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 the regions of the Moir\'e pattern with AA stacking. The resulting electrostatic potential gives rise to the dominant contribution to the electron-electron interaction within this low energy band, which becomes significantly distorted. The changes in the band structure are described by new local interactions, and lead to an assisted electron-hopping process. These couplings favor superconductivity at certain fillings.
@article{arxiv.1806.05990,
title = {Electrostatic effects, band distortions and superconductivity in twisted graphene bilayers},
author = {Francisco Guinea and Niels R. Walet},
journal= {arXiv preprint arXiv:1806.05990},
year = {2018}
}