Critical radius and magnetic field for vortex nucleation on a superconducting spherical surface

Spherical, two-dimensional electron systems are realized in nanoshells and multielectron bubbles in helium. In this contribution, we investigate the superconducting state of such shells using a variational Ginzburg-Landau formulation. A phase diagram as a function of the sphere radius and the magnetic field is derived, and we calculate a critical radius below which vortices cannot be nucleated on the superconducting spherical surface.