Observation of Fractionally Quantized Anomalous Hall Effect

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 MoTe${}_2$. At zero magnetic field, near filling factor $\nu =-1$ (one hole per moiré unit cell) we see an extended integer QAH plateau in the Hall resistance $R_{\text{xy}}$ that is quantized to $h/e^2\pm 0.1\%$ while the longitudinal resistance $R_{\text{xx}}$ vanishes. Remarkably, at $\nu =-2/3$ and $-3/5$ we see plateau features in $R_{\text{xy}}$ at $3h/2e^2\pm 1\%$ and $5h/3e^2\pm 3\%$, respectively, while $R_{\text{xx}}$ 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, $R_{\text{xy}}$ is approximately $2h/e^2$ near half filling ($\nu =-1/2$) and varies linearly as $\nu$ 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.

15 pages, 4 figures for main text. 8 extended data figures

References in corpus (9)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional statistics in anyon collisions
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Observation of the quantum-anomalous-Hall insulator to Anderson insulator quantum phase transition and its scaling behavior
• A super-massive Neptune-sized planet

Cited by in corpus (8)

• Quantum geometry in condensed matter
• Observation of the dual quantum spin Hall insulator by density-tuned correlations in a van der Waals monolayer
• Topological inverse Anderson insulator
• Spinon pairing induced by chiral in-plane exchange and the stabilization of odd-spin Chern number spin liquid in twisted ${\mathrm{MoTe}}_2$
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• On the zero-field quantization of the anomalous quantum Hall effect in moiré 2D layers
• Considerations for extracting moiré-level strain from dark field intensities in transmission electron microscopy
• Probing the fractional quantum Hall phases in valley-layer locked bilayer MoS${}_2$