  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 for- mation 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.
