Characteristic length of an AdS/CFT superconductor

TL;DR

The paper investigates a holographic superconductor model constructed from a charged scalar field in AdS_4-Schwarzschild spacetime to extract near-T_c transport and static properties via AdS/CFT in the probe limit. By analyzing static, spatially modulated perturbations, it derives the superconducting coherence length $\xi$ and shows it diverges as $\xi \propto \frac{1}{T_c}(1 - T/T_c)^{-1/2}$; it also computes a diamagnetic response to a small external magnetic field, obtaining a London-like relation $\langle J_y \rangle \propto -|\langle \mathcal{O}_I\rangle|^2 \delta A_y^{(0)}$ and a superfluid density $n_s \sim T_c - T$. These results are in accord with Ginzburg-Landau theory and bolster the picture that holographic superconductors can be described by a charged scalar field on a black hole via AdS/CFT. The discussion considers implications for type I/II behavior through the GL parameter $\kappa = \lambda/\xi$ and notes potential extensions to general scalar masses and dynamical photon effects, connecting to concurrent related work.

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.