Superconducting coherence length and magnetic penetration depth of a p-wave holographic superconductor

A classical SU(2) Einstein-Yang-Mills theory in (3 + 1)- dimensional anti-de Sitter spacetime is believed to be dual to a p-wave superconductor in (2 + 1)- dimensional flat spacetime. In order to calculate the superconducting coherence length xi of the holographic superconductor near the superconducting phase transition point, we make a perturbative study of the gravity theory analytically. The superconducting coherence length xi is found to be proportional to (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 Ginzburg-Landau theory.