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

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

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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.

Original language	English (US)
Article number	7826
Journal	Nature communications
Volume	13
Issue number	1
DOIs	https://doi.org/10.1038/s41467-022-35477-x
State	Published - Dec 2022

Bibliographical note

Funding Information:
R.H. acknowledges support from ARO grant no. W911NF-22-1-0056. S.H.S. acknowledges support from the W.M. Keck Foundation. P.K. acknowledge support from ARO MURI (W911NF-21-2-0147). R.E. acknowledge support from NSF DMR-1922172. L.Z. acknowledges support by NSF CAREER grant No. DMR-174774, AFOSR YIP grant No. FA9550-21-1-0065 and Alfred P. Sloan Foundation. J.P., A.J.M., and A.Y. acknowledge funding from the National Science Foundation Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM) under Cooperative Agreement No. DMR-2039380 and the Air Force Office of Scientific Research MURI project (FA9550-18-1-0480). A.J.M. was supported by the Kadanoff-Rice Postdoctoral Fellowship of the University of Chicago MRSEC (DMR-2 011854). A.Y. was supported by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program. Diffraction data collected by the authors for use in Figs. and have been adapted and reused in part from refs. , and as permitted by Springer Nature.

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title = "Torsional periodic lattice distortions and diffraction of twisted 2D materials",

abstract = "Twisted 2D materials form complex moir{\'e} 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 moir{\'e}s. 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.",

author = "Sung, {Suk Hyun} and Goh, {Yin Min} and Hyobin Yoo and Rebecca Engelke and Hongchao Xie and Kuan Zhang and Zidong Li and Andrew Ye and Deotare, {Parag B.} and Tadmor, {Ellad B.} and Mannix, {Andrew J.} and Jiwoong Park and Liuyan Zhao and Philip Kim and Robert Hovden",

note = "Funding Information: R.H. acknowledges support from ARO grant no. W911NF-22-1-0056. S.H.S. acknowledges support from the W.M. Keck Foundation. P.K. acknowledge support from ARO MURI (W911NF-21-2-0147). R.E. acknowledge support from NSF DMR-1922172. L.Z. acknowledges support by NSF CAREER grant No. DMR-174774, AFOSR YIP grant No. FA9550-21-1-0065 and Alfred P. Sloan Foundation. J.P., A.J.M., and A.Y. acknowledge funding from the National Science Foundation Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM) under Cooperative Agreement No. DMR-2039380 and the Air Force Office of Scientific Research MURI project (FA9550-18-1-0480). A.J.M. was supported by the Kadanoff-Rice Postdoctoral Fellowship of the University of Chicago MRSEC (DMR-2 011854). A.Y. was supported by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program. Diffraction data collected by the authors for use in Figs. and have been adapted and reused in part from refs. , and as permitted by Springer Nature. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

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T1 - Torsional periodic lattice distortions and diffraction of twisted 2D materials

AU - Sung, Suk Hyun

AU - Goh, Yin Min

AU - Yoo, Hyobin

AU - Engelke, Rebecca

AU - Xie, Hongchao

AU - Zhang, Kuan

AU - Li, Zidong

AU - Ye, Andrew

AU - Deotare, Parag B.

AU - Tadmor, Ellad B.

AU - Mannix, Andrew J.

AU - Park, Jiwoong

AU - Zhao, Liuyan

AU - Kim, Philip

AU - Hovden, Robert

N1 - Funding Information: R.H. acknowledges support from ARO grant no. W911NF-22-1-0056. S.H.S. acknowledges support from the W.M. Keck Foundation. P.K. acknowledge support from ARO MURI (W911NF-21-2-0147). R.E. acknowledge support from NSF DMR-1922172. L.Z. acknowledges support by NSF CAREER grant No. DMR-174774, AFOSR YIP grant No. FA9550-21-1-0065 and Alfred P. Sloan Foundation. J.P., A.J.M., and A.Y. acknowledge funding from the National Science Foundation Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM) under Cooperative Agreement No. DMR-2039380 and the Air Force Office of Scientific Research MURI project (FA9550-18-1-0480). A.J.M. was supported by the Kadanoff-Rice Postdoctoral Fellowship of the University of Chicago MRSEC (DMR-2 011854). A.Y. was supported by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program. Diffraction data collected by the authors for use in Figs. and have been adapted and reused in part from refs. , and as permitted by Springer Nature. Publisher Copyright: © 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

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Torsional periodic lattice distortions and diffraction of twisted 2D materials

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