Design for the Detection of the Singly-Connected Superconducting State

TL;DR

This paper investigates the stability of the singly-connected superconducting state in mesoscopic loops with nonuniform thickness, providing analytical insights and potential experimental guidance based on the Little-Parks effect.

Contribution

It offers an analytical study of the Little-Parks effect in nonuniform loops, revealing conditions for the stability of the singly-connected state and extending understanding beyond uniform cases.

Findings

The singly-connected state is stable within a specific phase diagram region.

Temperature stability range scales with the square of the thickness ratio.

Analytical solutions are derived for loops with piecewise constant thickness.

Abstract

We study the Little-Parks effect for mesoscopic loops with very nonuniform thickness. The results follow the trend of the phase diagram obtained for almost uniform thickness. In particular, the singly-connected state is stable on a line segment delimited by two critical points. Most of this study considers loops with piecewise constant thickness; in this case the Euler-Lagrange equation can be integrated analytically. Under appropriate conditions, the temperature range where the singly-connected state is stable is proportional to the square of the ratio between the maximal and the minimal thicknesses. Our results may serve as a guide for planning experiments.