New Classes of Quantum Anomalous Hall Crystals in Multilayer Graphene

The recent experimental observation of quantum anomalous Hall (QAH) effects in the rhombohedrally stacked pentalayer graphene has motivated theoretical discussions on the possibility of quantum anomalous Hall crystal (QAHC), a topological version of Wigner crystal. Conventional topological Wigner crystals typically have one electron per unit cell. In this Letter we propose new types of topological Wigner crystals labeled as QAHC-z, with z electrons per unit cell. In the pentalayer graphene system, we find parameter regimes where QAHC-2 and QAHC-3 have lower energy than the conventional QAHC-1 at total filling ν=1 per moiré unit cell. These states all have total Chern number C_{tot}=1 and are consistent with the QAH effect observed in the experiments. The larger period QAHC states have lower kinetic energy due to the unique Mexican-hat dispersion of the pentalayer graphene, which can compensate for the loss in the interaction energy. Unlike QAHC-1, QAHC-2, and QAHC-3 break the moiré translation symmetry and are sharply distinct from a moiré band insulator. We also briefly discuss the competition between integer QAH and fractional QAH states at filling ν=2/3. Moreover, we find that a stronger moiré potential can significantly change the phase diagram and even favors a QAHC-1 ansatz with C=2 Chern band.