Nucleation and structure of Van der Waals dislocations in 2D materials

Two-dimensional materials such as graphene, h-BN, transition metal dichalcogenides like MoS₂, etc., are an emerging class of technologically exiting materials with exotic mechanical and electronic properties. Moiré patterns are commonly observed when these materials are layered, or when they are grown on crystalline metal substrates. To understand these moiré patterns, we introduce the concept of interlayer or van der Waals (vdW) dislocations, and show that arrays of these vdW dislocations constitute the moiré patterns associated with regions of commensurability and incommensurability between the layers. We note that moiré patterns and defects in the moiré patterns themselves are the result of electronic structure signatures of the weak interactions between the layers, locked into place by strong in-plane interactions in the constituent layers. We explain the wide variety of experimentally observed moiré phenomena, including the distinct moiré patterns formed by various combinations of 2D materials on the same metal support layers, as well as point and line defects in moiré patterns. We then present a theory to explain the nucleation of the vdW dislocations in terms of energy reduction in the system. For example, when finite-sized flakes of 2D materials on larger crystalline substrates are made to grow or rotate, vdW dislocations are nucleated; this observation can be understood within the framework of critical thickness theory from classic thin film mechanics. Finally, we explore the connection between vdW dislocations and microstructure formation in 2D materials synthesis, focusing in particular on the distribution of angles and the formation of grain boundaries in polycrystalline 2D material layers.