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 motivated theoretical discussions on the possibility of quantum anomalous Hall crystal (QAHC), a topological version of Wigner crystal. Conventionally Wigner crystal was assumed to have a period a_crystal=1/√n locked to the density n. In this work we propose new types of topological Wigner crystal labeled as QAHC-z with period a_crystal=z/√n. In rhombohedrally stacked graphene aligned with hexagon boron nitride~(hBN), we find parameter regimes where QAHC-2 and QAHC-3 have lower energy than the conventional QAHC-1 at the total filling ν=1 per moiré unit cell. They all have total Chern number C=1 and are consistent with the QAH effect in the experiment. The larger period QAHC states gain from the kinetic energy due to the unique Mexican-hat dispersion, which can compensate the loss in the interaction energy. Unlike QAHC-1, QAHC-2 and QAHC-3 also break the moir\'e translation symmetry and are sharply distinct from a moir\'e band insulator. We also briefly discuss the competition between integer QAHC and fractional QAHC states at filling ν=2/3.