Torsional periodic lattice distortions and diffraction of twisted 2D materials

Suk Hyun Sung; Yin Min Goh; Hyobin Yoo; Rebecca Engelke; Hongchao Xie; Kuan Zhang; Zidong Li; Andrew Ye; Parag B Deotare; Ellad B Tadmor; Andrew J Mannix; Jiwoong Park; Liuyan Zhao; Philip Kim; Robert Hovden

doi:10.1038/s41467-022-35477-x

Torsional periodic lattice distortions and diffraction of twisted 2D materials

Nat Commun. 2022 Dec 19;13(1):7826. doi: 10.1038/s41467-022-35477-x.

Authors

Suk Hyun Sung¹, Yin Min Goh², Hyobin Yoo³, Rebecca Engelke⁴, Hongchao Xie², Kuan Zhang⁵, Zidong Li⁶, Andrew Ye⁷, Parag B Deotare^{6

8}, Ellad B Tadmor⁵, Andrew J Mannix⁹, Jiwoong Park^{7

10}, Liuyan Zhao², Philip Kim⁴, Robert Hovden^{11

12}

Affiliations

¹ Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109, USA.
² Department of Physics, University of Michigan, Ann Arbor, MI, 48109, USA.
³ Department of Physics, Sogang University, Seoul, 04107, Republic of Korea.
⁴ Department of Physics, Harvard University, Cambridge, MA, 02138, USA.
⁵ Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, 55455, USA.
⁶ Electrical and Computer Engineering Department, University of Michigan, Ann Arbor, MI, 48109, USA.
⁷ Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, 60637, USA.
⁸ Applied Physics Program, University of Michigan, Ann Arbor, MI, 48109, USA.
⁹ Department of Materials Science and Engineering, Stanford University, Stanford, CA, 94305, USA.
¹⁰ Department of Chemistry, University of Chicago, Chicago, IL, 60637, USA.
¹¹ Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109, USA. hovden@umich.edu.
¹² Applied Physics Program, University of Michigan, Ann Arbor, MI, 48109, USA. hovden@umich.edu.

Abstract

Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS₂, CrI₃, and WSe₂/MoSe₂.