Characteristic length of an AdS/CFT superconductor

TL;DR

This paper analyzes a holographic superconductor model using AdS/CFT, deriving the coherence length near T_c and demonstrating diamagnetic response consistent with Ginzburg-Landau theory, supporting the duality approach.

Contribution

It provides an analytical derivation of the coherence length and magnetic response in a holographic superconductor model, confirming the AdS/CFT correspondence's applicability.

Findings

Superconducting coherence length scales as 1/√(1-T/T_c).

A diamagnetic current proportional to the square of the order parameter is induced.

Results align with Ginzburg-Landau theory predictions.

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.