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Gap Structure of the Hofstadter System of Interacting Dirac Fermions in Graphene

The effects of mutual Coulomb interactions between Dirac fermions in monolayer graphene on the Hofstadter energy spectrum have been studied. Our studies indicate that the effects of the interaction depend strongly on the amplitude of the periodic potential. For large amplitudes the interaction effects are small and the properties of the system are primarily determined by the periodic potential but for small amplitudes the interaction greatly influences the band gap. The signature of the interaction effects in the Hofstadter system can be probed through magnetization where the Coulomb effects are dominant for small amplitudes of the periodic potential.