Structure of twisted and buckled bilayer graphene

Experiments on bilayer graphene unveiled a fascinating realization of stacking disorder where triangular domains with well-defined Bernal stacking are delimited by a hexagonal network of strain solitons. Here we show by means of numerical simulations that this is a consequence of a structural transformation of the moiré pattern inherent of twisted bilayer graphene taking place at twist angles θ below a crossover angle θ = 1.2 • . The transformation is governed by the interplay between the interlayer van der Waals interaction and the in-plane strain field, and is revealed by a change in the functional form of the twist energy density. This transformation unveils an electronic regime characteristic of vanishing twist angles in which the charge density converges, though not uniformly, to that of ideal bilayer graphene with Bernal stacking. On the other hand, the stacking domain boundaries form a distinct charge density pattern that provides the STM signature of the hexagonal solitonic network. * oleg.yazyev@epfl.ch arXiv:1711.08647v2 [cond-mat.mes-hall] 11 Apr 2018 Bilayer graphene (BLG) shares many of the properties of monolayer graphene while also showing a number of pronounced differences. For instance, its equilibrium structural configuration reveals the massive nature of its charge carriers [1], the possibility of inducing a tunable band gap by applying a transverse electric field [2-4] and quantum Hall valley ferromagnetism [5]. These properties are a result of the coupling between the two layers.In order to describe the atomic structure of bilayer graphene the relative position of the two layers has to be defined. In many situations it is sufficient to specify a unique interlayer displacement vector that defines the stacking configuration. As a general property of graphitic structures, the low-energy configuration is represented by the Bernal stacking [6,7]. However, the stacking configuration is not immune to disorder which can manifest, for example, in boundaries that connect two domains with energetically degenerate yet topologically inequivalent stacking configurations, AB and BA [8][9][10][11]. Such stacking domain boundaries are realized by strain solitons, which are segments with a characteristic width where the strain that arises from interfacing two inequivalent stacking domains is confined.Recent studies have shown that strain solitons can be displaced by the action of a scanning tunneling microscope tip, but do not vanish due to their topological nature [8,12]. From the theoretical point of view, the two-dimensional extension of the Frenkel-Kontorova model predicts the emergence of strain solitons with a typical width of a few nanometers [13] while their density is defined by the twist angle.In other situations the stacking configuration cannot be uniquely defined on the whole surface of the sample since the two layers cannot be superimposed by a rigid in-plane shift. This is the case of twisted bilayer graphene where one layer is rotated relative to another, a system that has been widely reported ...

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“…2(c). Moreover, ∆z adapts to ∆z SP and ∆z AA , respectively, at M and G, consistent with the local stacking configurations [36].…”

Section: Section Methods and Supplementary Materials)supporting

confidence: 69%

Structural and electronic transformation in low-angle twisted bilayer graphene

2017

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“…Others concentrate on strained graphene bilayers. The work by Jain et al [46] employs a potential that is specifically designed for the out of layer deformation, but may be less well suited to the details of the in-layer deformation. Nevertheless, this reference also contains an interesting discussion of the lattice deformation.…”

Section: Classical Atomistic Simulationsmentioning

confidence: 99%

“…Our calculation of deformation bears some similarity to the work by van Wijk et al [42,43], but the authors of those references mainly study a single layer on either bulk graphite or hBN. There are a few other papers that take a related approach [44][45][46][47][48][49] to lattice deformation, often in a slightly different context. We start out by selecting a few modern potentials for graphene, and will analyze in detail the deformation of the bilayer systems.…”

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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“…The real TBG is not a simple stack of rigid graphene layers as assumed in the previous section, but it has a spontaneous lattice relaxation and resulting AB/BA domain formation [31][32][33]35,[45][46][47][48][49][50][51][52][53] . Such a structural deformation modifies the electronic band structure 19,20,35,44,50,[52][53][54] .…”

Section: Effect Of Lattice Relaxationmentioning

confidence: 99%

Perfect one-dimensional chiral states in biased twisted bilayer graphene

Tsim

Nam²,

Koshino

2020

Phys. Rev. B

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We theoretically study the electronic structure of small-angle twisted bilayer graphene with a large potential asymmetry between the top and bottom layers. We show that the emergent topological channels known to appear on the triangular AB-BA domain boundary do not actually form a percolating network, but instead they provide independent, perfect one-dimensional eigenmodes propagating in three different directions. Using the continuum-model Hamiltonian, we demonstrate that an applied bias causes two well-defined energy windows which contain sparsely distributed one-dimensional eigenmodes. The origin of these energy windows can be understood using a twoband model of the intersecting electron and hole bands of single layer graphene. We also use the tight-binding model to implement the lattice deformations in twisted bilayer graphene, and discuss the effect of lattice relaxation on the one-dimensional eigenmodes. arXiv:2001.06257v2 [cond-mat.mes-hall]

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Structure of twisted and buckled bilayer graphene

Cited by 119 publications

References 51 publications

Structural and electronic transformation in low-angle twisted bilayer graphene

Structural and electronic transformation in low-angle twisted bilayer graphene

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

Perfect one-dimensional chiral states in biased twisted bilayer graphene

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