A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Chains

Abstract

In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross-section 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 numerical solutions for both models demonstrate the presence of large commensurate regions separated by localized incommensurate domain walls.

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Cited by in corpus (5)

• Moiré of Moiré: Modeling Mechanical Relaxation in Incommensurate Trilayer van der Waals 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 survey of interlayer interaction models for graphene and other 2D materials