Analytical and Numerical Study of Gauss-Bonnet Holographic Superconductors with Power-Maxwell Field

TL;DR

This paper combines analytical and numerical methods to study Gauss-Bonnet holographic superconductors with Power-Maxwell electrodynamics, revealing how the nonlinear electrodynamics parameter and Gauss-Bonnet term influence the critical temperature and phase transition.

Contribution

It introduces a comprehensive analysis of Power-Maxwell electrodynamics in Gauss-Bonnet holographic superconductors, highlighting how the nonlinear parameter affects critical temperature and phase transition properties.

Findings

Power-Maxwell electrodynamics can increase the critical temperature in the sublinear regime.

The gauge field power parameter q is restricted to 1/2<q<(d-1)/2 for finite boundary values.

The critical exponent remains universal at 1/2, independent of parameters.

Abstract

We provide an analytical as well as a numerical study of the holographic $s$-wave superconductors in Gauss-Bonnet gravity with Power-Maxwell electrodynamics. We limit our study to the case where scalar and gauge fields do not have an effect on the background metric. We use a variational method, based on Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. Interestingly enough, we observe that unlike Born-Infeld-like nonlinear electrodynamics which decrease the critical temperature compared to the linear Maxwell field, the Power-Maxwell electrodynamics is able to increase the critical temperature of the holographic superconductors in the sublinear regime. We find that requiring the finite value for the gauge field on the asymptotic boundary $r\rightarrow \infty$, restricts the power parameter, $q$, of the Power-Maxwell field to be in the range $1/2<q<{(d-1)}/{2}$. Our study indicates that it is quite possible to make condensation \emph{easier} as $q$ \emph{decreases} in its allowed range. We also find that for all values of $q$, the condensation can be affected by the Gauss-Bonnet coefficient $\alpha$. However, the presence of the Gauss-Bonnet term makes the transition slightly harder. Finally, we obtain an analytic expression for the order parameter and thus obtain the associated critical exponent near the phase transition. We find that the critical exponent has its universal value of $\beta=1/2$ regardless of the parameters $q$, $\alpha$ as well as dimension $d$, consistent with mean-field values obtained in previous studies.