Holographic Superconductor on Q-lattice

TL;DR

This paper develops a holographic superconductor model on Q-lattices, showing how Q-lattices influence the critical temperature, condensate behavior, and optical conductivity, with results aligning with conventional superconductors at large scalar charges.

Contribution

It introduces a gravitational dual model of a superconductor on Q-lattices and analyzes how Q-lattices affect superconducting properties and critical temperatures.

Findings

Q-lattices suppress the scalar condensate and lower the critical temperature.

In deep insulating phases, scalar condensation may not occur for small charges.

The optical conductivity retains a pole in the imaginary part, indicating a delta function in the real part.

Abstract

We construct the simplest gravitational dual model of a superconductor on Q-lattices. We analyze the condition for the existence of a critical temperature at which the charged scalar field will condense. In contrast to the holographic superconductor on ionic lattices, the presence of Q-lattices will suppress the condensate of the scalar field and lower the critical temperature. In particular, when the Q-lattice background is dual to a deep insulating phase, the condensation would never occur for some small charges. Furthermore, we numerically compute the optical conductivity in the superconducting regime. It turns out that the presence of Q-lattice does not remove the pole in the imaginary part of the conductivity, ensuring the appearance of a delta function in the real part. We also evaluate the gap which in general depends on the charge of the scalar field as well as the Q-lattice parameters. Nevertheless, when the charge of the scalar field is relatively large and approaches the probe limit, the gap becomes universal with $\omega_g \simeq 9T_c$ which is consistent with the result for conventional holographic superconductors.