Hybrid neural network potential for multilayer graphene

Monolayer and multilayer graphene are promising materials for applications such as electronic devices, sensors, energy generation and storage, and medicine. In order to perform large-scale atomistic simulations of the mechanical and thermal behavior of graphene-based devices, accurate interatomic potentials are required. Here, we present a new interatomic potential for multilayer graphene structures referred to as "hNN--Gr$_x$." This hybrid potential employs a neural network to describe short-range interactions and a theoretically-motivated analytical term to model long-range dispersion. The potential is trained against a large dataset of monolayer graphene, bilayer graphene, and graphite configurations obtained from ab initio total-energy calculations based on density functional theory (DFT). The potential provides accurate energy and forces for both intralayer and interlayer interactions, correctly reproducing DFT results for structural, energetic, and elastic properties such as the equilibrium layer spacing, interlayer binding energy, elastic moduli, and phonon dispersions to which it was not fit. The potential is used to study the effect of vacancies on thermal conductivity in monolayer graphene and interlayer friction in bilayer graphene. The potential is available through the OpenKIM interatomic potential repository at \url{https://openkim.org}.