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

Understand

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.