Electronic instabilities of the AA-honeycomb bilayer

A functional renormalization group approach is used to study the instabilities due to electron-electron interactions in a bilayer honeycomb lattice model with AA stacking, as it might be relevant for layered graphene with this structure. Starting with a tight-binding description for the four -bands, the modes of the dispersion are integrated out by successively lowering an infrared cutoff and the leading tendencies in the effective interactions are determined. The antiferromagnetic spin-density wave is an expected instability for dominant local repulsion among the electrons, but for nonlocal interaction terms also other instabilities occur. The phase diagrams depending on the model parameters are discussed. The results are compared to single-layer graphene and the more common AB-stacked bilayer, both qualitatively and quantitatively.