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

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.