Analytical study of holographic superconductor with backreaction in $4d$ Gauss-Bonnet gravity

TL;DR

This paper analytically explores how curvature corrections in four-dimensional Einstein-Gauss-Bonnet gravity influence holographic superconductors, focusing on critical temperature and condensation, and confirms findings with numerical results.

Contribution

It provides an analytical study of holographic superconductors with backreaction in 4D Einstein-Gauss-Bonnet gravity, revealing effects of curvature corrections on superconducting properties.

Findings

Critical temperature depends on Gauss-Bonnet coupling.

Condensation operator values are affected by curvature corrections.

Analytical results match numerical simulations.

Abstract

In this paper we have analytically investigated holographic superconductors in four dimensional Einstein-Gauss-Bonnet gravity background. Recently the novel four dimensional Einstein-Gauss-Bonnet gravity has been formulated by rescaling the Gauss-Bonnet coupling constant $\alpha\rightarrow \frac{\alpha}{d-4}$ and taking the limit $d\rightarrow 4$, and this predicts several interesting new features. To know the effect of the curvature correction on the $(2+1)$-dimensional superconductors, we have consider the $3+1$-dimensional Einstein-Gauss-Bonnet gravity. Using the Sturm-Liouville eigenvalue approach, the critical temperature and the condensation operator values has been investigated in this framework away from the probe limit. We recover the numerical results from our analytical investigation.