The study reveals how this material transitions from hosting valley-polarized, fractional topological states to valley-degenerate correlated states and even superconductivity as the angle changes. At a moiré hole filling factor of νh = 1/2, signatures of an anomalous composite Fermi liquid appear alongside fractional quantum anomalous Hall states. The work uncovers a unified twist-angle-driven phase evolution linking fractional topology, symmetry breaking, magnetic order and superconductivity, providing new insight into the emergent quantum phenomena in moiré systems.
Twist Angle Calibration via Quantum Oscillations
Researchers calibrated the twist angle of fifteen bilayer MoTe2 devices using quantum oscillations under magnetic fields, enabling a systematic mapping of the material’s transport phase diagram. These devices spanned a twist-angle range of 3.79° to 5.76°, a remarkably narrow window for observing substantial changes in quantum behavior. The calculated density of states, as a function of interlayer potential difference and filling factor, further informed the understanding of the observed phases, as shown in the example for a 5.8° twisted device.
The precision in angle calibration is critical for understanding the emergence of correlated electronic states within the moiré superlattice. The team’s approach allows for detailed investigation of how subtle changes in twist angle influence the electronic properties of the bilayer material, providing a foundation for controlling and manipulating these quantum phenomena.
MoTe2’s Tunable Moiré Flat Bands & Topology
Investigations into these moiré systems demonstrate that the low-energy valence bands at the K-valley closely resemble those predicted by continuum models, supporting topologically nontrivial moiré flat bands that emulate the Kane-Mele model. Applied vertical electric fields can induce layer polarization, driving a transition toward a topologically trivial regime, while the resulting quantum phases are predictably dependent on the twist angle.
While theoretical frameworks predicted sensitivity to twist angle, experiments have highlighted a distinction between MoTe2 and twisted bilayer WSe2, with MoTe2 exhibiting robust ferromagnetism alongside integer and fractional Chern insulators over a broad range of angles from 2.1° to 3.9°.
Valley-Polarized Chern Insulators at Small Twist Angles
These observations provide a detailed look at the interplay between topology and electron interactions within the material. As twist angle increases, the observed fractional topological phases are progressively suppressed, with the half-filled Chern band undergoing a reconstruction into symmetry-breaking integer Chern insulating states. At a filling factor of νh = 1, the material exhibits a transition from robust integer quantum anomalous Hall (IQAH) insulators at smaller angles to correlated insulators whose properties are tuned by an applied displacement field at larger angles.
This angle-dependent behavior highlights the sensitivity of the material’s quantum properties to its structural arrangement. Remarkably, superconductivity emerges at twist angles exceeding approximately 5.6°, appearing adjacent to the νh = 1 correlated insulator and mirroring phase diagrams recently reported for twisted bilayer WSe2.
At relatively small twist angles, partially-filled Chern bands host fractional quantum anomalous Hall (FQAH) states following the Jain sequence, together with signatures of an anomalous composite Fermi liquid at moiré hole filling factor νh = 1/2.
The observed transformation demonstrates a sensitivity to structural configuration not previously detailed in similar materials. This phase diagram closely resembles that recently reported in twisted bilayer WSe2. Grey regions on transport measurement maps denote areas inaccessible to electrical measurements, further defining the boundaries of these quantum states.
Correlated Insulating States in Layer-Polarized MoTe2
This observation indicates a systematic shift in the material’s quantum behavior, moving from strongly interacting, valley-polarized topological states at smaller twist angles to a valley-degenerate regime as the angle increases. The weakening of electronic interactions with increasing twist angle is further supported by the evolution of topologically trivial correlated insulating states in the layer-polarized configuration. As the twist angle increases, layer-polarized correlated insulating states become notably weaker, aligning with an increased bandwidth and a reduced interaction-to-kinetic-energy ratio.
These insulating states disappear sequentially with increasing angle, following the order of νh = 1/4, 1/3, 2/3, 1/2 and finally 1. Below approximately 5.2 degrees, a broad insulating region emerges, remaining continuous across filling factors; however, this continuous insulating behavior progressively shrinks with larger angles. Increasing twist angle progressively suppresses fractional topological phases and reconstructs the half-filled Chern band into symmetry-breaking integer Chern insulating states.
Remarkably, superconductivity appears near the correlated insulating state at νh = 1, a phenomenon detailed in the following section. This proximity contrasts with twisted bilayer tungsten diselenide (tWSe2), where ferromagnetism and quantum anomalous Hall states are difficult to stabilize, even at 2.7 degrees, with only trivial correlated insulating behavior reported at νh = 1.
In contrast, 4.69° twisted MoTe2 already exhibits integer quantum anomalous Hall states at νh = 1 and symmetry-breaking correlated insulating states at νh = 1/2. Calculated values of the Van Hove singularity (VHS) across both superconducting and correlated insulating states align well with experimentally extracted VHS data, as shown in temperature-dependent resistivity maps of device 15 at 5.76°.
Superconductivity emerges at twist angles exceeding approximately 5.6°, positioning it near a correlated insulating state and mirroring observations in twisted bilayer tungsten diselenide.
tMoTe2 vs. tWSe2: Contrasting Phase Diagrams
While both twisted bilayer molybdenum ditelluride (tMoTe2) and tungsten diselenide (tWSe2) exhibit valley-degenerate superconductivity emerging near correlated insulating states at larger twist angles, their responses to decreasing angle diverge significantly, revealing fundamental differences in their electronic behavior. Specifically, tMoTe2 demonstrates stronger correlation effects at comparable moiré wavelengths, a consequence of the larger effective mass of monolayer MoTe2, approximately 0.75 electron masses, compared to monolayer WSe2 at 0.4 electron masses.
This manifests as robust correlated insulating behavior in 5.76° tMoTe2, a state absent in 5.0° tWSe2 despite similar moiré wavelengths of 3.5 and 3.8 nanometers, respectively. The differing responses extend to superconducting transition temperatures; 5.0° tWSe2 achieves higher temperatures than its tMoTe2 counterpart, but as twist angles decrease and electronic correlations strengthen, the two materials follow distinct evolutionary paths. Conversely, 4. The most striking contrast emerges in the evolution of the νh-D phase diagrams at smaller twist angles.
For tMoTe2, the topologically trivial correlated insulator within the layer-hybridized regime rapidly diminishes with decreasing twist angle, yielding IQAH states as the system transitions into a topological phase. In stark opposition, the trivial correlated insulating phase in tWSe2 becomes increasingly robust at smaller angles, extending across a broader range of D-field values. Grey regions on the measured diagrams indicate areas where electrical transport measurements were inaccessible, limiting the full characterization of these phases.
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