Transferable Dispersion-Aware Machine Learning Interatomic Potentials for Multilayer Transition Metal Dichalcogenide Heterostructures

Stacking atomically thin layers of transition metal dichalcogenides (TMDs) to form heterostructures provides a powerful and versatile platform for investigating exotic quantum phases. Controlling the twist-angle between the TMDs creates moir\'e superlattices that fundamentally alter their electronic and optical response. This has led to fascinating discoveries such as novel excitons, fractional quantum hall states, and unconventional magnetism. The emergence of many of these unique electronic phases can be attributed to substantial structural rearrangement of atoms within the moir\'e pattern. Hence, understanding the structural reconstruction of TMD moir\'e superlattices is the essential first step to understanding its unique electronic and optical properties. However, due to the large number of atoms in a moir\'e unit-cell, studying this reconstruction using density functional theory (DFT) is computationally prohibitive. The spacing between atoms in TMD bilayers can be as large as 10 $\mathrm{\AA}$, making traditional neural network potentials (NNPs) inefficient to account for long-range van der Waals interactions. Here, we develop a new NNP architecture that is general, transferrable and includes long-range dispersion corrections that accounts for van der Waals interactions up to 12 $\mathrm{\AA}$ with minimal computational overhead. The NNP is fitted to van der Waals corrected DFT calculations for layered semiconducting TMDs containing transition metals Mo and W and chalcogens S, Se and Te. This NNP is accurate for monolayers, homobilayers and heterostructures as well as their interaction with commonly used hexagonal boron nitride substrates. The NNP shows excellent performance with respect to van der Waals-corrected DFT on equilibrium lattice parameters, potential energy surface and phonon dispersions. Furthermore, we accurately reproduce the experimentally measured reconstruction of twisted WS\text{$_2$} and MoS\text{$_2$}/WSe\text{$_2$} heterostructures and demonstrate the role played by the substrate in the measured corrugation amplitude. These results suggest that our NNP can be used to compute a wide range of properties of semiconducting TMDs with the accuracy of DFT while maintaining excellent computational efficiency.