Hierarchy of gaps and magnetic minibands in graphene in the presence of the Abrikosov vortex lattice

We determine the bands and gaps in graphene subjected to the magnetic field of an Abrikosov lattice of vortices in the underlying superconducting film. The spectrum features one nondispersive magnetic miniband at zero energy, separated by the largest gaps in the miniband spectrum from a pair of minibands resembling a slightly broadened first Landau level in graphene, suggesting the persistence of ν=±2 and ±6 quantum Hall effect states. Also, we identify an occasional merging point of magnetic minibands with a Dirac-type dispersion at the miniband edges.