Relaxation and Domain Wall Structure of Bilayer Moiré Systems

Paul Cazeaux, Drake Clark, Rebecca Engelke, Philip Kim, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Moiré patterns result from setting a 2D material such as graphene on another 2D material with a small twist angle or from the lattice mismatch of 2D heterostructures. We present a continuum model for the elastic energy of these bilayer moiré structures that includes an intralayer elastic energy and an interlayer misfit energy that is minimized at two stackings (disregistries). We show by theory and computation that the displacement field that minimizes the global elastic energy subject to a global boundary constraint gives large alternating regions of one of the two energy-minimizing stackings separated by domain walls. We derive a model for the domain wall structure from the continuum bilayer energy and give a rigorous asymptotic estimate for the structure. We also give an improved estimate for the L2-norm of the gradient on the moiré unit cell for twisted bilayers that scales at most inversely linearly with the twist angle, a result which is consistent with the formation of one-dimensional domain walls with a fixed width around triangular domains at very small twist angles.

Original languageEnglish (US)
Pages (from-to)443-466
Number of pages24
JournalJournal of Elasticity
Volume154
Issue number1-4
DOIs
StatePublished - Nov 2023

Bibliographical note

Funding Information:
PC’s research was supported in part by National Science Foundation Award DMS-189220 and Simons Collaboration Grants for Mathematicians No. 966604. DC’s research was supported in part by National Science Foundation Award DMS-1906129. RE’s and PK’s research was supported in part by National Science Foundation Award DMREF Award No. 1922165. ML’s research was supported in part by National Science Foundation Award DMREF Award No. 1922165 and Simons Targeted Grant Award No. 896630.

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.

Keywords

  • 2D materials
  • Domain walls
  • Elasticity
  • Moiré
  • Superlattice

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