paper

Characteristic length of an AdS/CFT superconductor

arXiv:0809.3079 · doi:10.1103/PhysRevD.78.106006

Abstract

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.

9 pages, no figure; v2: typos corrected; v3: version to appear in PRD, an early discussion based on convensional superconductor with dynamical photon removed and an argument about the type of the holographic superconductor added

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