Characteristic length of a holographic superconductor withd-wave gap

Abstract

After the discovery of the $s$-wave and $p$-wave holographic superconductors, holographic models of the $d$-wave superconductor have also been constructed recently. We study analytically the perturbation of the dual gravity theory to calculate the superconducting coherence length $\ensuremath{\xi}$ of the $d$-wave holographic superconductor near the superconducting phase transition point. The superconducting coherence length $\ensuremath{\xi}$ diverges as $(1\ensuremath{-}T/{T}_{c}{)}^{\ensuremath{-}1/2}$ near the critical temperature ${T}_{c}$. We also obtain the magnetic penetration depth $\ensuremath{\lambda}\ensuremath{\propto}({T}_{c}\ensuremath{-}T{)}^{\ensuremath{-}1/2}$ 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.