Malena I. Espanol, School of Mathematical and Statistical Sciences, Arizona State University
Authors: Dmitry Golovaty and Pat Wilber
2022 AWM Research Symposium
Recent Advancements in the Mathematics of Materials

A graphene sheet is a single-atom thick macromolecule of carbon atoms arranged in a honeycomb hexagonal lattice. When observing a graphene sheet suspended over a substrate, moiré patterns appear driven by lattice and orientation mismatches. In this talk, we start by presenting 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. We show that the continuum model recovers both qualitatively and quantitatively the behavior observed in the corresponding discrete model. We then extend the discrete-to-continuum procedure to square lattices and then to the honeycomb hexagonal lattices. In all cases, we observe the presence of large commensurate regions separated by localized incommensurate domain walls, in agreement with experiments.

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