Analytical Studies on Holographic Superconductors in Gauss-Bonnet Gravity

TL;DR

This paper analytically investigates holographic superconductors within Gauss-Bonnet gravity, revealing universal critical exponents and the impact of Gauss-Bonnet coefficients on condensation, aligning with numerical findings.

Contribution

It provides an analytical approach to study properties of holographic superconductors with Gauss-Bonnet gravity, extending understanding of phase transitions in these models.

Findings

Critical exponent of 1/2 near the critical temperature

Higher Gauss-Bonnet coefficients hinder boundary operator condensation

Results agree with previous numerical studies

Abstract

We use the variational method for the Sturm-Liouville eigenvalue problem to analytically calculate some properties of holographic superconductors with Gauss-Bonnet gravity in probe limit. By studying the holographic p-wave and s-wave superconductors in (3+1)-dimensional boundary field theories, it is found that near the critical temperature, the critical exponent of the condensation is 1/2 which is the universal value in mean-field theory. We also find that when Gauss-Bonnet coefficients grow bigger the operators on the boundary field theory will be harder to condense. These are in good agreement with the numerical results.