Abstract
The integer quantum anomalous Hall (QAH) effect is a lattice analog of the quantum Hall effect at zero magnetic field. This striking transport phenomenon occurs in electronic systems with topologically nontrivial bands and spontaneous time-reversal symmetry breaking. Discovery of its putative fractional counterpart in the presence of strong electron correlations, i.e., the fractional quantum anomalous Hall (FQAH) effect, 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 moir\'e unit cell) we see an extended integer QAH plateau in the Hall resistance Rxy that is quantized to h/e² ± 0.1 % while the longitudinal resistance Rxx vanishes. Remarkably, at ν=-2/3 and -3/5 we see plateau features in Rxy at 3h/2e² ± 1% and 5h/3e² ± 3%, respectively, while Rxx remains small. All these features shift linearly in an 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. In addition, at zero magnetic field, Rxy is approximately 2h/e² near half filling (ν = -1/2) and varies linearly as ν is tuned. This behavior resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field. Direct observation of the FQAH and associated effects paves the way for researching charge fractionalization and anyonic statistics at zero magnetic field.