Machine learning modeling of the self-assembly of one-dimensional nanostructures from two-dimensional MoS₂ monolayers with defect and strain engineering

The chalcogen point vacancies, ubiquitous in a wide range of two-dimensional (2D) transition-metal dichalcogenides (TMDs), are experimentally observed to agglomerate forming extended line defects. We show that a discrepancy in the density of defects between the two chalcogen sides of MoS₂ monolayers can lead to spontaneous curling and further self-assembly of various 1D nanostructures such as nanotubes and nanoscrolls. The large length and time scales needed to simulate this process make the usage of density functional theory (DFT) unfeasible. Instead of empirical potentials which suffer from their low accuracies, we develop a neural network potential (NNP) to drive our simulations at a comparable cost to empirical potentials while retaining the quantum-mechanical accuracy of DFT. The NNP model is first used to run Monte Carlo (MC) simulations to identify the long-scale arrangements of vacancy defects at various vacancy concentrations. Then, NNP is utilized to run molecular dynamics (MD) simulations to model the self-assembly process. We provide a meticulous investigation of the effects of vacancy concentration and degree of strain on the self-assembly process. The usage of a machine learning potential helps to accurately approximate the experimental reality of the self-assembly process, which leads to a more accurate geometry of the formed 1D nanostructures to study their electronic and magnetic properties.