Band structure and insulating states driven by Coulomb interaction in twisted bilayer graphene

We analyze the phase diagram of twisted graphene bilayers near a magic angle. We consider the effect of the long-range Coulomb interaction, treated within the self-consistent Hartree-Fock approximation, and we study arbitrary band fillings. We find a rich phase diagram, with different broken symmetry phases, although they do not show necessarily a gap at the Fermi energy. There are nontrivial effects of the electrostatic potential on the shape and the gaps of the bands in the broken symmetry phases. The results suggest that the nonsuperconducting broken symmetry phases observed experimentally are induced by the long-range exchange interaction.