Strain fields in twisted bilayer graphene.
Journal
Nature materials
ISSN: 1476-4660
Titre abrégé: Nat Mater
Pays: England
ID NLM: 101155473
Informations de publication
Date de publication:
07 2021
07 2021
Historique:
received:
18
11
2020
accepted:
02
03
2021
pubmed:
17
4
2021
medline:
17
4
2021
entrez:
16
4
2021
Statut:
ppublish
Résumé
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.
Identifiants
pubmed: 33859383
doi: 10.1038/s41563-021-00973-w
pii: 10.1038/s41563-021-00973-w
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.
Langues
eng
Sous-ensembles de citation
IM
Pagination
956-963Commentaires et corrections
Type : CommentIn
Références
Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).
doi: 10.1038/s41567-020-0906-9
Yankowitz, M., Ma, Q., Jarillo-Herrero, P. & LeRoy, B. J. van der Waals heterostructures combining graphene and hexagonal boron nitride. Nat. Rev. Phys. 1, 112–125 (2019).
doi: 10.1038/s42254-018-0016-0
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
doi: 10.1073/pnas.1108174108
Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).
doi: 10.1038/nphys2272
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
doi: 10.1038/nature26160
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
doi: 10.1126/science.aav1910
Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
doi: 10.1038/s41586-019-1695-0
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
doi: 10.1126/science.aaw3780
Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe
doi: 10.1038/s41586-019-0957-1
Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).
doi: 10.1038/s41586-019-0975-z
Jin, C. et al. Observation of moiré excitons in WSe
doi: 10.1038/s41586-019-0976-y
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
doi: 10.1038/s41563-020-0708-6
Woods, C. R. et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).
doi: 10.1038/nphys2954
van Wijk, M. M., Schuring, A., Katsnelson, M. I. & Fasolino, A. Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite. 2D Mater. 2, 034010 (2015).
doi: 10.1088/2053-1583/2/3/034010
Dai, S., Xiang, Y. & Srolovitz, D. J. Twisted bilayer graphene: moiré with a twist. Nano Lett. 16, 5923–5927 (2016).
doi: 10.1021/acs.nanolett.6b02870
Jain, S. K., Juričić, V. & Barkema, G. T. Structure of twisted and buckled bilayer graphene. 2D Mater. 4, 015018 (2016).
doi: 10.1088/2053-1583/4/1/015018
Nam, N. N. T. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017).
doi: 10.1103/PhysRevB.96.075311
Zhang, K. & Tadmor, E. B. Structural and electron diffraction scaling of twisted graphene bilayers. J. Mech. Phys. Solids 112, 225–238 (2018).
doi: 10.1016/j.jmps.2017.12.005
Yoo, H. et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).
doi: 10.1038/s41563-019-0346-z
Rosenberger, M. R. et al. Twist angle-dependent atomic reconstruction and moiré patterns in transition metal dichalcogenide heterostructures. ACS Nano 14, 4550–4558 (2020).
doi: 10.1021/acsnano.0c00088
Weston, A. et al. Atomic reconstruction in twisted bilayers of transition metal dichalcogenides. Nat. Nanotechnol. 15, 592–597 (2020).
doi: 10.1038/s41565-020-0682-9
Alden, J. S. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl Acad. Sci. USA 110, 11256–11260 (2013).
doi: 10.1073/pnas.1309394110
Uri, A. et al. Mapping the twist-angle disorder and Landau levels in magic-angle graphene. Nature 581, 47–52 (2020).
doi: 10.1038/s41586-020-2255-3
Wilson, J. H., Fu, Y., Das Sarma, S. & Pixley, J. H. Disorder in twisted bilayer graphene. Phys. Rev. Res. 2, 023325 (2020).
doi: 10.1103/PhysRevResearch.2.023325
Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).
doi: 10.1038/s41586-019-1431-9
Huder, L. et al. Electronic spectrum of twisted graphene layers under heterostrain. Phys. Rev. Lett. 120, 156405 (2018).
