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 theta approximate to 1.05 degrees 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 similar to 1 K, in agreement with the experiment. We predict that superconductivity can also be observed in TBG at many other angles 9 and higher electron densities in higher moire bands, which may also explain the possible granular superconductivity of highly oriented pyrolytic graphite. We support our conclusions by ab initio calculations.