Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene

Recent experiments showing an integer quantum anomalous Hall effect in pentalayer rhombohedral graphene have been interpreted in terms of a valley-polarized interaction-induced Chern band. The resulting many-body state can be viewed as an Anomalous Hall Crystal (AHC), with a further coupling to a weak moir\'e potential. We explain the origin of the Chern band and the corresponding AHC in the pentalayer system. We propose a simplified model that focuses on the physics near high symmetry Brillouin zone points to describe the competition between AHC and Wigner Crystal (WC) phases. We discuss the possible role of the moir\'e potential. We emphasize that even if in the moir\'e-less limit, the AHC is not favored over a correlated Fermi liquid, the moir\'e potential will push the system into a `moir\'e-enabled AHC'. We also suggest that there is a range of alignment angles between R5G and hBN where a C = 2 insulator may be found at integer filling.