New classes of quantum anomalous Hall crystals in multilayer graphene (2411.04174v2)

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. 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 $\nu=1$ per moir\'e 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 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 $\nu=2/3$. 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.