The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators—topologically nontrivial states of two-dimensional matter with broken time-reversal symmetry. In Chern insulators, nontrivial bulk band topology is expressed by chiral states that carry current along sample edges without dissipation. The quantum anomalous Hall (QAH) effect refers to QH effects that occur in the absence of external magnetic fields due to spontaneously broken time-reversal symmetry. The QAH effect has now been realized in four different classes of two-dimensional materials: (i) thin films of magnetically (Cr- and/or V-) doped topological insulators in the $(\mathrm{Bi},\mathrm{Sb}{)}_2{\mathrm{Te}}_3$ family, (ii) thin films of the intrinsic magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, (iii) moiré materials formed from graphene, and (iv) moiré materials formed from transition-metal dichalcogenides. In this Colloquium, the physical mechanisms responsible for each class of QAH insulator are reviewed, with both differences and commonalities highlighted, and potential applications of the QAH effect are commented upon.

中文翻译：

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座谈会：量子反常霍尔效应

量子霍尔（QH）效应，即量子化霍尔电阻与零纵向电阻相结合，是陈绝缘体的特征实验指纹——具有破缺时间反转对称性的二维物质的拓扑非平凡状态。在陈绝缘体中，非平凡的体能带拓扑由手性态表示，这些手性态沿着样本边缘承载电流而不耗散。量子反常霍尔（QAH）效应是指在没有外部磁场的情况下，由于时间反转对称性自发破缺而产生的QH效应。 QAH 效应现已在四种不同类别的二维材料中实现：(i) 磁性（Cr 和/或 V）掺杂拓扑绝缘体薄膜$（双,锑{）}_2{碲}_3$系列，（ii）本征磁拓扑绝缘体薄膜${\mathrm{锰铋}}_2{碲}_4$，(iii)由石墨烯形成的莫尔材料，以及(iv)由过渡金属二硫族化物形成的莫尔材料。在本次研讨会上，回顾了每类 QAH 绝缘体的物理机制，强调了差异和共性，并对 QAH 效应的潜在应用进行了评论。