Coulomb interaction, phonons, and superconductivity in twisted bilayer graphene

The polarizability of twisted bilayer graphene, due to the combined effect of electron-hole pairs, plasmons, and acoustic phonons, is analyzed. The screened Coulomb interaction allows for the formation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron-hole pairs. Scattering processes involving large momentum transfers, Umklapp processes, play a crucial role in the formation of Cooper pairs. The magnitude of the superconducting gap changes among the different pockets of the Fermi surface.