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

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 $(1-T\mathrm{/}{T}_c{)}^{-1\mathrm{/}2}$ near the critical temperature $T_c$. We also obtain the magnetic penetration depth $\lambda \propto (T_c-T{)}^{-1\mathrm{/}2}$ 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.