Holographic insulator/superconductor phase transitions with excited states

TL;DR

This paper explores holographic insulator/superconductor phase transitions with excited states in AdS soliton backgrounds, revealing higher critical chemical potentials for excited states and a second-order phase transition with linear charge density-chemical potential relation.

Contribution

It introduces an analytical approach using the improved Sturm-Liouville method to study excited states in holographic phase transitions, providing new insights into their critical properties.

Findings

Excited states have higher critical chemical potentials than ground states.

The difference in critical chemical potential between consecutive states is approximately 2.4.

Phase transitions are second order with a linear charge density-chemical potential relationship.

Abstract

We construct a family of solutions of the holographic insulator/superconductor phase transitions with the excited states in the AdS soliton background by using both the numerical and analytical methods. The interesting point is that the improved Sturm-Liouville method can not only analytically investigate the properties of the phase transition with the excited states, but also the distributions of the condensed fields in the vicinity of the critical point. We observe that, regardless of the type of the holographic model, the excited state has a higher critical chemical potential than the corresponding ground state, and the difference of the dimensionless critical chemical potential between the consecutive states is around 2.4, which is different from the finding of the metal/superconductor phase transition in the AdS black hole background. Furthermore, near the critical point, we find that the phase transition of the systems is of the second order and a linear relationship exists between the charge density and chemical potential for all the excited states in both s-wave and p-wave insulator/superconductor models.