Gauge Fluctuations in Superconducting Films

TL;DR

This paper investigates how gauge fluctuations affect the critical temperature of superconducting films modeled by Ginzburg-Landau theory, revealing a minimal thickness below which superconductivity vanishes.

Contribution

It introduces a novel approach using the Gaussian effective potential and regularization techniques to analyze gauge contributions in confined superconducting films.

Findings

Identification of gauge fluctuation effects on critical temperature

Existence of a minimal critical thickness for superconductivity

Quantitative relationship between film thickness and superconducting properties

Abstract

In this paper we consider a superconducting film modeled by the Ginzburg-Landau model, confined between two parallel planes a distance $L$ apart from one another. Our approach is based on the Gaussian effective potential in the transverse unitarity gauge, which allows to treat gauge contributions in a compact form. Using techniques from dimensional and $zeta$-function regularizations, modified by the confinement conditions, we investigate the critical temperature as a function of the film thickness $L$. The contributions from the scalar self-interaction and from the gauge fluctuations are clearly identified. The model suggests the existence of a minimal critical thickness below which superconductivity is suppressed.