Analytical Studies on Holographic Insulator/Superconductor Phase Transitions

TL;DR

This paper analytically examines the phase transitions between insulator and superconductor states in holographic models, confirming previous numerical results and deriving critical exponents and relations near the transition point.

Contribution

It provides analytical calculations of critical chemical potentials and condensation behaviors in holographic insulator/superconductor models at zero temperature.

Findings

Critical chemical potentials match previous numerical results.

Critical exponent for condensation is 1/2.

Linear relation between charge density and chemical potential near critical point.

Abstract

We investigate the analytical properties of the s-wave and p-wave holographic insulator/superconductor phase transitions at zero temperature. In the probe limit, we analytically calculate the critical chemical potentials at which the insulator/superconductor phase transition occurs. Those resulting analytical values perfectly match the previous numerical values. We also study the relations between the condensation values and the chemical potentials near the critical point. We find that the critical exponent for condensation operator is 1/2 for both models. The linear relations between the charge density and the chemical potential near the critical point are also deduced in this paper, which are qualitatively consistent with the previous numerical results.