Strain fields in twisted bilayer graphene

Kazmierczak, Nathanael P.; Van Winkle, Madeline; Ophus, Colin; Bustillo, Karen C.; Carr, Stephen; Brown, Hamish G.; Ciston, Jim; Taniguchi, Takashi; Watanabe, Kenji; Bediako, D. Kwabena

doi:10.1038/s41563-021-00973-w

Strain fields in twisted bilayer graphene

Journal Article · Thu Apr 15 00:00:00 EDT 2021 · Nature Materials

DOI:https://doi.org/10.1038/s41563-021-00973-w· OSTI ID:1818271

^[1]; ^[2]; ^[3]; ^[3]; ^[4]; Brown, Hamish G. ^[3]; Ciston, Jim ^[3]; ^[5]; ^[5]; ^[6]

Univ. of California, Berkeley, CA (United States); Calvin Univ., Grand Rapids, MI (United States)
Univ. of California, Berkeley, CA (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Brown Univ., Providence, RI (United States)
National Institute of Materials Science, Namiki, Tsukuba (Japan)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Canadian institute for Advanced Research, Toronto (Canada)

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles < 2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moiré heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anisotropically in saddle-point regions, generating distinctive striped strain phases. Our results establish the reconstruction mechanics underpinning the twist-angle-dependent electronic behaviour of twisted bilayer graphene and provide a framework for directly visualizing structural relaxation, disorder and strain in moiré materials.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: Office of Naval Research Young Investigator Program; National Science Foundation (NSF); USDOE

OSTI ID:: 1818271

Journal Information:: Nature Materials, Journal Name: Nature Materials Journal Issue: 7 Vol. 20; ISSN 1476-1122

Publisher:: Springer Nature - Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (46)

