Quantum anomalous Hall effect and related topological electronic states

TLDR

The quantum anomalous Hall effect (QAHE) is a Berry‑curvature–driven topological phase observed in magnetically doped topological‑insulator films, characterized by a nonzero Chern number and dissipationless edge currents that arise when time‑reversal symmetry is broken, linking it to other topological states such as TIs and semimetals and motivating first‑principles studies for material discovery. This review surveys the Berry‑phase mechanism underlying the QAHE and Chern insulators, outlines open challenges and future applications, and highlights remaining issues in the field. The authors employ the Wilson‑loop technique and band‑inversion analysis, supported by first‑principles calculations, to identify and design topological materials.

Abstract

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.