Dynamic Moir\'e Potentials and Robust Wigner Crystallization in Large-Scale Twisted Transition Metal Dichalcogenides

TL;DR

This paper introduces a machine-learning workflow to study the dynamical evolution of large-scale moiré systems in twisted TMDs, revealing how lattice vibrations influence electronic states and facilitate Wigner crystallization.

Contribution

It develops an integrated ML-based approach combining DeePMD, DeepH, and first-principles calculations to analyze time-dependent structural and electronic responses in large moiré supercells.

Findings

Lattice vibrations deepen moiré potential wells and narrow conduction bands.

Dynamical effects promote formation of localized electronic states.

DFT and DMRG simulations show robust Wigner crystallization and kagomé electron patterns.

Abstract

Understanding the dynamical evolution of large-scale moir\'e systems is crucial for connecting theoretical predictions with experimental observations. Here we develop a machine-learning-based workflow, integrating DeePMD and DeepH frameworks with first-principles calculations, to efficiently investigate time-dependent structural and electronic responses in twisted bilayer transition metal dichalcogenides (TMDs) with experimentally relevant moir\'e supercells containing over 3000 atoms. Using $\mathrm{WS_2}$ as a representative system, we show that low-temperature lattice vibrations and relaxation deepen the moir\'e potential wells, narrow the lowest conduction band, and facilitate the formation of strongly localized electronic states. Based on DFT-derived moir\'e potentials that incorporate these dynamical effects, density-matrix-renormalization-group (DMRG) simulations reveal robust Wigner crystallization and a kagom\'e-patterned three-electron state, consistent with recent experimental observations. Our workflow provides a practical route for exploring large moir\'e supercells beyond static configurations and offers new insight into the interplay between lattice dynamics, electronic localization, and emergent correlated states in twisted two-dimensional materials.