Quantum Anomalous Hall Effects

Quantum anomalous Hall effect is a kind of Hall effect. It is the "quantum" version of the anomalous Hall effect. While the anomalous Hall effect requires a combination of magnetic polarization and spin-orbit coupling to generate a finite Hall voltage even in the absence of an external magnetic field (hence called "anomalous"), the quantum anomalous Hall effect is its quantized version. The Hall conductivity acquires quantized values proportional to integer multiples of the conductance quantum ( {\displaystyle {\frac {e^{2}}{h}}} {\displaystyle {\frac {e^{2}}{h}}}), and is similar to the quantum Hall effect in this regard. The integer here is equal to the Chern number which arises out of topological properties of the material band structure. These effects are observed in systems called quantum anomalous Hall insulators (also called Chern insulators). The effect has been observed experimentally. In the present book, fifteen typical literatures about Quantum Anomalous Hall Effects published on international authoritative journals were selected to introduce the worldwide newest progress, which contains reviews or original researches on Stealing PINs via mobile sensors, predict autochthony, bust estimation and moment selection, etc. We hope this book can demonstrate advances in Quantum Anomalous Hall Effects as well as give references to the researchers, students and other related people.