Quantum anomalous Hall effect

Abstract Hall effect is a well-known electromagnetic phenomenon that has been widely applied in the semiconductor industry. The quantum Hall effect discovered in two-dimensional electronic systems under a strong magnetic field provided new insights into condensed matter physics, especially the topological aspect of electronic states. The quantum anomalous Hall effect is a special kind of the quantum Hall effect that occurs without a magnetic field. It has long been sought after because its realization will significantly facilitate the studies and applications of the quantum Hall physics. In this paper, we review how the idea of the quantum anomalous Hall effect was developed and how the effect was finally experimentally realized in thin films of a magnetically doped topological insulator.