Exploring charge density waves in twisted bilayer NbSe₂ with machine learning

Introducing a relative twist angle between 2D materials offers a new variable to tune these systems. Twisted bilayer graphene generated significant interest in this area, owing to the emergent superconductivity and correlated insulating states observed. Other 2D materials have been investigated in these moiré structures now, but one class of materials that has not been studied in depth is metallic transition metal dichalcogenides which host charge density waves (CDWs). How CDWs survive in the moiré supperlattice is not known, however. Traditional first-principles methods face limitations in answering this question, owing to the computational resources required for long-wavelength  moiré patterns. For example, a 1 degree twist angle moiré structure of NbSe₂ has over 10,000 atoms, making such simulations impractical. To overcome this challenge, and answer the question of how CDWs are modulated in  moiré superlattices, we develop a machine learning interatomic potential (MLIP) with the Allegro architecture, enabling scalable and accurate simulations. We investigate the formation and evolution of CDW twisted bilayers, validating our results against density functional theory calculations [1]. 

[1] Norma Rivano et al. Exploring Charge Density Waves in NbSe₂ with Machine Learning arXiv.2504.13675 (2025)