Numerical simulations of the quantized vortices on a thin superconducting hollow sphere

In this paper, we investigate the vortex nucleation on a thin superconducting hollow sphere. The problem is studied using a simplified system of Ginzburg–Landau equations. We present numerical algorithms which preserve the discrete gauge invariance for both time dependent and time independent simulations. The spatial discretization is based on a spherical centroidal Voronoi tessellation which offers a very effective high resolution mesh on the sphere for the order parameter as well as other physically interesting variables such as the super-current and the induced magnetic field. Various vortex configurations and energy diagrams are computed. Dynamic responses of the vortices to the applied current are also simulated.