Coincidence Lattices of 2D Crystals: Heterostructure Predictions and Applications

van der Waals heterostructures provide many novel applications due to a combination of properties. However, their experimental construction and theoretical simulation suffer from the incommensurability of 2D crystals with respect to their symmetry and their lattice constants. In this work, we present a simplified method to predict favorable combinations of 2D crystals based on the coincidence lattice method. We present a huge set of possible heterostructures made from transition-metal dichalcogenides, group IV dichalcogenides, graphene, and hexagonal boron nitride. The method is then validated for theoretically and experimentally studied 2D crystals and van der Waals-bonded heterostructures. The power of the approach is demonstrated by comparison of resulting supercell sizes, strain, and relative orientation with experimental and theoretical data available. To display the prospects of this approach, we simulate three heterostructures and analyze the resulting structural and electronic properties, finding favorable stackings and small changes in band alignments in the weakly interacting heterojunction.