Anomalous quantum oscillations in AA and AB bilayer graphene

We study the quantum oscillations in AA and AB graphene bilayers with broken intralayer P-symmetry in the presence of a gate voltage. We consider both doped (weakly) and undoped cases. The presence of a gate voltage leads to the appearance of an inverted band region in the spectrum of the bilayer, which results in additional peaks in the density of states oscillations. We demonstrate the existence of oscillations in the dielectric phase when the chemical potential is pinned within band gap. These effects are analyzed for different types of layer stacking in a bilayer. It is shown that the graphene bilayer is better suited for the experimental study of anomalous oscillations compared to narrow-gap topological insulator. It is worth mentioning that our results can be applied to other graphene-like bilayer materials, such as transition metal dichacolgenides bilayers.