Coexistence of the Meissner and vortex states on a nanoscale superconducting spherical shell

We show that on superconducting spherical nanoshells, the coexistence of the Meissner state with a variety of vortex patterns drives the phase transition to higher magnetic fields. The spherical geometry leads to a Magnus-Lorentz force pushing the nucleating vortices and antivortices toward the poles, overcoming local pinning centers, preventing vortex-antivortex recombination, and leading to the appearance of a Meissner belt around the sphere equator. In sufficiently small and thin spherical shells paramagnetic vortex states can be stable, enabling spatial separation of freely moving shells with different radii and vorticity in an inhomogeneous external magnetic field.