Implementation of high-order variational models made easy for image processing Lu, Wenqi; Duan, Jinming; Qiu, Zhaowen Mathematical Methods in the Applied Sciences, Vol. 39, Issue 14 https://doi.org/10.1002/mma.3858	journal	March 2016
Resolving the 180-degree ambiguity in vector magnetic field measurements: The ?minimum? energy solution Metcalf, Thomas R. Solar Physics, Vol. 155, Issue 2 https://doi.org/10.1007/BF00680593	journal	December 1994
An edge-weighted second order variational model for image decomposition Duan, Jinming; Qiu, Zhaowen; Lu, Wenqi Digital Signal Processing, Vol. 49 https://doi.org/10.1016/j.dsp.2015.10.010	journal	February 2016
Structural and electron diffraction scaling of twisted graphene bilayers Zhang, Kuan; Tadmor, Ellad B. Journal of the Mechanics and Physics of Solids, Vol. 112 https://doi.org/10.1016/j.jmps.2017.12.005	journal	March 2018
Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions Ophus, Colin; Ciston, Jim; Nelson, Chris T. Ultramicroscopy, Vol. 162 https://doi.org/10.1016/j.ultramic.2015.12.002	journal	March 2016
Holographic reconstruction of the interlayer distance of bilayer two-dimensional crystal samples from their convergent beam electron diffraction patterns Latychevskaia, Tatiana; Zou, Yichao; Woods, Colin Robert Ultramicroscopy, Vol. 219 https://doi.org/10.1016/j.ultramic.2020.113020	journal	December 2020
Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond Ophus, Colin Microscopy and Microanalysis, Vol. 25, Issue 3 https://doi.org/10.1017/S1431927619000497	journal	May 2019
py4DSTEM: A Software Package for Four-Dimensional Scanning Transmission Electron Microscopy Data Analysis Savitzky, Benjamin H.; Zeltmann, Steven E.; Hughes, Lauren A. Microscopy and Microanalysis https://doi.org/10.1017/S1431927621000477	journal	May 2021
van der Waals Heterostructures with High Accuracy Rotational Alignment Kim, Kyounghwan; Yankowitz, Matthew; Fallahazad, Babak Nano Letters, Vol. 16, Issue 3 https://doi.org/10.1021/acs.nanolett.5b05263	journal	February 2016
Twisted Bilayer Graphene: Moiré with a Twist Dai, Shuyang; Xiang, Yang; Srolovitz, David J. Nano Letters, Vol. 16, Issue 9 https://doi.org/10.1021/acs.nanolett.6b02870	journal	August 2016
Strain Mapping of Two-Dimensional Heterostructures with Subpicometer Precision Han, Yimo; Nguyen, Kayla; Cao, Michael Nano Letters, Vol. 18, Issue 6 https://doi.org/10.1021/acs.nanolett.8b00952	journal	May 2018
Twist Angle-Dependent Atomic Reconstruction and Moiré Patterns in Transition Metal Dichalcogenide Heterostructures Rosenberger, Matthew R.; Chuang, Hsun-Jen; Phillips, Madeleine ACS Nano, Vol. 14, Issue 4 https://doi.org/10.1021/acsnano.0c00088	journal	March 2020
Dislocations in bilayer graphene Butz, Benjamin; Dolle, Christian; Niekiel, Florian Nature, Vol. 505, Issue 7484 https://doi.org/10.1038/nature12780	journal	December 2013
Unconventional superconductivity in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Fang, Shiang Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26160	journal	March 2018
Emergence of superlattice Dirac points in graphene on hexagonal boron nitride Yankowitz, Matthew; Xue, Jiamin; Cormode, Daniel Nature Physics, Vol. 8, Issue 5 https://doi.org/10.1038/nphys2272	journal	March 2012
Commensurate–incommensurate transition in graphene on hexagonal boron nitride Woods, C. R.; Britnell, L.; Eckmann, A. Nature Physics, Vol. 10, Issue 6 https://doi.org/10.1038/nphys2954	journal	April 2014
Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene Yoo, Hyobin; Engelke, Rebecca; Carr, Stephen Nature Materials, Vol. 18, Issue 5 https://doi.org/10.1038/s41563-019-0346-z	journal	April 2019
Correlated electronic phases in twisted bilayer transition metal dichalcogenides Wang, Lei; Shih, En-Min; Ghiotto, Augusto Nature Materials, Vol. 19, Issue 8 https://doi.org/10.1038/s41563-020-0708-6	journal	June 2020
Atomic reconstruction in twisted bilayers of transition metal dichalcogenides Weston, Astrid; Zou, Yichao; Enaldiev, Vladimir Nature Nanotechnology, Vol. 15, Issue 7 https://doi.org/10.1038/s41565-020-0682-9	journal	May 2020
Visualization of moiré superlattices McGilly, Leo J.; Kerelsky, Alexander; Finney, Nathan R. Nature Nanotechnology, Vol. 15, Issue 7 https://doi.org/10.1038/s41565-020-0708-3	journal	June 2020
Superconductivity and strong correlations in moiré flat bands Balents, Leon; Dean, Cory R.; Efetov, Dmitri K. Nature Physics, Vol. 16, Issue 7 https://doi.org/10.1038/s41567-020-0906-9	journal	May 2020
Electron ptychography of 2D materials to deep sub-ångström resolution Jiang, Yi; Chen, Zhen; Han, Yimo Nature, Vol. 559, Issue 7714 https://doi.org/10.1038/s41586-018-0298-5	journal	July 2018
Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers Seyler, Kyle L.; Rivera, Pasqual; Yu, Hongyi Nature, Vol. 567, Issue 7746 https://doi.org/10.1038/s41586-019-0957-1	journal	February 2019
Evidence for moiré excitons in van der Waals heterostructures Tran, Kha; Moody, Galan; Wu, Fengcheng Nature, Vol. 567, Issue 7746 https://doi.org/10.1038/s41586-019-0975-z	journal	February 2019
Observation of moiré excitons in WSe2/WS2 heterostructure superlattices Jin, Chenhao; Regan, Emma C.; Yan, Aiming Nature, Vol. 567, Issue 7746 https://doi.org/10.1038/s41586-019-0976-y	journal	February 2019
Maximized electron interactions at the magic angle in twisted bilayer graphene Kerelsky, Alexander; McGilly, Leo J.; Kennes, Dante M. Nature, Vol. 572, Issue 7767 https://doi.org/10.1038/s41586-019-1431-9	journal	July 2019
Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene Lu, Xiaobo; Stepanov, Petr; Yang, Wei Nature, Vol. 574, Issue 7780 https://doi.org/10.1038/s41586-019-1695-0	journal	October 2019
Mapping the twist-angle disorder and Landau levels in magic-angle graphene Uri, A.; Grover, S.; Cao, Y. Nature, Vol. 581, Issue 7806 https://doi.org/10.1038/s41586-020-2255-3	journal	May 2020
van der Waals heterostructures combining graphene and hexagonal boron nitride Yankowitz, Matthew; Ma, Qiong; Jarillo-Herrero, Pablo Nature Reviews Physics, Vol. 1, Issue 2 https://doi.org/10.1038/s42254-018-0016-0	journal	January 2019
Strain mapping at nanometer resolution using advanced nano-beam electron diffraction Ozdol, V. B.; Gammer, C.; Jin, X. G. Applied Physics Letters, Vol. 106, Issue 25 https://doi.org/10.1063/1.4922994	journal	June 2015
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. Proceedings of the National Academy of Sciences, Vol. 108, Issue 30 https://doi.org/10.1073/pnas.1108174108	journal	July 2011
Strain solitons and topological defects in bilayer graphene Alden, J. S.; Tsen, A. W.; Huang, P. Y. Proceedings of the National Academy of Sciences, Vol. 110, Issue 28 https://doi.org/10.1073/pnas.1309394110	journal	June 2013
4D STEM: High efficiency phase contrast imaging using a fast pixelated detector Yang, H.; Jones, L.; Ryll, H. Journal of Physics: Conference Series, Vol. 644 https://doi.org/10.1088/1742-6596/644/1/012032	journal	October 2015
Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite Wijk, M. M. van; Schuring, A.; Katsnelson, M. I. 2D Materials, Vol. 2, Issue 3 https://doi.org/10.1088/2053-1583/2/3/034010	journal	July 2015
Structure of twisted and buckled bilayer graphene Jain, Sandeep K.; Juričić, Vladimir; Barkema, Gerard T. 2D Materials, Vol. 4, Issue 1 https://doi.org/10.1088/2053-1583/4/1/015018	journal	November 2016
Designing flat bands by strain Bi, Zhen; Yuan, Noah F. Q.; Fu, Liang Physical Review B, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevB.100.035448	journal	July 2019
Electronic structure theory of weakly interacting bilayers Fang, Shiang; Kaxiras, Efthimios Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevB.93.235153	journal	June 2016
Lattice relaxation and energy band modulation in twisted bilayer graphene Nam, Nguyen N. T.; Koshino, Mikito Physical Review B, Vol. 96, Issue 7 https://doi.org/10.1103/PhysRevB.96.075311	journal	August 2017
Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters Guinea, Francisco; Walet, Niels R. Physical Review B, Vol. 99, Issue 20 https://doi.org/10.1103/PhysRevB.99.205134	journal	May 2019
Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene Cao, Y.; Luo, J. Y.; Fatemi, V. Physical Review Letters, Vol. 117, Issue 11 https://doi.org/10.1103/PhysRevLett.117.116804	journal	September 2016
Electronic Spectrum of Twisted Graphene Layers under Heterostrain Huder, Loïc; Artaud, Alexandre; Le Quang, Toai Physical Review Letters, Vol. 120, Issue 15 https://doi.org/10.1103/PhysRevLett.120.156405	journal	April 2018
Exact continuum model for low-energy electronic states of twisted bilayer graphene Carr, Stephen; Fang, Shiang; Zhu, Ziyan Physical Review Research, Vol. 1, Issue 1 https://doi.org/10.1103/PhysRevResearch.1.013001	journal	August 2019
Disorder in twisted bilayer graphene Wilson, Justin H.; Fu, Yixing; Das Sarma, S. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023325	journal	June 2020
Engineering Mechanics: Statics Boresi, Ap; Schmidt, Rj; Rega, G. Applied Mechanics Reviews, Vol. 55, Issue 1 https://doi.org/10.1115/1.1445323	journal	January 2002
Tuning superconductivity in twisted bilayer graphene Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy Science, Vol. 363, Issue 6431 https://doi.org/10.1126/science.aav1910	journal	January 2019
Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene Sharpe, Aaron L.; Fox, Eli J.; Barnard, Arthur W. Science, Vol. 365, Issue 6453 https://doi.org/10.1126/science.aaw3780	journal	July 2019

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