Observation of fractionally quantized anomalous Hall effect

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. 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

$$\frac{3}{2}h/{e}^{2}\pm 1 \%$$

3 2 h / e 2 ± 1 % and

$$\frac{5}{3}h/{e}^{2}\pm 3 \%$$

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.