Analytical study on holographic superconductors in external magnetic field

TL;DR

This paper analytically studies holographic superconductors in external magnetic fields, revealing critical magnetic field behavior, the Meissner effect, and the influence of Gauss-Bonnet coupling on condensation in higher dimensions.

Contribution

It provides an analytical framework for understanding magnetic effects on holographic superconductors, including the critical field and Gauss-Bonnet coupling influence, extending previous numerical studies.

Findings

Critical magnetic field follows Ginzburg-Landau relation.

Magnetic field expels condensate, indicating Meissner effect.

Negative Gauss-Bonnet coupling enhances condensation under weak magnetic fields.

Abstract

We investigate the holographic superconductors immersed in an external magnetic field by using the analytical approach. We obtain the spatially dependent condensate solutions in the presence of the magnetism and find analytically that the upper critical magnetic field satisfies the relation given in the Ginzburg-Landau theory. We observe analytically the reminiscent of the Meissner effect where the magnetic field expels the condensate. Extending to the D-dimensional Gauss-Bonnet AdS black holes, we examine the influence given by the Gauss-Bonnet coupling on the condensation. Different from the positive coupling, we find that the negative Gauss-Bonnet coupling enhances the condensation when the external magnetism is not strong enough.