Observation of fractionally quantized anomalous Hall effect

Heonjoon Park; Jiaqi Cai; Eric Anderson; Yinong Zhang; Jiayi Zhu; Xiaoyu Liu; Chong Wang; William Holtzmann; Chaowei Hu; Zhaoyu Liu; Takashi Taniguchi; Kenji Watanabe; Jiun-Haw Chu; Ting Cao; Liang Fu; Wang Yao; Cui-Zu Chang; David Cobden; Di Xiao; Xiaodong Xu

doi:10.1038/s41586-023-06536-0

Observation of fractionally quantized anomalous Hall effect

Nature. 2023 Oct;622(7981):74-79. doi: 10.1038/s41586-023-06536-0. Epub 2023 Aug 17.

Authors

Heonjoon Park^#¹, Jiaqi Cai^#¹, Eric Anderson^#¹, Yinong Zhang¹, Jiayi Zhu¹, Xiaoyu Liu², Chong Wang², William Holtzmann¹, Chaowei Hu¹, Zhaoyu Liu¹, Takashi Taniguchi³, Kenji Watanabe⁴, Jiun-Haw Chu¹, Ting Cao², Liang Fu⁵, Wang Yao^{6

7}, Cui-Zu Chang⁸, David Cobden¹, Di Xiao^{1

2}, Xiaodong Xu^{9

10}

Affiliations

¹ Department of Physics, University of Washington, Seattle, WA, USA.
² Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA.
³ Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan.
⁴ Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan.
⁵ Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
⁶ Department of Physics, University of Hong Kong, Hong Kong, China.
⁷ HKU-UCAS Joint Institute of Theoretical and Computational Physics, University of Hong Kong, Hong Kong, China.
⁸ Department of Physics, The Pennsylvania State University, University Park, PA, USA.
⁹ Department of Physics, University of Washington, Seattle, WA, USA. xuxd@uw.edu.
¹⁰ Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA. xuxd@uw.edu.

^# Contributed equally.

PMID: 37591304
DOI: 10.1038/s41586-023-06536-0

Abstract

The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field^1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect^4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe₂. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance R_xy quantized to h/e² ± 0.1%, whereas the longitudinal resistance R_xx vanishes. Remarkably, at ν = -2/3 and -3/5, we see plateau features in R_xy at [Formula: see text] and [Formula: see text], respectively, whereas R_xx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, R_xy is approximately 2h/e² near half-filling (ν = -1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field^8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.