Mean-field theory for superconductivity in twisted bilayer graphene

Understand

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.