Title:New classes of quantum anomalous Hall crystals in multilayer graphene

Abstract: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. Conventionally Wigner crystal was assumed to have a period $a_{\text{crystal}}=1/\sqrt{n}$ locked to the density $n$. In this work we propose new types of topological Wigner crystals labeled as QAHC-$z$ with period $a_{\text{crystal}}=\sqrt{z/n}$. 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 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 better 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 also break the moiré translation symmetry and are sharply distinct from a moiré band insulator. We also briefly discuss the competition between integer QAHC and fractional QAHC states at filling $\nu=2/3$. Besides, we notice the importance of the moiré potential. A larger moiré potential can greatly change the phase diagram and even favors a QAHC-1 ansatz with $C=2$ Chern band.