Critical magnetic field in AdS/CFT superconductor

TL;DR

This work investigates a holographic (2+1)-D superconductor in the presence of an external magnetic field within the AdS/CFT framework. The authors couple a charged scalar to a magnetically charged AdS4 black hole and solve the coupled equations for the scalar and the electrostatic potential in a fixed background, identifying a condensate when the effective mass m_eff^2(r) = -2/L^2 - Phi^2/f crosses the Breitenlohner-Freedman bound m^2 L^2 > -9/4, with condensation more readily occurring at smaller H. They show a critical magnetic field H_c below which a nontrivial condensate exists, and construct a phase diagram in the (T,H) plane, where superconductivity occurs for T < T_c(H) and H < H_c(T). The results distinguish two condensates, O_1 and O_2, corresponding to bosonic and fermionic pairing, and illustrate a holographic Meissner-like response; they also discuss limitations due to neglecting backreaction and outline paths toward more complete holographic models. Overall, the paper provides a tractable framework for studying the interplay between magnetic fields and superconductivity in strongly coupled systems and offers insights into unconventional superconductors from a holographic perspective.

Abstract

We have studied a holographically dual description of superconductor in (2+1)-dimensions in the presence of applied magnetic field, and observed that there exists a critical value of magnetic field, below which a charged condensate can form via a second order phase transition.

Figures (3)

• Figure 1: The effective mass $m_{eff}^2$ evaluated at fixed temperature and boundary conditions at the horizon. From bottom up, the curves are with $H=0,0.5$ and $1$ respectively. The dashing line indicates the Bretenlohner-Freedman bound, below which the AdS vacuum is unstable under perturbation of $\Psi$ and condensation is expected.
• Figure 2: We plot order parameter $\langle{\cal O}_2\rangle$ as a function of temperature. The critical temperature $T_c$ decreases as applied magnetic field increases. Here $\tilde{H}$ is the normalized $H$ given by $H^{2/3}/T_0$, where $T_0=T_c$ at $H=0$.
• Figure 3: The phase diagram of $T_c$ against $H_c$. The superconducting phase where $\langle{\cal O}_2\rangle \neq 0$($\langle{\cal O}_1\rangle \neq 0$) exists in the lower left part below the solid (dashed) curve, while normal phase in the upper right part above the curve.