Vorticity and vortex-core states in type-II superconductors

The origin of the vortex-core states in s-wave and d_x²-y²-wave superconductors is investigated by means of some selected numerical experiments. By relaxing the self-consistency condition in the Bogoliubov--de Gennes equations and tuning the order parameter in the core region, it is shown that the suppression of the superfluid density in the core is not a necessary condition for the core states to form. This excludes ``potential well'' types of interpretations for the core states. The topological defect in the phase of the order parameter, however, plays a crucial role. This fact is explained by considering the effect of the vortex supercurrent on the Bogoliubov quasiparticles and illustrated by comparing conventional vortices to multiply quantized vortices and vortex-antivortex pairs. The core states are also found to be extremely robust against random disorder of the phase.