Analytic study of Gauss-Bonnet holographic superconductors in Born-Infeld electrodynamics

TL;DR

This paper analytically studies how Gauss-Bonnet gravity and Born-Infeld electrodynamics influence holographic s-wave superconductors, revealing effects on scalar hair formation and confirming universal critical behavior.

Contribution

It provides an analytic approach using Sturm-Liouville eigenvalue problem to explore properties of holographic superconductors with Gauss-Bonnet and Born-Infeld corrections, aligning well with numerical results.

Findings

Scalar hair formation is affected by Gauss-Bonnet and Born-Infeld parameters.

Critical exponent indicates universal mean field behavior.

Analytic results agree with numerical simulations.

Abstract

Using Sturm-Liouville (SL) eigenvalue problem, we investigate several properties of holographic s-wave superconductors in Gauss-Bonnet gravity with Born-Infeld electrodynamics in the probe limit. Our analytic scheme has been found to be in good agreement with the numerical results. From our analysis it is quite evident that the scalar hair formation at low temperatures is indeed affected by both the Gauss-Bonnet as well as the Born-Infeld coupling parameters. We also compute the critical exponent associated with the condensation near the critical temperature. The value of the critical exponent thus obtained indeed suggests a universal mean field behavior.