Analytical calculation on critical magnetic field in holographic superconductors with backreaction

TL;DR

This paper analytically examines how spacetime backreaction influences the critical magnetic field in holographic superconductors, revealing that backreaction enhances the upper critical magnetic field and depresses the critical temperature.

Contribution

It provides an analytical expression for the critical magnetic field considering backreaction effects, extending previous numerical and analytical studies.

Findings

Backreaction strengthens the upper critical magnetic field.

Backreaction depresses the critical temperature.

Analytical results align with previous numerical findings.

Abstract

We investigate the effect of spacetime backreaction on the upper critical magnetic field for s-wave holographic superconductors by using the matching method. The backreaction of the constant external magnetic field and the electric field to the background geometry leads to a dyonic black hole solution. The magnetic fields as well as the electric fields acting as gravitational sources tend to depress the critical temperature of the superconductor. We derive the analytical expression for the upper critical magnetic field up to $\mathcal{O}(\kappa^2)$ order and find that backreaction makes the upper critical magnetic field stronger. The result is consistent with the previous numerical and analytical results.