The Hall effect, the anomalous Hall effect (AHE) and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The AHE, in which a voltage transverse to the electric current appears even in the absence of an external magnetic field, was first detected in ferromagnetic (FM) metals in 1881 and later found to arise from the spin-orbit coupling (SOC) between the current and magnetic moments. Recent progress on the mechanism of AHE has established a link between the AHE and the topological nature of the Hall current by adopting the Berry-phase concepts in close analogy to the intrinsic spin Hall effect. Given the experimental discovery of the quantum Hall and the quantum spin Hall effects, it is natural to ask whether the AHE can also be quantized. In a quantized anomalous Hall (QAH) insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically non-trivial electronic structure, leading to the quantized Hall effect without any external magnetic field.
　  Topological insulators are special insulators with conductive surfaces. Recent theoretical and experimental studies have demonstrated the possibility of growing topological insulator thin films from semiconductor materials, layer by layer, using a highly precise technique called molecular beam epitaxy. In a recent paper, published on Science 329, 61 (2010), Prof. Fang and Dai from the Institute of Physics suggested that QAH effect can be realized in thin film made out of magnetic topological insulators.
　  Based on state-of-art first principles calculations, they predict that the tetradymite semiconductors Bi2Te3, Bi2Se3, and Sb2Te3 form magnetically ordered insulators when doped with transition metal elements (Cr or Fe), in sharp contrast to conventional dilute magnetic semiconductor where free carriers are necessary to mediate the magnetic coupling. Magnetic order in two-dimensional thin films gives rise to a topological electronic structure characterized by a finite Chern number, with quantized Hall conductance e2/h. Experimental realization of the long sought-after QAH insulator state could enable robust dissipationless charge transport at room temperature.
　  This work was supported by the National Natural Science Foundation of China, the Ministry of Science and Technology of China, and the knowledge innovation project of Chinese Academy of Sciences.