Characteristic length of a Holographic Superconductor with $d$-wave gap

TL;DR

This paper analytically calculates the characteristic length scales, coherence length and magnetic penetration depth, of a $d$-wave holographic superconductor near the critical temperature, showing they diverge with the same critical exponent as in Ginzburg-Landau theory.

Contribution

It provides an analytical derivation of the coherence length and penetration depth for $d$-wave holographic superconductors, extending previous models to include $d$-wave symmetry.

Findings

Coherence length diverges as (1-T/T_c)^(-1/2) near T_c

Magnetic penetration depth scales as (T_c - T)^(-1/2)

Results agree with Ginzburg-Landau theory and previous $s$- and $p$-wave models

Abstract

After the discovery of the $s$-wave and $p$-wave holographic superconductors, holographic models of $d$-wave superconductor have also been constructed recently. We study analytically the perturbation of the dual gravity theory to calculate the superconducting coherence length $\xi$ of the $d$-wave holographic superconductor near the superconducting phase transition point. The superconducting coherence length $\xi$ divergents as $(1-T/T_c)^{-1/2}$ near the critical temperature $T_c$. We also obtain the magnetic penetration depth $\lambda\propto(T_c-T)^{-1/2}$ by adding a small external homogeneous magnetic field. The results agree with the $s$-wave and $p$-wave models, which are also the same as the Ginzburg-Landau theory.