Superconductivity and Spin Density Wave in Aa Stacked Bilayer Graphene

This work theoretically analyzes electronic ordering in AA-stacked bilayer graphene and the role played by the Coulomb interaction in these many-body phenomena. We use random phase approximation to account for screening. The screened interaction between charge carriers located in the same graphene layer is much stronger than that between the electrons moving in different layers (moreover, under certain circumstances the inter-layer effective interaction becomes attractive). At zero doping, the Coulomb repulsion stabilizes the spin-density wave state. The Néel temperature for this phase is estimated to be about several tens of kelvin. The spin-density wave is the dominating order in undoped system, but it is destroyed completely by sufficiently strong doping, allowing a superconducting phase to emerge. Investigating possible superconductivity mechanisms, we find that the effective inter-layer interaction can give rise to superconductivity. However, the corresponding critical temperature is negligibly small, and phonon-mediated attraction must be introduced into the model to make the superconductivity observable. Strong intra-layer Coulomb repulsion favors the order parameters that couple electrons in different layers. Two types of the superconducting phase can respect this constraint. The first type is a superconductivity with Cooper pairs having zero total momentum. Such superconductivity exists if the coupling between electrons with momenta near different Dirac cones dominates, or Fermi surface trigonal warping is significant. When the interaction between electrons near the same Dirac cones is larger, and the trigonal warping is weak, the Cooper pairs have non-zero momentum evenin the ground state. Superconductivity is sensitive to doping.