Modeling mechanical relaxation in incommensurate trilayer van der Waals heterostructures

Ziyan Zhu, Paul Cazeaux, Mitchell Luskin, and Efthimios Kaxiras
Phys. Rev. B 101, 224107 – Published 8 June 2020

Abstract

The incommensurate stacking of multilayered two-dimensional materials is a challenging problem from a theoretical perspective and an intriguing avenue for manipulating their physical properties. Here we present a multiscale model to obtain the mechanical relaxation pattern of twisted trilayer van der Waals (vdW) heterostructures with two independent twist angles, a generally incommensurate system without a supercell description. We adopt the configuration space as a natural description of such incommensurate layered materials, based on the local environment of atomic positions, bypassing the need for commensurate approximations. To obtain the relaxation pattern, we perform energy minimization with respect to the relaxation displacement vectors. We use a continuum model in combination with the generalized stacking fault energy to describe the interlayer coupling, obtained from first-principles calculations based on density functional theory. We show that the relaxation patterns of twisted trilayer graphene and WSe2 are “moiré of moiré,” as a result of the incommensurate coupling two bilayer moiré patterns. We also show that, in contrast to the symmetry-preserving in-plane relaxation in twisted bilayers, trilayer relaxation can break the two fold rotational symmetry about the xy plane when the two twist angles are equal.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
4 More
  • Received 13 November 2019
  • Revised 19 April 2020
  • Accepted 20 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.224107

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ziyan Zhu1, Paul Cazeaux2, Mitchell Luskin3, and Efthimios Kaxiras1,4

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, USA
  • 3School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 4John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 101, Iss. 22 — 1 June 2020

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×