Charge density wave order in twisted niobium diselenide: a machine-learning interatomic approach

Niobium diselenide has garnered significant attention over the past decade due to the coexistence of superconductivity and charge density waves (CDWs), observable down to the monolayer limit. Introducing relative twist angles between monolayers, in the field of twistronics, offers a new variable to tune these systems, yet a fundamental question remains: do CDWs persist in moiré structures, and how are they altered compared to the pristine monolayer/bilayer? Traditional first-principles methods face limitations due to the computational resources required for long-wavelength moiré patterns; for instance, a 1-degree twist angle necessitates modeling over 10,000 atoms, making simulations impractical. This study employs ab-initio data to develop machine learning interatomic potentials with the ALLEGRO architecture, enabling scalable and accurate simulations. We investigate the formation and evolution of CDW order in monolayers and twisted bilayers, validating our results against density functional theory calculations with minimal errors in energy and forces. Our findings demonstrate the persistence of CDWs in moiré structures, characterized by a mosaic-like pattern. Beyond niobium diselenide, our goal is to establish a protocol for studying CDWs in two-dimensional systems. We outline strategies for producing training data and perform a detailed hyperparameter scan to identify key aspects for studying these systems. Expanding our approach to multilayers while considering factors like doping, strain, and substrates may refine CDW behaviors, paving the way for new technological applications and scientific insights.