Effects of backreaction and exponential nonlinear electrodynamics on the holographic superconductors

TL;DR

This paper analytically investigates how exponential nonlinear electrodynamics and backreaction influence the properties and phase transition behavior of a (2+1)-dimensional holographic superconductor, revealing that these effects make scalar condensation more difficult but preserve the second-order transition with mean-field critical exponent.

Contribution

It provides an analytical study of the combined effects of exponential nonlinear electrodynamics and backreaction on holographic superconductors, highlighting their impact on critical temperature and phase transition.

Findings

Nonlinear electrodynamics affects superconductor properties.

Backreaction makes scalar condensation harder.

Phase transition remains second order with mean-field exponent.

Abstract

We analytically study the properties of a $(2+1)$-dimensional $s$-wave holographic superconductor in the presence of exponential nonlinear electrodynamics. We consider the case in which the scalar and gauge fields back react on the background metric. Employing the analytical Sturm-Liouville method, we find that in the black hole background, the nonlinear electrodynamics correction will affect the properties of the holographic superconductors. We find that with increasing both backreaction and nonlinear parameters, the scalar hair condensation on the boundary will develop more difficult. We obtain the relation connecting the critical temperature with the charge density. Our analytical results support that, even in the presence of the nonlinear electrodynamics and backreaction, the phase transition for the holographic superconductor still belongs to the second order and the critical exponent of the system always takes the mean-field value $1/2$.