Gauge fluctuations and transition temperature for superconducting wires

TL;DR

This paper analyzes how gauge fluctuations affect the critical temperature of superconducting wires with rectangular cross-sections using the Ginzburg-Landau model and advanced regularization techniques.

Contribution

It introduces a method to incorporate gauge fluctuations in confined geometries and derives equations for the critical temperature dependence on wire dimensions.

Findings

Critical temperature decreases with decreasing wire size.

Derived equations relate transition temperature to transverse dimensions.

Qualitative agreement with experimental observations.

Abstract

We consider the Ginzburg-Landau model, confined in an infinitely long rectangular wire of cross-section $L_{1}\times L_{2}$. Our approach is based on the Gaussian effective potential in the transverse unitarity gauge, which allows to treat gauge contributions in a compact form. The contributions from the scalar self-interaction and from the gauge fluctuations are clearly identified. Using techniques from dimensional and $zeta$-function regularizations, modified by the confinement conditions, we investigate the critical temperature for a wire of transverse dimensions $L_1$, $L_2$. Taking the mass term in the form $m_{0}^2=a(T/T_0 - 1)$, where $T_0$ is the bulk transition temperature, we obtain equations for the critical temperature as a function of the $L_{i}'s$ and of $T_{0}$, and determine the limiting sizes sustaining the transition. A qualitative comparison with some experimental observations is done.