Topologically Protected Helical States in Minimally Twisted Bilayer Graphene

Huang, Sunxiang; Kim, Kyounghwan; Efimkin, Dmitry K.; Lovorn, Timothy; Taniguchi, Takashi; Watanabe, Kenji; MacDonald, Allan H.; Tutuc, Emanuel; LeRoy, Brian J.

doi:10.1103/physrevlett.121.037702

Cited by 225 publications

(213 citation statements)

References 42 publications

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“…Similar features are seen in the ideal bilayer although with markedly reduced contrast between the AB/BA boundary regions. This localization on dislocation lines, along with the AA charge expulsion, have recently been reported in a scanning tunneling microscopy experiment 21 . Having established feature level agreement with experiment, we can now probe deeper into the underlying electronic structure of the valley region via examination of the corresponding Fermi surfaces (FS).…”

Section: B Fermiology At Tiny Anglessupporting

confidence: 69%

Perfect and Controllable Nesting in Minimally Twisted Bilayer Graphene

et al. 2019

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Parallel ("nested") regions of a Fermi surface (FS) drive instabilities of the electron fluid, for example the spin density wave in elemental chromium. In one-dimensional materials, the FS is trivially fully nested (a single nesting vector connects two "Fermi dots"), while in higher dimensions only a fraction of the FS consists of parallel sheets. We demonstrate that the tiny angle regime of twist bilayer graphene (TBLG) possess a phase, accessible by interlayer bias, in which the FS consists entirely of nestable "Fermi lines": the first example of a completely nested FS in a 2d material. This nested phase is found both in the ideal as well as relaxed structure of the twist bilayer. We demonstrate excellent agreement with recent STM images of topological states in this material and elucidate the connection between these and the underlying Fermiology. We show that the geometry of the "Fermi lines" network is controllable by the strength of the applied interlayer bias, and thus that TBLG offers unprecedented access to the physics of FS nesting in 2d materials. 1 arXiv:1908.08318v1 [cond-mat.mtrl-sci] 22 Aug 2019 of the FS consists of nested sheets) and notoriously difficult to control 10,11 . In contrast, the nesting exhibited by the twist bilayer is both complete (100% nested) and, as we show, can be fully controlled by tuning of the interlayer bias.This "nesting phase" of the twist bilayer is found in a large regime of angle-field space and is, remarkably, found both for the ideal twist geometry as well as the structural dislocation network that it reconstructs to at tiny angles 12-14 . The finding of a robust moiré-induced 2d "Fermi line" analogy of the 1d "Fermi dot" topology, controllable via bias, both offers unprecedented access to the physics of FS nesting, as well as highlighting the remarkable electronic structures that can be created by moiré geometries and their structural dislocation networks in 2d materials. II. RESULTS A. ModelThe physics of the tiny angle regime of the twist bilayer is an essentially multiscale problem involving both the lattice constant of graphene -the scale at which atomic relaxation 2 FIG. 1: Fully nested Fermiology in the graphene twist bilayer and the corresponding dislocation network (θ = 0.51 • , E = 90 mV/Å). Below ∼ 1 • twist bilayer graphene relaxes into an ordered network of dislocations, with the smoothly varying stacking order of the ideal twist geometry (a) becoming series of sharp AB and BA domains (b), each separated by pure shear partial dislocations with high von Mises strain (J 2 ) (c,d). Pseudo-magnetic fields of the order of 40 T are induced in the AB and BA regions with alternating sign between the latter (e,f). In the density of states (DOS) the zero mode is substantially broadened, with the valley region shifting upwards in energy (g).However, while atomic relaxation induces dramatic changes to the Fermiology in the zero mode region (l,m), in the valley region a remarkably stable Fermi topology of fully nested Fermi lines is seen (nesting vector indicated by...

