The quantum anomalous Hall effect (QAHE), carrying dissipationless chiral edge states, occurs without any magnetic field. Two main strategies were proposed to host QAHE: the magnetic topological insulator thin films and graphene systems. Only the former one was realized in experiment at low temperature. In this paper, by dealing with the two-dimensional electron gas with an anti-dot lattice, a realistic platform is proposed to host the QAHE with both Chern number $\mathcal{C}=-1$ and $\mathcal{C}=2$. Based on the calculation of Berry curvature and spacial wave function, the topological nature of the QAH edge states is well demonstrated. In the QAH region, the conductance shows quantized plateaus and their values are robust against Anderson disorder. In addition, we have also studied the effects of the size and shape of the anti-dot lattice on QAHE and they provide extra manners to adjust the system parameters. Taking the advantages of the well developed micro-manufacture technique in semiconductors, the proposal is experimentally accessible in micro-scale.

中文翻译：

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二维电子气中量子反常霍尔效应的实现

携带无耗散手征边缘态的量子反常霍尔效应 (QAHE) 在没有任何磁场的情况下发生。提出了两种主要策略来承载 QAHE：磁性拓扑绝缘体薄膜和石墨烯系统。只有前一种在低温实验中实现。在本文中，通过处理具有反点晶格的二维电子气，提出了一个现实的平台来承载陈数 $\mathcal{C}=-1$ 和 $\mathcal{C} 的 QAHE =2美元。基于贝里曲率和空间波函数的计算，很好地证明了 QAH 边缘态的拓扑性质。在 QAH 区域，电导显示出量化的平台期，并且它们的值对安德森障碍具有稳健性。此外，我们还研究了反点阵的大小和形状对QAHE的影响，它们为调整系统参数提供了额外的方式。利用半导体中发达的微制造技术的优势，该提议可在微尺度上进行实验。