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 work 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 moir\'e unit cell. These states all have total Chern number Ctot=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 moir\'e translation symmetry and are sharply distinct from a moir\'e 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 moir\'e potential can significantly change the phase diagram and even favors a QAHC-1 ansatz with C=2 Chern band.
@article{arxiv.2411.04174,
title = {New classes of quantum anomalous Hall crystals in multilayer graphene},
author = {Boran Zhou and Ya-Hui Zhang},
journal= {arXiv preprint arXiv:2411.04174},
year = {2025}
}