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    Unified machine-learning framework for structural reconstruction and flat-band formation in twisted bilayer MoSi2N4

    Jiamin Luo1, Chunhui Li2, Lei Shan1,3,*, and Long Cheng1,†

    • *Contact author: leishan@hnu.edu.cn
    • †Contact author: lcheng@hnu.edu.cn

    Phys. Rev. B 114, 045432 – Published 28 July, 2026

    DOI: https://doi.org/10.1103/mlhw-9s3m

    Abstract

    Flat-band engineering in moiré materials is highly sensitive to twist angles, while accurate large-scale simulations remain computationally prohibitive. Here, we develop a unified machine-learning framework that integrates machine-learning interatomic potentials with Hamiltonian graph neural networks to simultaneously capture the lattice reconstruction and electronic structures in twisted bilayer (tb) MoSi2N4. This approach enables efficient and accurate simulations of large-scale moiré superlattices beyond the capability of conventional first-principles methods. We show that flat bands in tb−MoSi2N4 can emerge through two distinct mechanisms. When thermal lattice relaxation is included, strong in-plane reconstruction and out-of-plane corrugation generate a highly inhomogeneous moiré potential landscape, leading to strong electronic localization and ultraflat bands predominantly in the valence band. In contrast, even without lattice relaxation, reducing the interlayer spacing enhances interlayer orbital hybridization, leading to substantial band renormalization and multiple flat bands in the conduction band. Remarkably, flat bands emerge at relatively large twist angles (∼6∘), in contrast to the magic-angle condition in twisted bilayer graphene. The absence of a strict magic-angle condition originates from the distinct physical mechanisms of band flattening, where strong lattice reconstruction and stacking-dependent interlayer coupling create deep moiré potential wells without requiring fine-tuned twist angles. Beyond tb−MoSi2N4, the framework exhibits robust transferability to multilayer and twisted multilayer systems. These results establish a unified physical picture linking lattice reconstruction, interlayer coupling, and flat-band formation; provide an efficient route for large-scale moiré simulations; and offer new opportunities for engineering flat-band physics in two-dimensional materials.

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