Observation of Fractionally Quantized Anomalous Hall Effect.

The integer quantum anomalous Hall (QAH) effect is a lattice analog of the quantum Hall effect at zero magnetic field 1-3 . This striking phenomenon occurs in systems with topologically nontrivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, i.e., the fractional quantum anomalous Hall (FQAH) effect 4-7 , would open a new chapter in condensed matter physics. Here, we report direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe 2 . At zero magnetic field, near filling factor [Formula: see text] (one hole per moiré unit cell) we see an integer QAH plateau in the Hall resistance R xy quantized to [Formula: see text] while longitudinal resistance R xx vanishes. Remarkably, at [Formula: see text] and [Formula: see text] we see plateau features in R xy at [Formula: see text] and [Formula: see text], respectively, while R xx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers [Formula: see text], [Formula: see text], and [Formula: see text], precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, R xy is approximately 2[Formula: see text] near half filling ([Formula: see text]) and varies linearly as [Formula: see text] 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 8-14 . Direct observation of the FQAH and associated effects paves the way for researching charge fractionalization and anyonic statistics at zero magnetic field.