Investigation on the Ground States of a Model Thin-Film Superconductor on a Sphere

TL;DR

This study investigates the ground state configurations of a model type-II superconductor with vortices on a spherical surface, revealing unique defect structures and differences from flat-plane vortex lattices.

Contribution

It combines numerical simulations and elasticity theory to analyze vortex arrangements on a sphere, highlighting the role of disclination defects in the ground state.

Findings

Ground states form a triangular vortex network with twelve five-coordinated centers.

Low-energy states are associated with high-symmetry vortex arrangements.

The spherical system's thermodynamic limit differs from the flat plane due to disclination defects.

Abstract

We consider the problem of finding the ground state of a model type-II superconductor on the two-dimensional surface of a sphere, penetrated by $N$ vortices. Numerical work shows the ground states to consist of a triangular network of the vortices with twelve five-coordinated centres. Values of $N$ are found with particularly low energy ground states, due to structures of high symmetry. The large $N$ limit is treated within elasticity theory to compare with the triangular vortex lattice that forms the ground state on an infinite flat plane. Together with numerical work this demonstrates that the thermodynamic limit $N\rightarrow\infty$ of the spherical system remains different from the flat plane due to the presence of twelve disclination defects.