Phase transition curves for mesoscopic superconducting samples

TL;DR

This paper analyzes the phase transition behavior of mesoscopic superconductors under large magnetic flux, deriving asymptotic formulas and comparing theoretical predictions with experimental data.

Contribution

It introduces new asymptotic formulas for the ground state of the Schrödinger equation in high flux regimes, highlighting the influence of domain smoothness.

Findings

Asymptotic formula for the ground state in large flux

Shape of phase transition curve depends on domain smoothness

Theoretical results align with recent experimental observations

Abstract

We compute the phase transition curves for mesoscopic superconductors. Special emphasis is given to the limiting shape of the curve when the magnetic flux is large. We derive an asymptotic formula for the ground state of the Schr\"odinger equation in the presence of large applied flux. The expansion is shown to be sensitive to the smoothness of the domain. The theoretical results are compared to recent experiments.