  We investigate in more detail the holographic model of a superconductor
recently found by Hartnoll, Herzog, and Horowitz [Phys. Rev. Lett. 101,
031601], which is constructed from a condensate of a charged scalar field in
AdS_4-Schwarzschild background. By analytically studying the perturbation of
the gravitational system near the critical temperature T_c, we obtain the
superconducting coherence length proportional to 1/\sqrt{1-T/T_c} via AdS/CFT
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.