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Section: B Fermiology At Tiny Anglessupporting

confidence: 69%

Perfect and Controllable Nesting in Minimally Twisted Bilayer Graphene

et al. 2019

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“…The discovery of strong interactions and superconductivity in twisted graphene bilayers has been one of the main achievement in two-dimensional materials in the past year; it has been chosen as the Physics World breakthrough of the year 2018 [1][2][3], see also Ref. [4]. This field has grown so rapidly that it now carries its own dedicated label, "twistronics".…”

Section: Introductionmentioning

confidence: 99%

Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters

2019

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We analyze a description of twisted graphene bilayers, that incorporates the deformation of the layers using state of the art interlayer atomic potentials, and a modification of the hopping parameters between layers in the light of the classic Slonczewski-Weiss-McClure parametrisation. We obtain narrow bands in all cases, but that their nature can be rather different. We will show how to describe the results by equivalent continuum models. Even though such models can be constructed, their complexity can vary, requiring many coupling parameters to be included, and the full in-layer dispersion must be taken into account. The combination of all these effects will have a large impact on the wave functions of the flat bands, and that modifications in details of the underlying models can lead to significant changes. A robust conclusion is that the natural strength of the interlayer couplings is higher than usually assumed, leading to shifts in the definition of the magic angles. The structure at the edges of the narrow bands, at the Γ point of the Brillouin Zone is also strongly dependent on parametrization. As a result, the existence, and size, of band gaps between the flat bands and the neighboring ones are changed. Hence, the definition of Wannier functions, and descriptions based on local interactions are strongly dependent on the description of the model at the atomic scale. * Francisco. Guinea@imdea.org † Niels.Walet@manchester.ac.uk; https://www.research.manchester.ac.uk/portal/niels.walet.html AA AB FIG. 1. Examples of a graphene bilayer in (approximate) AA and AB alignment. arXiv:1903.00364v2 [cond-mat.str-el]

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“…1 Since then networks of domain walls separating commensurate domains have been obsevered using various experimental methods. [2][3][4][5][6][7][8][9][10][11] The effect of domain walls on electronic, 7,10-24 magnetic 6,24,25 and optical 26 properties of graphene has been studied. Unusual plasmon reflection at domain walls opens up possibilities to manipulate two-dimensional plasmons.…”

Section: Introductionmentioning

confidence: 99%

Energetics and Structure of Domain Wall Networks in Minimally Twisted Bilayer Graphene under Strain

Lebedeva

Popov

2019

J. Phys. Chem. C

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The parameters of the triangular domain wall network in bilayer graphene with a simultaneously twisted and biaxially stretched bottom layer are studied using the two-chain Frenkel-Kontorova model. It is demonstrated that if the graphene layers are free to rotate, they prefer to stay coaligned upon stretching the bottom layer and the regular triangular network of tensile domain walls is formed upon the commensurate-incommensurate phase transition. If the angle between the layers is fixed, the regular triangular network of shear domain walls is observed at zero elongation of the bottom layer. Upon stretching the bottom layer, however, the domain walls transform into the tensile ones and the size of the commensurate domains decreases. We also show that the parameters of the isosceles triangular domain wall network in twisted bilayer graphene under shear strain can be determined through purely geometrical considerations. Experimental analysis of the orientation of domain walls and period of the triangular network would, on the one hand, contribute to understanding of the interlayer interaction of graphene layers, and, on the other hand, serve for detection of relative strains and rotation between the layers. Vice versa external strains can be used to control the parameters of the triangular domain wall network and, therefore, electronic properties of twisted bilayer graphene. arXiv:2001.10791v1 [cond-mat.mes-hall]

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Topologically Protected Helical States in Minimally Twisted Bilayer Graphene

Cited by 225 publications

References 42 publications

Perfect and Controllable Nesting in Minimally Twisted Bilayer Graphene

Perfect and Controllable Nesting in Minimally Twisted Bilayer Graphene

Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters

Energetics and Structure of Domain Wall Networks in Minimally Twisted Bilayer Graphene under Strain

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