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artifacts which affect the image of the two layers identically which cancels out in the relative measurement. Alternatively, with a well calibrated microscope and if biaxial heterostrain is low enough, it is possible to determine twist and uniaxial heterostrain from the knowledge of the moiré period in all directions. On the contrary it is much more difficult to determine homostrain which necessitates a calibration sample.
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and to be the main factor in the flat band width of those systems. Heterostrain has a much larger impact on electronic properties than homostrain. It explains some of the sample variability which had previously been puzzeling. Research is now moving towards understanding the impact of spatial fluctuations of heterostrain.
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Heterostrain is generated during the fabrication of the 2D materials stack. It can result from a meta-stable configuration during bottom up assembly or from the layer manipulation in the tear and stack technique. It has been shown to be ubiquitous in twisted graphene layers near the magic twist angle
450:
Kapfer, Mäelle; Jessen, Bjarke S.; Eisele, Megan E.; Fu, Matthew; Danielsen, Dorte R.; Darlington, Thomas P.; Moore, Samuel L.; Finney, Nathan R.; Marchese, Ariane; Hsieh, Valerie; Majchrzak, Paulina; Jiang, Zhihao; Biswas, Deepnarayan; Dudin, Pavel; Avila, José (2023). "Programming twist angle and
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which provides images showing both the atomic lattice of the first layer and the moiré superlattice. Relating the atomic lattice to the moiré lattice allows to determine entirely the relative arrangement of the layers (biaxial, uniaxial heterostrain and twist). The method is immune to calibration
39:
in which the properties of 2D materials are controlled by strain. Recent works have reported a deterministic control of heterostrain by sample processing or with the tip of an AFM of particular interest in twisted heterostructures. Heterostrain alone (without twist) has also been identified as a
749:
Engelke, Rebecca; Yoo, Hyobin; Carr, Stephen; Xu, Kevin; Cazeaux, Paul; Allen, Richard; Valdivia, Andres Mier; Luskin, Mitchell; Kaxiras, Efthimios; Kim, Minhyong; Han, Jung Hoon; Kim, Philip (2022-07-16). "Non-Abelian topological defects and strain mapping in 2D moiré materials".
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Kapfer, Maëlle; Jessen, Bjarke S.; Eisele, Megan E.; Fu, Matthew; Danielsen, Dorte R.; Darlington, Thomas P.; Moore, Samuel L.; Finney, Nathan R.; Marchese, Ariane; Hsieh, Valerie; Majchrzak, Paulina; Jiang, Zhihao; Biswas, Deepnarayan; Dudin, Pavel; Avila, José (2023-08-11).
52:. It means that the two layers constituting the structure are subject to different strains. This is in contrast with homostrain in which the two layers as subject to the same strain. Heterostrain is designated as "relative strain" by some authors.
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Peña, Tara; Dey, Aditya; Chowdhury, Shoieb A.; Azizimanesh, Ahmad; Hou, Wenhui; Sewaket, Arfan; Watson, Carla L.; Askari, Hesam; Wu, Stephen M. (2023). "Moiré engineering in 2D heterostructures with process-induced strain".
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Kim, Kyounghwan; Yankowitz, Matthew; Fallahazad, Babak; Kang, Sangwoo; Movva, Hema C. P.; Huang, Shengqiang; Larentis, Stefano; Corbet, Chris M.; Taniguchi, Takashi; Watanabe, Kenji; Banerjee, Sanjay K. (2016-03-09).
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Mesple, Florie; Walet, Niels R.; Trambly de
Laissardière, Guy; Guinea, Francisco; Došenović, Djordje; Okuno, Hanako; Paillet, Colin; Michon, Adrien; Chapelier, Claude; Renard, Vincent T. (September 2023).
35:, heterostrain can have important consequences on the electronic and optical properties of the resulting structure. As such, the control of heterostrain is emerging as a sub-field of
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Kerelsky, Alexander; McGilly, Leo J.; Kennes, Dante M.; Xian, Lede; Yankowitz, Matthew; Chen, Shaowen; Watanabe, K.; Taniguchi, T.; Hone, James; Dean, Cory; Rubio, Angel (2019).
