Topological insulator and the quantum anomalous Hall effect

The quantum Hall effect (QHE) is a quantum phenomenon that occurs on a macroscopic length scale as the result of the non-trivial topological property of a two-dimensional electron system in a strong magnetic field. It has long been expected that QHE can be realized without an external magnetic field such that the effect can be applied in electric devices that consume little energy. The zero-magnetic-field QHE can appear in thin films of magnetic topological insulators as the quantized version of the anomalous Hall effect; i.e., the quantum anomalous Hall effect (QAHE). Here, we review how the ideas of the topological insulator and QAHE were developed and how the QAHE was finally experimentally realized in thin films of a magnetically doped topological insulator. We also discuss the prospect of application of the QAHE in low-energy-consuming devices.