Topological Materials: Quantum Anomalous Hall System

The quantum anomalous Hall effect (QAHE) is a quantized Hall effect that occurs at zero magnetic field. Its mechanism and properties are different from those of conventional quantum Hall effects (QHEs) induced by magnetic field. The first theory of a QHE without a magnetic field was proposed in 1988. Yet, it has taken 25 years to be experimentally realized, which has now happened thanks to the development of the topological insulator—a conceptually new topological state of matter. Here, we review QAHE, beginning with the original theoretical idea and concluding with its final implementation using experimentally accessible materials. The current status and future direction of the field are also discussed.