Vortex configurations on a thin superconducting spherical shell in the presence of a magnetic dipole

Abstract

In this work we study vortex configurations on a thin superconducting spherical shell of radius R and thickness d ( R ≫ d ⩾ ξ ) with a magnetic dipole inside it. The point magnetic dipole (with magnetic moment, m z ) is oriented along one of the sphere main axis. It is placed a distance z 0 from the center of the sphere. Due to the symmetry of the sample, there are vortices and antivortices pancakes on the shell resulting in zero total vorticity. The vortex interactions with the shielding currents produced by the external fields – as well as with other vortices – are calculated within the London limit. The vortex configurations are obtained by solving numerically the Bardeen–Stephen equation of motion for the vortices. For z 0 ≈ 0 the most frequent vortex configurations present equal arrangements of vortices and antivortices on the north and south hemispheres. For z 0 ≈ 0.5 R , the diversity of vortex configurations increases, with a higher number of configurations (in comparison to smaller z 0 ) having different vortices and antivortices distributions on each shell hemisphere. We also study the equilibrium states dependence on the magnetic dipole strength and position.