Nonperturbative XY-model approach to strong coupling superconductivity in two and three dimensions

TL;DR

This paper develops a nonperturbative XY-model approach to analyze the crossover from weak to strong coupling superconductivity in 2D and 3D electron gases, deriving analytic expressions for transition temperatures and phase coherence.

Contribution

It introduces an analytic, nonperturbative method using XY-models to determine superconducting transition temperatures across coupling regimes in two and three dimensions.

Findings

Transition temperature T_c increases monotonically with coupling strength.

Derived formulas for the merging of phase decoherence and pair formation temperatures.

Analytic expressions for phase fluctuation stiffness in different dimensions.

Abstract

For an electron gas with delta-function attraction we investigate the crossover from weak- to strong-coupling supercoductivity in two and three dimensions. We derive analytic expressions for the stiffness of phase fluctuations and set up effective XY-models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature T_c as a monotonous function of the coupling strength and carrier density both in two and three dimensions, and give analytic formulas for the merging of the temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.