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 \moire potential. We explain the origin of the Chern band and the corresponding AHC in the pentalayer system. To describe the competition between AHC and Wigner Crystal (WC) phases, we propose a simplified low-energy description that predicts the Hartree-Fock phase diagram to good accuracy. This theory can be fruitfully viewed as `superconducting ring' in momentum space, where the emergence of Chern number is analogous to the flux quantization in a Little-Parks experiment. We discuss the possible role of the \moire potential, and emphasize that even if in the moir\'e-less limit, the AHC is not favored (beyond Hartree-Fock) over a correlated Fermi liquid, the \moire 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.