中文摘要：

量子反常霍尔绝缘体，有时也被称为陈数绝缘体，是不同于普通绝缘体和拓扑绝缘体的一类新的二维绝缘体，该体系具有可被实验观测的特殊物理性质一量子反常霍尔效应。该体系的物态不能用朗道对称性破缺理论来描写，而要用到拓扑物态的概念。它的发现也经历了从反常霍尔效应的内秉物性阐释，到量子自旋霍尔效应与拓扑绝缘体的发现，再到磁性拓扑绝缘体的理论预测与实现，并最终成功实验观测的漫长过程。由于量子反常霍尔效应的实现不需要外加磁场，而此时样品的边缘态可以被看成一根无能耗的理想导线，因此人们对于其将来可能的应用充满了期待。本文将从理论的角度简单综述该领域的发展历程、基本概念、以及相关的材料系统。

英文摘要：

Quantum anomalous Hall insulator, also called as Chern insulator, is a new two- dimensional insulator distinguished from normal insulator and topological insulator by possess- ing a special and experimentally observable physical property--quantum anomalous Hall effect （QAHE）. This is a novel quantum state can not be described by the Landau symmetry breaking theory but by the concept of topology of band structure. Its discovery experienced a long his- tory： from the explanation of intrinsic contribution to anomalous Hall effect, to the discovery of quantum spin Hall effect and topological insulator, to the prediction and realization of magnetic topological insulator, and finally to the experimental observation of it. Since QAHE does not require external magnetic field and has dissipationless （without lost of kinetic energy that being transferred to thermal energy） conducting edge states which can be used as an ideal conducting wire, it is expected to have various potential applications in future. This paper gives a review of this field on its history, basic concepts and related materials from the theoretical point of view.