Epitaxial two-dimensional membranes under intrinsic and extrinsic strains

Abstract

Two-dimensional (2D) materials naturally form moiré patterns with other crystalline layers, such as other 2D material or the surface of a substrate. These patterns add a nanoscale characteristic length in the form of a superlattice: the moiré wavelength. Understanding the origin and characteristics of these patterns is crucial to design/interpret moiré-induced physical properties. Here, we use a mixed continuum mechanics + atomistic modeling to study two experimentally relevant epitaxial 2D materials -- graphene on Ir(111) and MoS${}_2$ on Au(111) -- under extrinsic and intrinsic strain. We consider three different scenarios affecting substantially the lattice constant of the 2D materials, the wavelength and corrugation of the moiré pattern. (i) Under the influence of the interaction with the substrate, bending energy produces non trivial variations of the moiré properties, even when the strain is small; (ii) When locked on a progressively strained substrate via the valleys of the moiré, the membranes' nanorippling amplitude goes through several jumps related to relatively smaller jumps in the interatomic distance of the 2D materials; (iii) Finally, increasing the zero-deformation value of this interatomic distance (possibly controlable with temperature or illumination in experiments) the moiré wavelength can either increase or decrease.

arXiv commentaccepted for publication in Phys. Rev. B, 10 pages, 5 figures

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