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 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 xi of the d-wave holographic superconductor near the superconducting phase transition point. The superconducting coherence length xi diverges as (1 - T/T-c)(-1/2) near the critical temperature T-c. We also obtain the magnetic penetration depth lambda proportional to (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.