We present a theory of phonon-mediated superconductivity in near magic angle twisted bilayer graphene. Using a microscopic model for phonon coupling to moir\'e band electrons, we find that phonons generate attractive interactions in both s and d wave pairing channels and that the attraction is strong enough to explain the experimental superconducting transition temperatures. Before including Coulomb repulsion, the s-wave channel is more favorable; however, on-site Coulomb repulsion can suppress s-wave pairing relative to d-wave. The pair amplitude varies spatially with the moir\'e period, and is identical in the two layers in the s-wave channel but phase shifted by π in the d-wave channel. We discuss experiments that can distinguish the two pairing states.
@article{arxiv.1805.08735,
title = {Theory of phonon-mediated superconductivity in twisted bilayer graphene},
author = {Fengcheng Wu and A. H. MacDonald and Ivar Martin},
journal= {arXiv preprint arXiv:1805.08735},
year = {2018}
}