Narrow bands, electrostatic interactions and band topology in graphene stacks

The occurrence of superconducting and insulating phases is well-established in twisted graphene bilayers, and they have also been reported in other arrangements of graphene layers. We investigate three such arrangements: untwisted AB bilayer graphene on an hBN substrate, two graphene bilayers twisted with respect to each other, and a single ABC stacked graphene trilayer on an hBN substrate. Narrow bands with different topology occur in all cases, producing a high density of states which enhances the role of interactions. We investigate the effect of the long range Coulomb interaction, treated within the self consistent Hartree-Fock approximation. We find that the on-site part of the Fock potential strongly modifies the band structure at charge neutrality. The Hartree part does not significantly modify the shape and width of the bands in the three cases considered here, in contrast to the effect that such a potential has in twisted bilayer graphene.