The Coleman-Weinberg effective potential in the theory of superconductivity

TL;DR

This paper applies the Coleman-Weinberg effective potential to a quasi-2D non-relativistic four-Fermi model at finite temperature, refining the critical temperature estimate for superconductivity beyond mean-field theory.

Contribution

It introduces a next-to-leading order analysis of the effective potential in superconductivity, incorporating the Coleman-Weinberg approach and revising the Thouless criterion.

Findings

Critical temperature tends to zero in 2D limit, consistent with Coleman theorem.

Imaginary part of the one-loop correction relates to the Thouless criterion.

Refined critical temperature differs from mean-field predictions.

Abstract

A quasi two-dimensional non-relativistic four-Fermi theory is studied at finite temperatures in the next-to-leading order approximation using the Coleman-Weinberg effective potential. The appearance of an imaginary part to the one-loop correction is discussed in the context of condensed matter theory where it is referred to as the Thouless criterion for superconductivity. By reference to the appropriate modified effective potential one may revise the Thouless criterion to obtain a critical temperature in next-to-leading order that, unlike the mean-field temperature, tends to zero in the two-dimensional limit in agreement with the Coleman theorem.