Structural and electron diffraction scaling of twisted graphene bilayers

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Abstract

Multiscale simulations are used to study the structural relaxation in twisted graphene bilayers and the associated electron diffraction patterns. The initial twist forms an incommensurate moiré pattern that relaxes to a commensurate microstructure comprised of a repeating pattern of alternating low-energy AB and BA domains surrounding a high-energy AA domain. The simulations show that the relaxation mechanism involves a localized rotation and shrinking of the AA domains that scales in two regimes with the imposed twist. For small twisting angles, the localized rotation tends to a constant; for large twist, the rotation scales linearly with it. This behavior is tied to the inverse scaling of the moiré pattern size with twist angle and is explained theoretically using a linear elasticity model. The results are validated experimentally through a simulated electron diffraction analysis of the relaxed structures. A complex electron diffraction pattern involving the appearance of weak satellite peaks is predicted for the small twist regime. This new diffraction pattern is explained using an analytical model in which the relaxation kinematics are described as an exponentially-decaying (Gaussian) rotation field centered on the AA domains. Both the angle-dependent scaling and diffraction patterns are in quantitative agreement with experimental observations. A Matlab program for extracting the Gaussian model parameters accompanies this paper.

Original languageEnglish (US)
Pages (from-to)225-238
Number of pages14
JournalJournal of the Mechanics and Physics of Solids
Volume112
DOIs
StatePublished - Mar 1 2018

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Electron diffraction
Graphene
Diffraction patterns
graphene
diffraction patterns
electron diffraction
scaling
diffraction
Structural relaxation
twisting
Analytical models
Elasticity
Kinematics
kinematics
elastic properties
simulation
Satellites
microstructure
Microstructure
energy

Keywords

  • Electron diffraction
  • Moiré pattern
  • Multiscale simulation
  • Twisted graphene bilayers

Cite this

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title = "Structural and electron diffraction scaling of twisted graphene bilayers",
abstract = "Multiscale simulations are used to study the structural relaxation in twisted graphene bilayers and the associated electron diffraction patterns. The initial twist forms an incommensurate moir{\'e} pattern that relaxes to a commensurate microstructure comprised of a repeating pattern of alternating low-energy AB and BA domains surrounding a high-energy AA domain. The simulations show that the relaxation mechanism involves a localized rotation and shrinking of the AA domains that scales in two regimes with the imposed twist. For small twisting angles, the localized rotation tends to a constant; for large twist, the rotation scales linearly with it. This behavior is tied to the inverse scaling of the moir{\'e} pattern size with twist angle and is explained theoretically using a linear elasticity model. The results are validated experimentally through a simulated electron diffraction analysis of the relaxed structures. A complex electron diffraction pattern involving the appearance of weak satellite peaks is predicted for the small twist regime. This new diffraction pattern is explained using an analytical model in which the relaxation kinematics are described as an exponentially-decaying (Gaussian) rotation field centered on the AA domains. Both the angle-dependent scaling and diffraction patterns are in quantitative agreement with experimental observations. A Matlab program for extracting the Gaussian model parameters accompanies this paper.",
keywords = "Electron diffraction, Moir{\'e} pattern, Multiscale simulation, Twisted graphene bilayers",
author = "Kuan Zhang and Tadmor, {Ellad B}",
year = "2018",
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T1 - Structural and electron diffraction scaling of twisted graphene bilayers

AU - Zhang, Kuan

AU - Tadmor, Ellad B

PY - 2018/3/1

Y1 - 2018/3/1

N2 - Multiscale simulations are used to study the structural relaxation in twisted graphene bilayers and the associated electron diffraction patterns. The initial twist forms an incommensurate moiré pattern that relaxes to a commensurate microstructure comprised of a repeating pattern of alternating low-energy AB and BA domains surrounding a high-energy AA domain. The simulations show that the relaxation mechanism involves a localized rotation and shrinking of the AA domains that scales in two regimes with the imposed twist. For small twisting angles, the localized rotation tends to a constant; for large twist, the rotation scales linearly with it. This behavior is tied to the inverse scaling of the moiré pattern size with twist angle and is explained theoretically using a linear elasticity model. The results are validated experimentally through a simulated electron diffraction analysis of the relaxed structures. A complex electron diffraction pattern involving the appearance of weak satellite peaks is predicted for the small twist regime. This new diffraction pattern is explained using an analytical model in which the relaxation kinematics are described as an exponentially-decaying (Gaussian) rotation field centered on the AA domains. Both the angle-dependent scaling and diffraction patterns are in quantitative agreement with experimental observations. A Matlab program for extracting the Gaussian model parameters accompanies this paper.

AB - Multiscale simulations are used to study the structural relaxation in twisted graphene bilayers and the associated electron diffraction patterns. The initial twist forms an incommensurate moiré pattern that relaxes to a commensurate microstructure comprised of a repeating pattern of alternating low-energy AB and BA domains surrounding a high-energy AA domain. The simulations show that the relaxation mechanism involves a localized rotation and shrinking of the AA domains that scales in two regimes with the imposed twist. For small twisting angles, the localized rotation tends to a constant; for large twist, the rotation scales linearly with it. This behavior is tied to the inverse scaling of the moiré pattern size with twist angle and is explained theoretically using a linear elasticity model. The results are validated experimentally through a simulated electron diffraction analysis of the relaxed structures. A complex electron diffraction pattern involving the appearance of weak satellite peaks is predicted for the small twist regime. This new diffraction pattern is explained using an analytical model in which the relaxation kinematics are described as an exponentially-decaying (Gaussian) rotation field centered on the AA domains. Both the angle-dependent scaling and diffraction patterns are in quantitative agreement with experimental observations. A Matlab program for extracting the Gaussian model parameters accompanies this paper.

KW - Electron diffraction

KW - Moiré pattern

KW - Multiscale simulation

KW - Twisted graphene bilayers

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