Numerical study of the properties of a holographic superconductor from an anti-de Sitter-Einstein-Born-Infeld black hole with backreaction

TL;DR

This paper numerically investigates how backreaction and nonlinearity influence the properties of holographic superconductors within an anti-de Sitter-Einstein-Born-Infeld black hole framework, revealing complex effects on condensation and conductivity.

Contribution

It provides a non-perturbative analysis of backreaction and Born-Infeld nonlinearity effects on holographic superconductor properties, including condensation, conductivity, and superfluid density.

Findings

Increasing nonlinearity hinders condensate formation at small backreaction.

At high backreaction, nonlinearity facilitates condensate formation.

Deviations from the universal gap ratio increase with backreaction.

Abstract

We study numerically an $s$-wave holographic superconductor from an anti-de Sitter-Einstein-Born-Infeld black hole with backreaction in the context of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. By introducing a parameter $G$ to tune the effects of the backreaction, we can study non-perturbatively how the condensation and conductivity of the superconductor change as the backreaction increases. We find that for small values of $G$, increasing the nonlinearity of the Born-Infeld model makes the formation of the condensate harder -- consistent with previous results reported in the literature -- while for values of $G$ close to one, the opposite effect occurs; increasing the nonlinearity slightly facilitates its formation. This result is confirmed by making similar studies for the electrical conductivity of the superconductor and the penetration depth of the Meissner effect. Moreover, we analize in detail the superfluid density in these systems. We also determine how the ratio $\omega_g/T_c$ varies for different intensities of nonlinearity and backreaction, showing in particular that large deviations from the so-called universal value arise as backreaction becomes stronger.