Superlattice structures in twisted bilayers of folded graphene

Schmidt, Hennrik; Rode, Johannes; Смирнов, Д.; Haug, Rolf J.

doi:10.1038/ncomms6742

Cited by 79 publications

(93 citation statements)

References 39 publications

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“…The case of small angles became interesting after experimental studies of misaligned double layer graphene [10,11] because of the strong effect on the electronic structure, such as the appearance of secundary Dirac cones and van Hove singularities [12,13,14,15]. In most theoretical works [12,16] the moiré patterns were modeled by rigid misaligned layers and the effective potential on the electrons was considered as the superposition of crystalline potentials from the two rotated layers.…”

Section: Introductionmentioning

confidence: 99%

Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite

Wijk¹,

Schuring²,

Katsnelson³

et al. 2015

2D Mater.

186

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Abstract. We study the effect of atomic relaxation on the structure of moiré patterns in twisted graphene on graphite and double layer graphene by large scale atomistic simulations. The reconstructed structure can be described as a superlattice of 'hot spots' with vortex-like behaviour of in-plane atomic displacements and increasing out-of-plane displacements with decreasing angle. These lattice distortions affect both scalar and vector potential and the resulting electronic properties. At low misorientation angles (<∼1• ) the optimized structures deviate drastically from the sinusoidal modulation which is often assumed in calculations of the electronic properties. The proposed structure might be verified by scanning probe microscopy measurements.arXiv:1503.02540v1 [cond-mat.mes-hall]

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Section: Introductionmentioning

confidence: 99%

Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite

Wijk¹,

Schuring²,

Katsnelson³

et al. 2015

2D Mater.

186

View full text Add to dashboard Cite

show abstract

“…which do not depend on the wave vectors k, k except via the coupling condition (6). Equations (12-13) allow us to set up a compact Hamiltonian H 0 that, as has been shown in Ref.…”

Section: Model a Electronic Structurementioning

confidence: 99%

“…Let • . The red squares in panel (a) depict all states k of layer µ = +1 that are coupled to a given state k (blue X) in layer λ = −1, according to the coupling condition (6). The black hexagon depicts the reciprocal twist bilayer unit cell defined by these coupling vectors, here centered at the unrotated K-point.…”

Section: Model a Electronic Structurementioning

confidence: 99%

“…A Fermi surface topology that changes dramatically as a function of energy 2,4 , in combination with the fact that the Fermi energy is a parameter that, experimentally, can be controlled via doping, implies that the twist bilayer is a material for which the transport properties are of great interest. However, thus far experiments have been performed only for the large angle limit 6,35,45 , and theoretical calculations restricted to the case of interlayer transport [46][47][48] . The purpose of the present paper, therefore, is to present a systematic investigation of the in-plane transport of the twist bilayer for the complete range of twist angles 1…”

Section: Introductionmentioning

confidence: 99%

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Electron-phonon scattering and in-plane electric conductivity in twisted bilayer graphene

et al. 2016

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We have surveyed the in-plane transport properties of the graphene twist bilayer using (i) a lowenergy effective Hamiltonian for the underlying electronic structure, (ii) an isotropic elastic phonon model, and (iii) the linear Boltzmann equation for elastic electron-phonon scattering. We find that transport in the twist bilayer is profoundly sensitive to the rotation angle of the constituent layers. Similar to the electronic structure of the twist bilayer the transport is qualitatively different in three distinct angle regimes. At large angles (θ > ≈10• ) and at temperatures below an interlayer BlochGrüneisen temperature of ≈ 10 K the conductivity is independent of the twist angle i.e. the layers are fully decoupled. Above this temperature the layers, even though decoupled in the ground state, are re-coupled by electron-phonon scattering and the transport is different both from single layer graphene as well as the Bernal bilayer. In the small angle regime θ < ≈2• the conductivity drops by two orders of magnitude and develops a rich energy dependence, reflecting the complexity of the underlying topological changes (Lifshitz transitions) of the Fermi surface. At intermediate angles the conductivity decreases continuously as the twist angle is reduced, while the energy dependence of the conductivity presents two sharp transitions, that occur at specific angle dependent energies, and that may be related to (i) the well studied van Hove singularity of the twist bilayer and (ii) a Lifshitz transition that occurs when trigonally placed electron pockets decorate the strongly warped Dirac cone. Interestingly, we find that, while the electron-phonon scattering is dominated by layer symmetric flexural phonons in the small angle limit, at large angles, in contrast, it is the layer anti-symmetric flexural mode that is most important. We examine the role of a layer perpendicular electric field finding that it affects the conductivity strongly at low temperatures whereas this effect is washed out by Fermi smearing at room temperatures.

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“…For graphene, this definition can be used, but the true spin is replaced by the sublattice pseudospin. The 2D chiral massless-Dirac-fermions give rise to the most interesting aspects of graphene, offering a perfect platform for exploring its amazing physical phenomena, such as chiral Klein tunneling [6,12,14,15], exceptional ballistic transport [16][17][18], and the self-similar Hofstadter butterfly spectrum [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Landau quantization of Dirac fermions in graphene and its multilayers

et al. 2017

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When electrons are confined in a two-dimensional (2D) system, typical quantum-mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum-mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behaviors of Dirac fermions in monolayer and multilayer graphene by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Through STS measurement of the strong magnetic fields, distinct Landau-level spectra and rich level-splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fundamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties.

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Superlattice structures in twisted bilayers of folded graphene

Cited by 79 publications

References 39 publications

Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite

Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite

Electron-phonon scattering and in-plane electric conductivity in twisted bilayer graphene

Landau quantization of Dirac fermions in graphene and its multilayers

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