Exponential nonlinear electrodynamics and backreaction effects on Holographic superconductor in the Lifshitz black hole background

TL;DR

This paper analytically investigates how exponential nonlinear electrodynamics and Lifshitz dynamical exponent influence the properties of holographic superconductors, revealing that increased nonlinearity and z hinder condensation and lower critical magnetic fields.

Contribution

It provides an analytical study of holographic superconductors with exponential nonlinear electrodynamics in Lifshitz backgrounds, including effects of backreaction and magnetic fields.

Findings

Critical temperature decreases with increasing nonlinearity and z.

Backreaction significantly affects critical temperature at small z.

Critical magnetic field diminishes as z increases, vanishing at T_c.

Abstract

We analytically describe the properties of the s-wave holographic superconductor with the Exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm-Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. Also we find that the effects of backreaction has a more important role on the critical temperature and condensation operator in small values of Lifshitz dynamical exponent, while z is around one. In addition, the properties of the upper critical magnetic field in Lifshitz black hole background using Sturm-Liouville approach is investigated to describe the phase diagram of the corresponding holographic superconductor in the prob limit. We observe that the critical magnetic field decreases with increasing Lifshitz dynamical exponent, z, and it goes to zero at critical temperature, independent of the Lifshitz dynamical exponent, z.