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 $\nu =1$ per moiré unit cell. These states all have total Chern number $C_{\mathrm{tot}}=1$ 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 $\nu =2/3$. 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.

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• Fractional quantum Hall effect
• Quantum anomalous Hall effect
• Graphene
• Wigner crystal