标题： 具有更高陈数的莫尔能带中的量子反常霍尔晶体 显示英文标题

标题： Quantum anomalous Hall crystals in moiré bands with higher Chern number

摘要： 在莫尔材料中实现分数陈绝缘体引发了在这个平台上寻找更多新型物质相的研究。特别是，最近的工作已经证明了实现量子反常霍尔晶体（QAHCs）的可能性，这些晶体结合了无磁场下的量子霍尔效应和自发破缺的离散平移对称性。在这里，我们采用精确对角化来证明稳定QAHCs的存在，这些QAHCs来源于填充数为$\frac{2}{3}$的莫尔能带，其陈数为$C=2$。我们的计算表明，这些拓扑晶体具有量化的霍尔电导率$1$（以$e^2/h$为单位）和三倍的原胞，它们在扭曲双层-三层石墨烯的理想模型中是稳定的——为这种异质结构中的实验观测提供了一种新的解释。此外，我们预测QAHC在扭曲双双层石墨烯的实际模型中仍然稳定，并且我们还提供了实现该相位的一系列优化调节参数，即扭转角度和电场。总体而言，我们的工作展示了在奇分母填充下$C=2$能带中QAHC的稳定性，为未来实验提供了具体的指导方针，并建立了手性多层石墨烯作为研究超越朗道能级范式的拓扑相的理论平台。 显示英文摘要

摘要： The realization of fractional Chern insulators in moir\'e materials has sparked the search for further novel phases of matter in this platform. In particular, recent works have demonstrated the possibility of realizing quantum anomalous Hall crystals (QAHCs), which combine the zero-field quantum Hall effect with spontaneously broken discrete translation symmetry. Here, we employ exact diagonalization to demonstrate the existence of stable QAHCs arising from $\frac{2}{3}$-filled moir\'e bands with Chern number $C=2$. Our calculations show that these topological crystals, which are characterized by a quantized Hall conductivity of $1$ (in units of $e^2/h$) and a tripled unit cell, are robust in an ideal model of twisted bilayer-trilayer graphene -- providing a novel explanation for experimental observations in this heterostructure. Furthermore, we predict that the QAHC remains robust in a realistic model of twisted double bilayer graphene and, in addition, we provide a range of optimal tuning parameters, namely twist angle and electric field, for experimentally realizing this phase. Overall, our work demonstrates the stability of QAHCs at odd-denominator filling of $C=2$ bands, provides specific guidelines for future experiments, and establishes chiral multilayer graphene as a theoretical platform for studying topological phases beyond the Landau-level paradigm.