Vortex core states in superconducting graphene

The electronic structure of vortex states in superconducting graphene is studied within the Bogoliubov-de Gennes theory applied to excitations near the Dirac point. We consider the subgap spectrum transformations which occur with a change in the doping level. For an arbitrary vorticity and doping level we investigate the problem of existence of zero-energy modes. The crossover to a Caroli-de Gennes-Matricon type of spectrum is studied. Results of numerical computations are reported that illustrate the behavior of the spectrum with a change in the doping level.