d-Wave holographic superconductors with backreaction in external magnetic fields

TL;DR

This paper investigates d-wave holographic superconductors under external magnetic fields, analyzing the effects of backreaction and magnetic fields on critical temperature and magnetic field limits through analytic and numerical methods.

Contribution

It provides a combined analytic and numerical study of magnetic field effects on d-wave holographic superconductors, including backreaction effects on critical parameters.

Findings

Upper critical magnetic field follows Ginzburg-Landau relation.

Critical temperature decreases with increasing magnetic and electric fields.

Backreaction reduces the critical temperature and modifies the upper critical magnetic field.

Abstract

We study the d-wave holographic superconductors (the d-wave model proposed in [arXiv:1003.2991[hep-th]]) immersed in constant external magnetic fields by using the analytic matching method and numerical computation. In the probe limit, we calculate the spatially dependent condensate solution in the presence of the magnetism and find that the expression for the upper critical magnetic field satisfies the relation given in the Ginzburg-Landau theory. The result shows that the upper critical field gradually increases to its maximum value $B_{c2}$ at absolute zero temperature T=0, while vanishing at the critical temperature $T=T_c$. Moving away from the probe limit, we investigate the effect of spacetime backreaction on the critical temperature and the upper critical magnetic field. The magnetic fields as well as the electric fields acting as gravitational sources reduce the critical temperature of the superconductor and actually result in a dyonic black hole solution to the leading order. We obtain the expression for the upper critical magnetic field up to $\mathcal{O}(\kappa^2)$ order. The analytic result is consistent with the numerical findings.