Holographic Superconductors with Power-Maxwell field

TL;DR

This paper explores holographic superconductors with a Power-Maxwell field, analyzing how the power parameter affects scalar condensation and demonstrating a universal critical exponent of 1/2 across different nonlinear electrodynamics.

Contribution

It introduces a complex charged scalar field coupled with Power-Maxwell electrodynamics in a Schwarzschild AdS black hole background, revealing new asymptotic behaviors and universal critical properties.

Findings

Larger power parameter q hinders scalar hair condensation.

Critical exponent remains 1/2 for various q values.

Power-Maxwell field exhibits unique asymptotic solutions near boundary.

Abstract

With the Sturm-Liouville analytical and numerical methods, we investigate the behaviors of the holographic superconductors by introducing a complex charged scalar field coupled with a Power-Maxwell field in the background of $d$-dimensional Schwarzschild AdS black hole. We note that the Power-Maxwell field takes the special asymptotical solution near boundary which is different from all known cases. We find that the larger power parameter $q$ for the Power-Maxwell field makes it harder for the scalar hair to be condensated. We also find that, for different $q$, the critical exponent of the system is still 1/2, which seems to be an universal property for various nonlinear electrodynamics if the scalar field takes the form of this paper.