Nucleation of Superconductivity in a Mesoscopic Loop of Finite Width

TL;DR

This paper investigates how the superconducting transition temperature in mesoscopic loops varies with magnetic field, revealing a dimensional crossover from periodic to quasi-linear behavior as the loop width increases.

Contribution

It provides a detailed analysis of the Tc(H) boundary in finite-width mesoscopic loops, extending understanding beyond thin-wire and disk geometries, and identifies a crossover similar to 2D-3D transitions.

Findings

Tc(H) oscillations are periodic for thin-wire loops.

A crossover to quasi-linear Tc(H) behavior occurs at higher fields.

A giant vortex state with surface superconductivity forms in high fields.

Abstract

The normal/superconducting phase boundary Tc has been calculated for mesoscopic loops, as a function of an applied perpendicular magnetic field H. While for thin-wire loops and filled disks the Tc(H) curves are well known, the intermediate case, namely mesoscopic loops of finite wire width, have been studied much less. The linearized first Ginzburg-Landau equation is solved with the proper normal/vacuum boundary conditions both at the internal and at the external loop radius. For thin-wire loops the Tc(H) oscillations are perfectly periodic, and the Tc(H) background is parabolic (this is the usual Little-Parks effect). For loops of thicker wire width, there is a crossover magnetic field above which Tc(H) becomes quasi-linear, with the period identical to the Tc(H) of a filled disk (i.e. pseudoperiodic oscillations). This dimensional transition is similar to the 2D-3D transition for thin films in a parallel field, where vortices start penetrating the material as soon as the film thickness exceeds the temperature dependent coherence length by a factor 1.8. For the presently studied loops, the crossover point is controlled by a similar condition. In the high field '3D' regime, a giant vortex state establishes, where only a surface superconducting sheath near the sample's outer radius is present.