A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Two-Dimensional Lattices

Abstract

In this paper we propose a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The two lattices have slightly different lattice parameters and there is a small relative rotation between them. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. The continuum model recovers both qualitatively and quantitatively the behavior observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching, and bending deformation that accommodate the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters that can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the detail of deformation associated with the domain walls.

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• Van der Waals heterostructures
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• A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Two-Dimensional Lattices
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Cited by in corpus (9)

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• Moiré of Moiré: Modeling Mechanical Relaxation in Incommensurate Trilayer van der Waals Heterostructures
• Energy minimization of 2D incommensurate heterostructures
• Low-energy moiré phonons in twisted bilayer van der Waals heterostructures
• A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Two-Dimensional Lattices
• A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Two-Dimensional Lattices: The hexagonal case
• A mesoscopic model of nanoclusters self-assembly on a graphene Moiré
• Electronic Observables for Relaxed Bilayer 2D Heterostructures in Momentum Space
• A survey of interlayer interaction models for graphene and other 2D materials