Higher dimensional holographic superconductors in Born–Infeld electrodynamics with back-reaction

Debabrata Ghorai,Sunandan Gangopadhyay

doi:10.1140/epjc/s10052-016-4005-0

Abstract

In this paper, we analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born-Infeld electrodynamics taking into account the backreaction of the spacetime using the Sturm-Liouville eigenvalue method. In the background of pure Einstein and Gauss-Bonnet gravity, based on a perturbative approach, we obtain the relation between the critical temperature and the charge density. Higher value of the backreaction and Born-Infeld parameters result in a harder condensation to form in both cases. The analytical results are found to agree with the existing numerical results. We also derive an expression for the condensation operator in $d$-dimensions which yields the critical exponent to be $1/2$.

Highlights

It is well known that weakly coupled superconductors can be described with great accuracy by the BCS theory of superconductivity [1], which is based on the fact that the interaction between electrons resulting from the virtual exchange of phonons is attractive when the energy difference between the states of the electrons is less than the energy of the phonon
We study the relation between the critical temperature and the charge density taking into account the effect of the Gauss–Bonnet coupling parameter α
We have analytically calculated the relation between the critical temperature and the charge density of higher dimensional holographic superconductors in the framework of Born–Infeld electrodynamics taking into account the effect of back-reaction of the matter fields on the spacetime metric

Summary

Introduction

It is well known that weakly coupled superconductors can be described with great accuracy by the BCS theory of superconductivity [1], which is based on the fact that the interaction between electrons resulting from the virtual exchange of phonons is attractive when the energy difference between the states of the electrons is less than the energy of the phonon. In [16,32] analytical studies in GB gravity have been carried out using the matching as well as the SL method thereby revealing that higher curvature corrections make the formation of the scalar hair harder These studies are based on the probe limit which neglects the back-reactions of matter fields on the spacetime metric [38,39,40,41,42]. 3, taking into account the effect of the Born–Infeld electrodynamics and the back-reaction of the matter fields on the spacetime metric in Einstein and Gauss–Bonnet gravity, we compute the critical temperature in terms of a solution to the Sturm–Liouville eigenvalue problem.

Basic formalism

Back-reaction effect in Einstein gravity

Back-reaction effect in Gauss–Bonnet gravity

Condensation values and critical exponent

Conclusions