Elusive Quantum State with Fractional Charge Finally Detected in Twisted Material

Scientists are increasingly focused on understanding fractional charge excitations within strongly correlated materials. Haiyang Pan, Shunshun Yang, and Yuzhu Wang, from Nanyang Technological University, along with Xiangbin Cai, Wei Wang, and Yan Zhao et al., report the observation of a -1/3 fractional quantum anomalous Hall (FQAH) state in twisted MoTe2 bilayers. This finding is significant because the theoretically predicted v = -1/3 FQAH state has proven difficult to detect, with ongoing discussion regarding whether it represents a charge density wave or a topological Chern insulator. By employing photoluminescence and reflective magnetic circular dichroism, the researchers demonstrate ferromagnetic behaviour at multiple filling factors, providing evidence for a fragile, yet topologically non-trivial, state at v = -1/3, supported by exact diagonalization calculations.

This state, theoretically predicted but previously unobserved in similar materials, exhibits fractional charge excitations crucial for advancing quantum materials research.

The work details the detection of ferromagnetic states at filling factors of ν = -1, -2/3, and -1/3, all precisely controlled using a vertical electric field. Corresponding Curie temperatures of approximately 11 K, 3.5 K, and 2.4 K were measured for these states, revealing a fragile nature of the -1/3 state, potentially explaining its absence in earlier investigations.
Utilising photoluminescence (PL) and reflective magnetic circular dichroism (RMCD) techniques, researchers identified these states and their tunable properties within the twisted MoTe2 system. The observed PL spectra at ν = -1/3 demonstrate dispersion with increasing out-of-plane magnetic field, strongly indicating a nontrivial topological origin for this state.

This dispersion behaviour provides key evidence supporting the topological nature of the observed quantum state, distinguishing it from alternative explanations like charge density wave formation. Theoretical calculations, employing the exact diagonalization method, corroborate the interpretation of this state as topologically non-trivial, reinforcing the experimental findings.

The identification of the ν = -1/3 FQAH state addresses a long-standing question in the field of twisted moiré systems and fractional quantum Hall physics. This breakthrough builds upon recent observations of other FQAH states in two-dimensional materials, completing a crucial piece of the puzzle for understanding the Jain sequence in these platforms.

The fragile nature of the -1/3 state, emerging over a narrower electric field range and at lower temperatures, highlights the sensitivity of these correlated phases to material quality and experimental conditions. This research paves the way for exploring novel quantum phenomena and potentially developing advanced electronic devices based on topologically protected states.

Optical characterisation of correlated insulating states and fractional quantum anomalous Hall phases

Photoluminescence and reflective magnetic circular dichroism techniques were central to identifying fractional quantum anomalous Hall states in twisted MoTe2 bilayers. Researchers employed these optical methods to probe the emergence of ferromagnetic behaviour at filling factors of -1, -2/3, and -1/3, all controlled via a vertically applied electric field.

Corresponding Curie temperatures of approximately 11 K, 3.5 K, and 2.4 K were determined for these states, revealing a decreasing magnetic order strength as the filling factor decreased. The study focused on the fragile -1/3 state, which appeared over a restricted electric field range and at lower temperatures compared to integer and other fractional states.

Photoluminescence spectra at a filling factor of -1/3 exhibited dispersion with increasing out-of-plane magnetic field, supporting a nontrivial topological origin for this state. This dispersion behaviour provided key evidence against a simple charge density wave interpretation and suggested the presence of topologically protected edge states.

Device fabrication involved creating rhombohedral-stacked MoTe2 bilayer structures with dual gate configurations for precise optical measurements. A targeted twist angle of 3.5° was selected, falling within the range known to promote the emergence of ferromagnetic states. This specific angle facilitated access to topological moiré flat bands and the associated quantum anomalous Hall and fractional quantum anomalous Hall phases. Theoretical calculations, utilising the exact diagonalization method, corroborated the interpretation of the -1/3 state as topologically non-trivial, reinforcing the experimental findings and providing a deeper understanding of the underlying physics.

Correlated Phase Signatures and Electric Field-Tunable Ferromagnetism in Twisted MoTe2 Bilayers

Photoluminescence (PL) intensity measurements reveal prominent features at filling factors of -1/3, -2/3, and -1 on the hole-doped side of the twisted MoTe2 bilayer device. These observations were obtained at a base temperature of 1.5 K, with the PL intensity exhibiting sharp suppression and a blueshift in emission peak when correlated phases form.

The reduction in PL intensity arises from gap opening in these correlated phases, decreasing the free carrier density available for trion emission. Analysis of the PL data allows for the determination of a moiré density of 3.59x 10 12cm -2 , corresponding to an effective twist angle of 3.5°. Reflective magnetic circular dichroism (RMCD) measurements demonstrate electric field-tunable ferromagnetism associated with these states, notably extending to the fractional filling of ν = -1/3.

This ferromagnetic response at ν = -1/3 is a key finding, differing from previous reports that did not observe such signatures at this fractional filling. Temperature-dependent RMCD measurements at ν = -1/3 yield a Curie temperature of 2.4 K, which is lower than the 3.5 K observed for the ν = -2/3 state, suggesting a weaker spin exchange strength.

The carrier density corresponding to ν = -1/3 evolves linearly with magnetic field, consistent with a topologically non-trivial origin as supported by theoretical calculations. ΔRMCD signal analysis reveals enhanced responses near correlated insulating states at ν = -1, -2/3, and -1/3, evidencing intrinsically spin-polarized correlations. The Curie temperature for the ν = -1 state is approximately 11 K, providing further characterization of the ferromagnetic behaviour across different filling factors.

The -1/3 state emerges over a narrower electric field range and at a lower temperature compared to the integer and other fractional states, indicating a fragile nature that may explain its absence in prior studies. PL spectra at ν = -1/3 disperse with increasing out-of-plane magnetic field, supporting a nontrivial topological origin for this state.

Ferromagnetic order and fractional anomalous Hall effect in MoTe2 bilayers

Detection of a fractional anomalous Hall state at filling factor -1/3 in twisted MoTe2 bilayers has been achieved using photoluminescence and reflective magnetic circular dichroism techniques. These measurements reveal ferromagnetic order at filling factors of -1, -2/3, and -1/3, all controlled via an applied electric field, with corresponding Curie temperatures of approximately 11 K, 3.5 K, and 2.4 K respectively.

The observation of the -1/3 state is particularly noteworthy as it emerges under specific conditions, a narrow electric field range and lower temperature, suggesting a fragile state previously difficult to observe. The findings are supported by theoretical calculations employing the exact diagonalization method, which corroborate the interpretation of a topologically non-trivial state at this filling factor.

Importantly, the observed orbital density is uniform, excluding the possibility of charge density wave formation and aligning with the characteristics of a fractional Chern insulator. These combined experimental and theoretical results establish the emergence of a fractional quantum anomalous Hall state at ν = -1/3, consistent with prior observations of similar states.

The authors acknowledge the limited range over which the -1/3 state is observed, indicating its sensitivity to experimental conditions. Future research will focus on directly detecting the chiral edge state or quantized Hall resistance through transport measurements, requiring improvements in device uniformity and contact engineering. Further spectroscopic studies and device engineering may also reveal additional fractional phenomena and facilitate control of these exotic states for potential quantum information technologies.