doi: 10.1103/PhysRevLett.120.156405
Bi, Z., Yuan, N. F. Q. & Fu, L. Designing flat bands by strain. Phys. Rev. B 100, 035448 (2019).
doi: 10.1103/PhysRevB.100.035448
McGilly, L. J. et al. Visualization of moiré superlattices. Nat. Nanotechnol. 15, 580–584 (2020).
doi: 10.1038/s41565-020-0708-3
Han, Y. et al. Strain mapping of two-dimensional heterostructures with subpicometer precision. Nano Lett. 18, 3746–3751 (2018).
doi: 10.1021/acs.nanolett.8b00952
Yang, H. et al. 4D STEM: high efficiency phase contrast imaging using a fast pixelated detector. J. Phys. Conf. Ser. 644, 012032 (2015).
doi: 10.1088/1742-6596/644/1/012032
Jiang, Y. et al. Electron ptychography of 2D materials to deep sub-ångström resolution. Nature 559, 343–349 (2018).
doi: 10.1038/s41586-018-0298-5
Ophus, C. Four-dimensional scanning transmission electron microscopy (4D-STEM): from scanning nanodiffraction to ptychography and beyond. Microsc. Microanal. 25, 563–582 (2019).
doi: 10.1017/S1431927619000497
Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).
doi: 10.1021/acs.nanolett.5b05263
Ozdol, V. B. et al. Strain mapping at nanometer resolution using advanced nano-beam electron diffraction. Appl. Phys. Lett. 106, 253107 (2015).
doi: 10.1063/1.4922994
Kelly, P. Solid Mechanics Lecture Notes (Univ. of Auckland, 2013).
McGinty, B. Continuum Mechanics (2012); https://www.continuummechanics.org
Butz, B. et al. Dislocations in bilayer graphene. Nature 505, 533–537 (2014).
doi: 10.1038/nature12780
Fang, S. & Kaxiras, E. Electronic structure theory of weakly interacting bilayers. Phys. Rev. B 93, 235153 (2016).
doi: 10.1103/PhysRevB.93.235153
Carr, S., Fang, S., Zhu, Z. & Kaxiras, E. Exact continuum model for low energy electronic states of twisted bilayer graphene. Phys. Rev. Res. 1, 013001 (2019).
doi: 10.1103/PhysRevResearch.1.013001
Guinea, F. & Walet, N. R. Continuum models for twisted bilayer graphene: effect of lattice deformation and hopping parameters. Phys. Rev. B 99, 205134 (2019).
doi: 10.1103/PhysRevB.99.205134
Latychevskaia, T. et al. Holographic reconstruction of interlayer distance of bilayer two-dimensional crystal samples from their convergent beam electron diffraction patterns. Ultramicroscopy 219, 113021 (2020).
doi: 10.1016/j.ultramic.2020.113020
Cao, Y. et al. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117, 116804 (2016).
doi: 10.1103/PhysRevLett.117.116804
Boresi, A. P. & Schmidt, R. J. in Advanced Mechanics of Materials 55–72 (Wiley, 2003).
Metcalf, T. R. Resolving the 180-degree ambiguity in vector magnetic field measurements: the ‘minimum’ energy solution. Sol. Phys. 155, 235–242 (1994).
doi: 10.1007/BF00680593
Lu, W. et al. Implementation of higher-order variational models made easy for image processing. Math. Methods Appl. Sci. 39, 4208–4233 (2016).
doi: 10.1002/mma.3858
Duan, J. et al. An edge-weighted second order variational model for image decomposition. Digit. Signal Process. 49, 162–181 (2016).
doi: 10.1016/j.dsp.2015.10.010
Savitzky, B. et al. py4DSTEM: a software package for multimodal analysis of four-dimensional scanning transmission electron microscopy datasets. Preprint at https://arxiv.org/abs/2003.09523 (2020).
Ophus, C., Ciston, J. & Nelson, C. T. Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions. Ultramicroscopy 162, 1–9 (2016).
doi: 10.1016/j.ultramic.2015.12.002