MODELING OF ELECTRONIC DYNAMICS IN TWISTED BILAYER GRAPHENE

Tianyu Kong, Diyi Liu, Mitchell Luskin, Alexander B. Watson

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer-MacDonald PDE model, which is periodic with respect to the bilayer's moiré pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes-Thomas estimates. We then provide extensive numerical computations, which clarify the range of validity of the Bistritzer-MacDonald model.

Original languageEnglish (US)
Pages (from-to)1011-1038
Number of pages28
JournalSIAM Journal on Applied Mathematics
Volume84
Issue number3
DOIs
StatePublished - May 2024

Bibliographical note

Publisher Copyright:
© 2024 Society for Industrial and Applied Mathematics.

Keywords

  • 2D materials
  • electronic properties of materials
  • moiré materials
  • numerical analysis
  • partial differential equations
  • twisted bilayer graphene

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