Holographic insulator/superconductor phase transition by matching method and thermodynamic geometry

TL;DR

This paper analytically studies the insulator/superconductor phase transition in a 5D AdS soliton background using matching method and thermodynamic geometry, deriving critical chemical potential and condensation operator expressions.

Contribution

It introduces an analytical approach combining matching method and thermodynamic geometry to analyze phase transitions in holographic models, providing explicit expressions and cross-method validation.

Findings

Critical chemical potential obtained analytically

Condensation operator expression derived

Results agree with existing numerical data

Abstract

In this work, we have analytically analyzed the insulator/superconductor phase transition in the presence of a 5-dimensional $AdS$ soliton background using matching method and thermodynamic geometry approach. We have first employed the matching method to obtain the critical chemical potential. We then move on to investigate the free energy and thermodynamic geometry of this model in 3+1 dimensions. This investigation of the thermodynamic geometry leads to the critical chemical potential of the system from the condition of the divergence of the scalar curvature. We have then compared the value of the critical chemical potential $\mu_{c}$ in dimension $d=5$ obtained from these two different methods, namely, the matching method and the thermodynamic geometry procedure. We have also obtained an expression for the condensation operator using the matching method. Our findings agree very well with the numerical findings in the literature.