The upper critical magnetic field of holographic superconductor with conformally invariant power-Maxwell electrodynamics

TL;DR

This paper investigates the upper critical magnetic field of a holographic superconductor with conformally invariant power-Maxwell electrodynamics, revealing how the phase behavior depends on the power exponent and dimensionality.

Contribution

It introduces a study of holographic superconductors with power-Maxwell fields, emphasizing the conformal invariance condition and analyzing the critical magnetic field in various dimensions.

Findings

Critical temperature depends on charge density, dimension, and power exponent.

Conformal invariance occurs at q=d/4, affecting phase behavior.

In 5D, the critical magnetic field differs from the Maxwell case.

Abstract

The properties of $(d-1)$-dimensional $s$-wave holographic superconductor in the presence of power-Maxwell field is explored. We study the probe limit in which the scalar and gauge fields do not backreact on the background geometry. Our study is based on the matching of solutions on the boundary and on the horizon at some intermediate point. At first, the case without external magnetic field is considered, and the critical temperature is obtained in terms of the charge density, the dimensionality, and the power-Maxwell exponent. Then, a magnetic field is turned on in the $d$-dimensional bulk which can influence the $(d-1)$-dimensional holographic superconductor at the boundary. The phase behavior of the corresponding holographic superconductor is obtained by computing the upper critical magnetic field in the presence of power-Maxwell electrodynamics, characterized by the power exponent $q$. Interestingly, it is observed that in the presence of magnetic field, the physically acceptable phase behavior of the holographic superconductor is obtained for $q={d}/{4}$, which guaranties the conformal invariance of the power-Maxwell Lagrangian. The case of physical interest in five spacetime dimensions ($d=5$, and $q=5/4$) is considered in detail, and compared with the results obtained for the usual Maxwell electrodynamics $q=1$ in the same dimensions.