标题： 多层石墨烯中的新型量子反常霍尔晶体 显示英文标题

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

摘要： 最近在 rhombohedrally 堆叠的五层石墨烯中观测到的量子异常霍尔（QAH）效应激发了关于量子异常霍尔晶体（QAHC）可能性的理论讨论，这是一种拓扑版本的外尔晶体。 传统的拓扑外尔晶体通常每个单位细胞有一个电子。 在这项工作中，我们提出了新的拓扑外尔晶体类型，标记为 QAHC-$z$，每个单位细胞有$z$个电子。 在五层石墨烯系统中，我们发现参数区域，在这些区域内，QAHC-2 和 QAHC-3 在总填充数$\nu=1$每摩尔单元格中的能量低于常规 QAHC-1。 这些状态总陈数为$C_\mathrm{tot}=1$，与实验中观察到的 QAH 效应一致。 较大的周期 QAHC 状态由于五层石墨烯独特的墨西哥帽色散具有较低的动能，这可以补偿相互作用能的损失。 与 QAHC-1 不同，QAHC-2 和 QAHC-3 打破了摩尔平移对称性，并且明显不同于摩尔带绝缘体。 我们还简要讨论了整数量子异常霍尔和分数量子异常霍尔态在填充$\nu=2/3$时的竞争关系。 此外，我们发现更强的摩尔势能可以显著改变相图，甚至更倾向于$C=2$陈带的 QAHC-1 猜想。 显示英文摘要

摘要： 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.