Quantum anomalous Hall phases in gated rhombohedral graphene

We consider a coupled system of Dirac operators that models spin- and valley-polarized gated rhombohedral graphene (RHG) with an arbitrary number of layers. We classify all quantum anomalous Hall phases that are compatible with the model and show that a bulk-edge correspondence exists between bulk phases and chiral edge states carrying a quantized anomalous Hall current. When the displacement field is sufficiently small compared to the interlayer coupling in the RHG application, we retrieve the known phases where the charge is given by the number of graphene layers. When the displacement field increases, we identify all possible topological phase transitions and corresponding quantized chiral edge charges. Numerical simulations confirm the theoretical findings.