Theory of Quasicrystals in Twisted Bilayer Graphene on Hexagonal Boron Nitride

POSTER

Abstract

We discuss the theoretical aspects of lattice relaxation in twisted bilayer graphene on hexagonal boron nitride (hBN) that are inspired by experimental investigations conducted by X. Lai et al. Despite the incommensurate nature of the graphene-hBN moiré interference pattern with respect to the twisted bilayer graphene (TBG) lattice, except for a few isolated commensurate twists, we discover a broad spectrum of relative alignments where lattice relaxation leads to the reestablishment of commensuration. Beyond a specific range of relative twists, where there is no separation between the moiré pattern and the emergent moiré-of-moiré scale, relaxation can no longer restore commensurability. In this regime, we observe the formation of a moiré quasicrystal characterized by the superposition of incommensurate periodicities. We also explore the implications for transport experiments involving these devices. Adjusting the alignment of TBG and hBN presents an intriguing means to manipulate and explore interactive physics within moiré patterns with new emergent periodicities.

* Work supported by the US Department of Energy DOE-FG02-99ER45742 (XL, EYA); the Gordon and Betty Moore Foundation EPiQS initiative grant GBMF9453 (XL, EYA); the Air Force Office of Scientific Research under Grant No. FA9550-20-1-0136 (JHP); NSF CAREER grant DMR-1941569 (JHP); the Sloan Research Fellowship (JHP); NSF CAREER grant DMR-2238895 (JHW). The Flatiron Institute is a division of the Simons Foundation.

Presenters

  • Daniele Guerci

    Center for Computational Quantum Physics, Flatiron Institute

Authors

  • Daniele Guerci

    Center for Computational Quantum Physics, Flatiron Institute

  • Xinyuan Lai

    Rutgers University, New Brunswick

  • Guohong Li

    Rutgers University, New Brunswick, Rutgers University

  • Kenji Watanabe

    National Institute for Materials Science, NIMS, Research Center for Electronic and Optical Materials, National Institute for Materials Science, Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan, National Institute for Material Science

  • Takashi Taniguchi

    Kyoto Univ, National Institute for Materials Science, Research Center for Materials Nanoarchitectonics, Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, National Institute for Materials Sciences, NIMS, International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan, National Institute for Material Science, International Center for Materials Nanoarchitectonics, NIMS, Japan, International Center for Materials Nanoarchitectonics, Tsukuba, National Institue for Materials Science, Kyoto University, National Institute of Materials Science, International Center for Materials Nanoarchitectonics and National Institute for Materials Science

  • Justin H Wilson

    Louisiana State University

  • Jed H Pixley

    Rutgers University

  • Eva Y Andrei

    Rutgers University