Critical Fields of mesoscopic superconductors

TL;DR

This paper provides a Ginzburg-Landau theoretical analysis of oscillations in the upper critical field of mesoscopic superconductors, explaining phenomena like the cusp in the phase boundary and the relation between critical fields.

Contribution

It offers a quantitative Ginzburg-Landau model to explain critical field oscillations and boundary effects in mesoscopic superconductors, advancing understanding of their magnetic properties.

Findings

Identification of a cusp in the $H-T$ phase boundary at small fields.

Demonstration that nucleation at the boundary leads to $H_{c3}$ as the upper critical field.

Clarification of the transition from $H_{c1}$ to $H_{c3}$ in mesoscopic samples.

Abstract

Recent measurements have shown oscillations in the upper critical field of simply connected mesoscopic superconductors. A quantitative theory of these effects is given here on the basis of a Ginzburg-Landau description. For small fields, the $H-T$ phase boundary exhibits a cusp where the screening currents change sign for the first time thus defining a lower critical field $H_{c1}$. In the limit where many flux quanta are threading the sample, nucleation occurs at the boundary and the upper critical field becomes identical with the surface critical field $H_{c3}$.