Characteristic length of an AdS/CFT superconductor

We investigate in more detail the holographic model of a superconductor recently found by Hartnoll, Herzog, and Horowitz, which is constructed from a condensate of a charged scalar field in AdS4-Schwarzschild background. By analytically studying the perturbation of the gravitational system near the critical temperature Tc, we obtain the superconducting coherence length proportional to 1/1-T/Tc via AdS/CFT (anti-de Sitter/conformal field theory) correspondence. By adding a small external homogeneous magnetic field to the system, we find that a stationary diamagnetic current proportional to the square of the order parameter is induced by the magnetic field. These results agree with Ginzburg-Landau theory and strongly support the idea that a superconductor can be described by a charged scalar field on a black hole via AdS/CFT duality.