Why are most 2D lattices hexagonal? The stability of 2D lattices predicted by a simple mechanics model

For more than half a century, physicists rejected the existence of two-dimensional (2D) materials since they theoretically underestimated the stability. However, the discovery of one-atom-thick graphene proved the inapplicability of this theory. Due to the lack of a proper and universal theory, the prediction of new 2D materials has become a case-by-case process involving a large number of simulations and experiments, which limits the finding of new materials. In this paper, we develop a mechanics model that reveals the hexagonal nature of 2D lattices and elucidates the physical origin of the stability. The proposed model employs the bending stiffness and energy to provide insight into the stability of possible 2D lattices. For instance, chair-type buckled 2D lattices are easier to synthesize than washboard and boat-type lattices. These results are in agreement with the experimental findings. Furthermore, the proposed model can be used as a tool for predicting the stability of novel 2D lattices.