Analytic study of properties of holographic superconductors in Born-Infeld electrodynamics

TL;DR

This paper analytically examines how Born-Infeld electrodynamics influences the properties of holographic s-wave superconductors in Schwarzschild-AdS spacetime, revealing the impact of the coupling parameter on condensation and critical temperature.

Contribution

It provides an analytical study using Sturm-Liouville methods to explore the effects of Born-Infeld electrodynamics on holographic superconductors, complementing previous numerical findings.

Findings

Higher Born-Infeld parameter makes condensation harder to form.

Critical temperature decreases with increasing Born-Infeld coupling.

Critical exponent near transition matches numerical results.

Abstract

In this paper, based on the Sturm-Liouville eigenvalue problem, we analytically investigate several properties of holographic s-wave superconductors in the background of a Schwarzschild-AdS spacetime in the framework of Born-Infeld electrodynamics. Based on a perturbative approach, we explicitly find the relation between the critical temperature and the charge density and also the fact that the Born-Infeld coupling parameter indeed affects the formation of scalar hair at low temperatures. Higher value of the Born-Infeld parameter results in a harder condensation to form. We further compute the critical exponent associated with the condensation near the critical temperature. The analytical results obtained are found to be in good agreement with the existing numerical results.