Vortex States of a Three-Dimensional Mesoscopic Superconducting Torus in an External Magnetic Field

The time-dependent Ginzburg–Landau equations have been solved numerically by the finite-element method for a three-dimensional mesoscopic superconducting torus. We obtain the different vortex patterns as a function of the applied field perpendicular to its surface. And we find that multivortex states are ground state in a three-dimensional mesoscopic torus. These results show that our approach is effective and useful to interpret experimental data on vortex states in mesoscopic superconductors.