Electrostatic effects, band distortions and superconductivity in twisted graphene bilayers

Bilayer graphene twisted by a small angle shows a significant charge modulation away from neutrality, as the charge in the narrow bands near the Dirac point is mostly localized in a fraction of the Moiré unit cell. The resulting electrostatic potential leads to a filling dependent change in the low energy bands, of a magnitude comparable, or larger than the bandwidth. These modifications can be expressed in terms of new electron-electron interactions, which, when expressed in a local basis, describe electron assisted hopping terms. These interactions favor superconductivity at certain fillings.