Twisted Bilayer Graphene: A Phonon-Driven Superconductor.

We study the electron-phonon coupling in twisted bilayer graphene (TBG), which was recently experimentally observed to exhibit superconductivity around the magic twist angle θ≈1.05°. We show that phonon-mediated electron attraction at the magic angle is strong enough to induce a conventional intervalley pairing between graphene valleys K and K^{'} with a superconducting critical temperature T_{c}∼1  K, in agreement with the experiment. We predict that superconductivity can also be observed in TBG at many other angles θ and higher electron densities in higher moiré bands, which may also explain the possible granular superconductivity of highly oriented pyrolytic graphite. We support our conclusions by ab initio calculations.