Excited states of holographic superconductors

TL;DR

This paper numerically explores excited states of holographic superconductors, revealing new solutions with unique conductivity features and a lower critical temperature, advancing understanding of their quantum properties.

Contribution

It introduces a novel family of excited state solutions in holographic superconductors and analyzes their distinct conductivity and condensate behaviors.

Findings

Existence of excited state solutions with lower critical temperature.

Additional pole in Im[σ] and delta function in Re[σ] at low temperature.

Confirmation of excited states through conductivity analysis.

Abstract

In this paper we re-investigate the model of the anti-de Sitter gravity coupled to Maxwell and charged scalar fields, which has been studied as the gravitational dual to a superconductor for a long time since the famous work [Phys.\ Rev.\ Lett.\ {\bf 101}, 031601 (2008)]. By numerical method, we present a novel family of solutions of holographical superconductor with excited states, and find there exists a lower critical temperature in the corresponding excited state. Moreover, we study the condensate and conductivity in the excited states. It is very interesting that the conductivity $\sigma$ of each excited state has an additional pole in $\text{Im}[\sigma]$ and a delta function in $\text{Re}[\sigma]$ arising at the low temperature inside the gap, which is just the evidence of the existence of excited states.