  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.
