- Open Access
Nonmonotonic Band Flattening near the Magic Angle of Twisted Bilayer
Phys. Rev. X 15, 041043 – Published 5 December, 2025
DOI: https://doi.org/10.1103/q11l-9jy1
Abstract
Twisted bilayer () is an emergent platform for exploring exotic quantum phases driven by the interplay between nontrivial band topology and strong electron correlations. Direct experimental access to its momentum-resolved electronic structure is essential for uncovering the microscopic origins of the correlated topological phases therein. Here, we report angle-resolved photoemission spectroscopy measurements of , revealing pronounced twist-angle-dependent band reconstruction shaped by orbital character, interlayer coupling, and moiré potential modulation. Density functional theory captures the qualitative evolution, yet underestimates key energy scales across twist angles, highlighting the importance of electronic correlations. Notably, the hole effective mass at the point exhibits a nonmonotonic dependence on twist angle, peaking near 2°, consistent with band flattening at the magic angle predicted by continuum models. Via electrostatic gating and surface dosing, we further visualize the evolution of electronic structure versus doping, enabling direct observation of the conduction band minimum and confirm as a direct band gap semiconductor. These results establish a spectroscopic foundation for modeling and engineering emergent quantum phases in this moiré platform.
Physics Subject Headings (PhySH)
Popular Summary
Twisted bilayer () is an emerging platform for exploring exotic quantum phases that arise from the interplay between strong electron interactions and nontrivial band topology. Previous work has mostly relied on transport measurements, leaving open questions about the material’s underlying electronic structure. Here, we use angle-resolved photoemission spectroscopy (ARPES) to directly observe how the electronic bands of change with twist angle and doping.
The energy band shapes shift dramatically as the layers are rotated. In particular, the curvature of the topmost valence band—related to how easily holes can move—changes in a nonmonotonic way: It becomes flattest near a twist angle of 2°, matching predictions of a “magic angle” where electron motion slows and correlations strengthen. Using high-spatial-resolution ARPES measurements, we quantify how this curvature, or “effective mass,” varies with both allowed electron momenta and twist angle. The most pronounced flattening occurs near 2°, particularly in the regions of momentum space that govern transport properties, signaling the strongest localization of electrons and identifying the regime where correlated topological phases are most likely to appear.
We also track how the band structure evolves when extra holes or electrons are added, using both electrostatic gating and potassium dosing. The potassium dosing allows us to see the bottom of the conduction band directly, confirming that is a direct-gap semiconductor with an energy gap of 1.14 eV.
These results provide a detailed spectroscopic view of how twist angle and doping shape the electronic structure of . Our findings establish this system as a tunable platform for engineering interaction-driven quantum phases and motivate future low-temperature ARPES studies to resolve the predicted minibands near the magic angle.
Article Text
Supplemental Material
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