Gaussian Effective Potential and superconductivity

TL;DR

This paper applies the Gaussian Effective Potential method to three-dimensional U(1) scalar electrodynamics in a fixed gauge, providing improved theoretical insights into superconductivity near the critical region.

Contribution

It introduces a fixed unitarity gauge approach to the Gaussian Effective Potential, avoiding unphysical degrees of freedom and better matching experimental data near criticality.

Findings

Determines electromagnetic and scalar field masses via coupled variational equations.

Prevents unphysical degrees of freedom by fixing the gauge.

Interpolates experimental data near the critical region.

Abstract

The Gaussian Effective Potential in a fixed transverse unitarity gauge is studied for the static three-dimensional U(1) scalar electrodynamics (Ginzburg-Landau phenomenological theory of superconductivity). In the broken-symmetry phase the mass of the electromagnetic field (inverse penetration depth) and the mass of the scalar field (inverse correlation length) are both determined by solution of the coupled variational equations. At variance with previous calculations, the choice of a fixed unitarity gauge prevents from the occurrence of any unphysical degree of freedom. The theory provides a nice interpolation of the experimental data when approaching the critical region, where the standard mean-field method is doomed to failure.