Exact Gravity Dual of a Gapless Superconductor

TL;DR

This work constructs an exact gravity dual of a gapless superconductor by coupling a charged scalar to gravity on a topological AdS black hole, yielding a hairy MTZ solution below a critical temperature Tc. The dual boundary theory exhibits a condensate consisting of two operators and a conductivity determined by electromagnetic perturbations, with a third-order phase transition at Tc and gapless transport properties governed by a Goldstone-like mode. The analysis combines analytic treatments of the MTZ/TBH phases, a stability study, and numerical results for the conductivity and densities, showing robust superconducting behavior with modulated normal fluid density a low temperatures. The setup advances holographic superconductivity by providing an exact, backreacting gravitational background and reveals distinctive features tied to hyperbolic horizons and scalar hair, with potential extensions to richer string/M-theory embeddings.

Abstract

A model of an exact gravity dual of a gapless superconductor is presented in which the condensate is provided by a charged scalar field coupled to a bulk black hole of hyperbolic horizon in asymptotically AdS spacetime. Below a critical temperature, the black hole acquires its hair through a phase transition while an electromagnetic perturbation of the background Maxwell field determines the conductivity of the boundary theory.

Figures (8)

• Figure 1: The perturbation $\phi_1$ versus $r$ for $\mu=0.02$ and negative ($r_0=-0.01,$ left graph) or positive ($r_0=-0.01,$ right graph) value for $r_0.$
• Figure 2: The condensates $\sqrt G \langle\mathcal{O}_1\rangle$ (upper curve) and $\sqrt G \langle\mathcal{O}_2\rangle$ (lower curve) as functions of $T/T_0$ (eq. (\ref{['eqO']})).
• Figure 3: The logarithm of the normal fluid density as a function of the logarithm of the temperature for $q/\sqrt G=0.5$ (left) and $q/\sqrt G=5.0$ (right). The solid lines represent the fits $\ln n_n =0.0538 \ln T +0.149$ (left) and $\ln n_n=2.45 \ln T +5.3$ (right).
• Figure 4: The logarithm of the real part of the conductivity as a function of the logarithm of the temperature for $q/\sqrt G=0.1$ (crosses, the uppermost symbols),$\, 0.2,0.5,1.0,2.0.$
• Figure 5: Superfluid density as a function of $(T-T_0)^2$ for $q/\sqrt G=0.5$ (left) and $q/\sqrt G=5.0$ (right). The solid lines represent the fits $n_s=0.552 (T-T_0)^2$ (left) and $n_s=52.9 (T-T_0)^2$ (right).