Abstract
Two dimensional (2D) materials consist of one to a few atomic layers, where the intra-layer atoms are chemically bonded and the atomic layers are weakly bonded. The high bonding anisotropicity in 2D materials make their growth on a substrate substantially different from the conventional thin film growth. Here, we proposed a general theoretical framework for the epitaxial growth of a 2D material on an arbitrary substrate. Our extensive density functional theory (DFT) calculations show that the propagating edge of a 2D material tends to align along a high symmetry direction of the substrate and, as a conclusion, the interplay between the symmetries of the 2D material and the substrate plays a critical role in the epitaxial growth of the 2D material. Based on our results, we have outlined that orientational uniformity of 2D material islands on a substrate can be realized only if the symmetry group of the substrate is a subgroup of that of the 2D material. Our predictions are in perfect agreement with most experimental observations on 2D materials' growth on various substrates known up to now. We believe that this general guideline will lead to the large-scale synthesis of wafer-scale single crystals of various 2D materials in the near future.