# Holographic Superconductors with Higher Curvature Corrections

## TL;DR

This paper investigates how higher curvature corrections in Einstein-Gauss-Bonnet gravity influence (3+1)-dimensional holographic superconductors, revealing that such corrections hinder condensation and alter conductivity properties.

## Contribution

It provides the first analytical proof and approximation method for the impact of higher curvature corrections on holographic superconductor phase transitions.

## Key findings

- Higher curvature corrections make superconducting condensation more difficult.
- The universal conductivity ratio $g / T_c    is not stable under these corrections.
- The analytical method also explains (2+1)-dimensional superconductors.

## Abstract

We study (3+1)-dimensional holographic superconductors in Einstein-Gauss-Bonnet gravity both numerically and analytically. It is found that higher curvature corrections make condensation harder. We give an analytic proof of this result, and directly demonstrate an analytic approximation method that explains the qualitative features of superconductors as well as giving quantitatively good numerical results. We also calculate conductivity and $\omega_g / T_c $, for $\omega_g$ and $T_c$ the gap in the frequency dependent conductivity and the critical temperature respectively. It turns out that the `universal' behaviour of conductivity, $\omega_g / T_c \simeq 8$, is not stable to the higher curvature corrections. In the appendix, for completeness, we show our analytic method can also explain (2+1)-dimensional superconductors.