Quantum anomalous Hall effect in real materials

Under a strong magnetic field, the quantum Hall (QH) effect can be observed in two-dimensional electronic gas systems. If the quantized Hall conductivity is acquired in a system without the need of an external magnetic field, then it will give rise to a new quantum state, the quantum anomalous Hall (QAH) state. The QAH state is a novel quantum state that is insulating in the bulk but exhibits unique conducting edge states topologically protected from backscattering and holds great potential for applications in low-power-consumption electronics. The realization of the QAH effect in real materials is of great significance. In this paper, we systematically review the theoretical proposals that have been brought forward to realize the QAH effect in various real material systems or structures, including magnetically doped topological insulators, graphene-based systems, silicene-based systems, two-dimensional organometallic frameworks, quantum wells, and functionalized Sb(111) monolayers, etc. Our paper can help our readers to quickly grasp the recent developments in this field.