Observation of Fractionally Quantized Anomalous Hall Effect (2308.02657v1)

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 moir\'e 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.

• The paper reports the direct observation of both integer and fractional QAH effects in a twisted bilayer MoTe₂ system at zero magnetic field.
• The paper demonstrates that distinct Hall resistance plateaus at v = -1, -2/3, and -3/5 confirm quantization with Chern numbers of -1, -2/3, and -3/5 respectively.
• The paper observes a half-filled state near v = -1/2 resembling composite Fermi liquid behavior, indicating a compressible phase with potential for novel quantum explorations.

Observation of Fractionally Quantized Anomalous Hall Effect

The paper of exotic quantum phases continues to enrich the field of condensed matter physics. One such intriguing area is the exploration of the quantum Hall effects under minimal magnetic field conditions, specifically through the quantum anomalous Hall (QAH) effect. This paper reports the direct empirical observation of both integer and fractional QAH effects within a twisted bilayer MoTe₂ system. These observations not only reinforce the theoretical premise of QAH phenomena being possible without external magnetic fields but also extend the scope to fractional cases, showcasing the intriguing interplay between strong electron correlations and topology.

Key Findings:

The research delineates the electrical transport measurements on a twisted bilayer MoTe₂, revealing distinct plateaus in the Hall resistance (R_xy) and specific longitudinal resistance (R_xx) behaviors indicative of both integer and fractional QAH states. The salient findings include:

• Integer QAH State: At zero magnetic field and a filling factor, v = -1, an extended plateau in R_xy is observed, quantized to h/e² with vanishing R_xx, underlining the expected integer QAH effect with a Chern number of C = -1.
• Fractional QAH States: Remarkable observations include distinct features at v = -2/3 and v = -3/5, where R_xy demonstrates fractional plateaus quantized to 3h/2e² and 5h/3e², with respective small R_xx. The behavior exhibits Chern numbers of C = -2/3 and C = -3/5, reflecting fractional quantization analogous to fractional quantum Hall effects traditionally seen under high magnetic fields.
• Half-filled QAH State: Near the half filling (v = -1/2), the system shows a resistance behavior that resembles composite Fermi liquid states, suggesting a compressible phase without a clear energy gap, aligning with theoretical predictions for a zero-field composite Fermi liquid state.

Implications and Future Directions:

The confirmation of FQAH states at zero magnetic field opens new avenues in condensed matter physics, particularly concerning topological quantum computing and the paper of exotic excitations like anyons, which are posited to obey non-trivial statistics. Practically, the observation in MoTe₂ suggests a viable material platform for such studies, highlighting its robustness and tunability via electric fields and specific twist angles.

Moving forward, continued research could focus on refining the experimental setup to explore other fractional fillings and potential interactions with optical phonons or other quasiparticles. There is also a keen interest in understanding the transitions between these topological states under varying external conditions, like pressure or electrical gating.

Further theoretical and experimental studies are warranted to explore the conditions under which the fractional quantization persists and to better understand the anyonic excitations potentially present in these systems. The insights gained from these experiments could proliferate new quantum phases and have profound impacts on the development of topological quantum devices. The continued advancement in material quality and fabrication techniques ensures that these ambitious goals remain a tangible pursuit for the condensed matter community.