Quantized Anomalous Hall Effect in Magnetic Topological Insulators

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.