From Breakthrough to Review: The Quantum Anomalous Hall Effect

A central theme in condensed matter physics is to create and understand the exotic states of matter by incorporating magnetism into topological materials. One prime example is the quantum anomalous Hall (QAH) state. The QAH effect can be considered as a zero magnetic field manifestation of the integer quantum Hall effect, which carries spin-polarized dissipation-free chiral edge current. After decades of theoretical prediction, the experimental realization of the QAH state became possible in 2006 with the discovery of topological insulators (TIs). In 2013, the QAH effect was first observed in Cr-doped (Bi,Sb)₂Te₃ films, followed in 2015 by a nearly-ideal quantization in V-doped (Bi,Sb)₂Te₃ films. In this talk, I will trace the experimental path that led to these breakthroughs and discuss how the QAH field has since grown into a vibrant and rapidly developing area of research. I will highlight magnetic TI multilayers as a platform for axion insulators, tunable high-Chern-number QAH states, parity-anomaly states, and semi-Weyl semimetal phases, and discuss their integration with superconductors to pursue chiral Majorana modes. Since 2020, a growing class of manually exfoliated layered materials, including intrinsic magnetic TI MnBi₂Te₄, twisted bilayer graphene, and AB stacked MoTe₂/WSe₂, has also been shown to host the QAH effect. In 2022, together with Chao-Xing Liu and Allan MacDonald, we wrote a comprehensive Reviews of Modern Physics article on the QAH effect. I will share the perspective behind writing this article and how we organized a rapidly evolving literature. Finally, I will discuss the recent discovery of fractional QAH states in rhombohedral multilayer graphene and twisted transition-metal dichalcogenide moiré materials, and their implications for the future of QAH physics.