Observation of fractionally quantized anomalous Hall effect - Park, Heonjoon; Cai, Jiaqi; Anderson, Eric; Zhang, Yinong; Zhu, Jiayi; Liu, Xiaoyu; Wang, Chong; Holtzmann, William; Hu, Chaowei; Liu, Zhaoyu; Taniguchi, Takashi; Watanabe, Kenji; et al. (Nature (London), 2023)
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 MoTe 2 . 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 / e 2 ± 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 3 2 h / e 2 ± 1 % and 5 3 h / e 2 ± 3 % , 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 2 h / e 2 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. Transport measurements in twisted bilayer MoTe 2 reveal quantized Hall resistance plateaus and composite Fermi liquid-like behaviour under zero magnetic field, constituting a direct observation of integer and fractional quantum anomalous Hall effects.