Superconductivity and spin density wave in AA stacked bilayer graphene

This work theoretically analyzes electronic ordering in AA-stacked bilayer graphene and the role of the Coulomb interaction in these many-body phenomena. Using the random phase approximation to account for screening, we find intra-layer effective interactions to be much stronger than inter-layer interactions; under certain circumstances, the latter may also become attractive. At zero doping, the Coulomb repulsion stabilizes the spin-density wave state, with a N{\'e}el temperature in the tens of Kelvin. While dominant in the undoped system, the spin-density wave is destroyed by sufficiently strong doping and a superconducting phase emerges. We find that the effective Coulomb inter-layer interaction can give rise to superconductivity. However, the corresponding critical temperature is negligibly small, and phonon-mediated attraction must be introduced to observe it. Strong intra-layer repulsion suppresses order parameters that couple two intra-layer electrons. We point out a possible superconducting state with finite Cooper pair momentum.