Modeling mechanical relaxation in misaligned 2D heterostructures*

Two-dimensional van der Waals layered materials (e.g., twisted bilayer graphene) provide a platform to study correlated many-body physics and have potential device applications. However, these layered systems are computationally challenging to model by conventional methods due to their large supercells. Here, we present a multi-scale model to efficiently calculate the mechanical relaxation pattern in incommensurate van der Waals heterostructures at arbitrary twist angles and lattice mismatch. We adopt a continuum model to describe lattice relaxation and a generalized stacking fault energy, computed from the density functional theory, to account for interlayer couplings. We obtain the optimized structure by minimizing the total energy. Our model extends the computationally accessible regime to layered systems with relatively small twist angles and large moiré patterns. This model can be applied to a wide range of materials, including those with no empirical interlayer coupling potential available, such as graphene and the transition metal dichalcogenides.