Recent experiments show how a bilayer graphene twisted around a certain magic angle becomes superconducting as it is doped into a region with approximate flat bands. We investigate the mean-field s-wave superconducting state in such a system and show how the state evolves as the twist angle is tuned, and as a function of the doping level. We argue that part of the experimental findings could well be understood to result from an attractive electron--electron interaction mediated by electron--phonon coupling, but the flat-band nature of the excitation spectrum makes also superconductivity quite unusual. For example, as the flat-band states are highly localized around certain spots in the structure, also the superconducting order parameter becomes strongly inhomogeneous.
@article{arxiv.1805.01039,
title = {Mean-field theory for superconductivity in twisted bilayer graphene},
author = {T. J. Peltonen and R. Ojajärvi and T. T. Heikkilä},
journal= {arXiv preprint arXiv:1805.01039},
year = {2018}
}