We consider a coupled system of Dirac operators that finds applications as a macroscopic model of spin and valley polarized gated rhombohedral graphene (RHG) with an arbitrary number of layers as well as in replica models of Floquet topological insulators. We classify all quantum anomalous Hall phases that are compatible with the model and show that a bulk-edge correspondence between bulk phases and chiral edge states carrying a quantized anomalous Hall charge applies. When the displacement field is sufficiently small compared to the inter-layer 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.
Frazier et al. (Fri,) studied this question.