We investigate the doping of AA-stacked graphene bilayers. By applying a mean field theory at zero temperature we find that, at half-filling, the bilayer is an antiferromagnetic insulator. Upon doping, the homogeneous phase becomes unstable with respect to phase separation. The separated phases are undoped antiferromagnetic insulator and metal with a nonzero concentration of charge carriers. At sufficiently high doping, the insulating areas shrink and disappear, and the system becomes a homogeneous metal. The conductivity changes drastically upon doping, so the bilayer may be used as a switch in electronic devices. The effects of finite temperature are also discussed.

• Received 21 October 2012

DOI:https://doi.org/10.1103/PhysRevB.87.121401