Abstract
We investigate in more detail the holographic model of a superconductor recently found by Hartnoll, Herzog, and Horowitz [Phys. Rev. Lett. 101, 031601 (2008)], which is constructed from a condensate of a charged scalar field in AdS{sub 4}-Schwarzschild background. By analytically studying the perturbation of the gravitational system near the critical temperature T{sub c}, we obtain the superconducting coherence length proportional to 1/{radical}(1-T/T{sub c}) 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.
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