutions for fields with positive masses. We investigate singular, zero temperature solutions in the Einstein limit but find them to be incompatible with the concept of GB gravity being a perturbative expansion of Einstein gravity. We study the conductivity of the system, finding that the inclusion of backreaction hinders the development of poles in the conductivity that are associated with quasi-normal modes approaching the real axis from elsewhere in the complex plane.