Quantum anomalous Hall effect and related topological electronic states

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.

PACS:

• 73.43-f quantum Hall effect
• 03.65.Vf Berry's phase
• 71.20-b band structure
• 14.80.Hv magnetic monopoles

Keywords:

• anomalous Hall effect
• quantum anomalous Hall effect
• topological invariants
• Chern number and Chern insulators
• topological electronic states
• first-principles calculation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

H.M.W., X.D. and Z.F. are supported by the National Science Foundation of China, the 973 program of China [grant number 2011CBA00108 and 2013CB921700], and the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (No. XDB07020100). R.Y. and X.H. are supported by the WPI Initiative on Materials Nanoarchitectonics, and partially by Grant-in-Aid for Scientific Research under the Innovative Area “Topological Quantum Phenomena” [grant number 25103723], MEXT, Japan.