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

Abstract: We determine the structure of band and gaps in graphene encapsulated in hexagonal boron nitride and subjected to magnetic field of Abrikosov lattice of vortices in the underlying superconducting film. The spectrum features one non-dispersive magnetic miniband at zero energy, separated by the largest gaps in the miniband spectrum from a pair of minibands resembling slightly broadened first Landau levels in graphene, suggesting the persistence of $\nu = \pm 2$ quantum Hall effect states. Also, we identify occasional merging point of magnetic minibands which feature Dirac-type dispersion at the consecutive miniband edges.