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Huder, LoĂŻc; Artaud, Alexandre; Le Quang, Toai; de
Laissardière, Guy Trambly; Jansen, Aloysius G. M.; Lapertot, Gérard; Chapelier, Claude; Renard, Vincent T. (2018-04-12).
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Mesple, Florie; Missaoui, Ahmed; Cea, Tommaso; Huder, Loic; Guinea, Francisco; Trambly de
Laissardière, Guy; Chapelier, Claude; Renard, Vincent T. (2021-09-17).
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signaling the regions where the atomic lattices of the two layers are in or out of registry. The shape of the moiré pattern depends on the type of strain.
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In nature, the two graphene layers usually stack with a shift of half a unit cell. This configuration is the most energetically favorable and is found in
31:
are stacked on top of each other. These layers can experience the same deformation (homostrain) or different deformations (heterostrain). In addition to
40:
parameter to tune the electronic properties of van der Waals structures as for example in twisted graphene layers with biaxial heterostrain.
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If the layer is strained in the same way along two directions (biaxial heterostrain), the moiré is a two-dimensional superstructure.
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to simplify the designation of possible strain situations in van der Waals heterostructures where two (or more)
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Parker, Daniel E.; Soejima, Tomohiro; Hauschild, Johannes; Zaletel, Michael P.; Bultinck, Nick (2021-07-06).
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layers is considered. The description can be generalized for the case of different 2D materials forming an
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If the layer is deformed along one direction (uniaxial heterostrain), the moiré is one dimensional.
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Artaud, A.; Magaud, L.; Le Quang, T.; Guisset, V.; David, P.; Chapelier, C.; Coraux, J. (2016).
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In
General, a layer can be deformed by an arbitrary combination of both types of heterostrain.
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387:"Twist versus heterostrain control of optical properties of moiré exciton minibands"
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Heterostrain is constructed from the Greek prefix hetero- (different) and the noun
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848:"Maximized electron interactions at the magic angle in twisted bilayer graphene"
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314:"Heterostrain Determines Flat Bands in Magic-Angle Twisted Graphene Layers"
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922:"van der Waals Heterostructures with High Accuracy Rotational Alignment"
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552:"Moiré engineering in 2D heterostructures with process-induced strain"
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684:"Giant Atomic Swirl in Graphene Bilayers with Biaxial Heterostrain"
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176:"Electronic Spectrum of Twisted Graphene Layers under Heterostrain"
977:"Strain-Induced Quantum Phase Transitions in Magic-Angle Graphene"
610:"Programming twist angle and strain profiles in 2D materials"
75:. If one layer is strained while the other is left intact, a
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Zheng, Huiyuan; Zhai, Dawei; Yao, Wang (2021-10-01).
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Bi, Zhen; Yuan, Noah F. Q.; Fu, Liang (2019-07-31).
1066:"Moiré disorder effect in twisted bilayer graphene"
1064:Nakatsuji, Naoto; Koshino, Mikito (2022-06-14).
56:Manifestation and measurement of heterostrain
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451:strain profiles in 2D materials".
101:Graphene layers in Bernal stacking
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144:Origin and impact of heterostrain
244:"Designing flat bands by strain"
135:Heterostrain can be measured by
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60:For simplicity, the case of two
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1100:10.1103/PhysRevB.105.245408
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29:two-dimensional materials
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874:2019Natur.572...95K
799:2016NatSR...625670A
710:2023AdM....3506312M
636:2023Sci...381..677K
578:2023ApPhL.122n3101P
550:Tara, Pena (2023).
521:2023ApPhL.122n3101P
475:2023Sci...381..677K
413:2021TDM.....8d4016Z
340:2021PhRvL.127l6405M
270:2019PhRvB.100c5448B
202:2018PhRvL.120o6405H
777:Scientific Reports
688:Advanced Materials
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1070:Physical Review B
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153:References
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1027:0031-9007
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833:27181495
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73:graphite
62:graphene
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