Superconductivity in twisted graphene layers: electronic structure and interactions.*

A special feature of the states in the low energy bands of twisted graphene bilayers is that their charge distribution shows a significant momentum dependence. As a result, the filling of these bands leads to electrostatic potentials, which, in turn, modify the energy levels and the structure of the bands. The dependence of the band shape on the band filling can be described in terms of the emergence of new electron-electron interactions. We quantify and analyze these interactions, and discuss their relation with the observed superconducting and insulating states.