Vortices in a Thin Film Superconductor with a Spherical Geometry

TL;DR

This study uses Monte Carlo simulations to investigate vortex behavior in a spherical thin film superconductor, revealing a continuous transition at zero temperature and contrasting with other boundary conditions.

Contribution

It demonstrates that spherical geometry prevents a vortex solid phase transition, providing new insights into vortex matter in curved superconducting films.

Findings

No phase transition to vortex solid in spherical geometry

Correlation lengths show identical temperature dependence

System remains in vortex liquid phase at all accessible temperatures

Abstract

We report results from Monte Carlo simulations of a thin film superconductor in a spherical geometry within the lowest Landau level approximation. We observe the absence of a phase transition to a low temperature vortex solid phase with these boundary conditions; the system remains in the vortex liquid phase for all accessible temperatures. The correlation lengths are measured for phase coherence and density modulation. Both lengths display identical temperature dependences, with an asymptotic scaling form consistent with a continuous zero temperature transition. This contrasts with the first order freezing transition which is seen in the alternative quasi-periodic boundary conditions. The high temperature perturbation theory and the ground states of the spherical system suggest that the thermodynamic limit of the spherical geometry is the same as that on the flat plane. We discuss the advantages and drawbacks of simulations with different geometries, and compare with current experimental conclusions. The effect of having a large scale inhomogeneity in the applied field is also considered.