Emergent 
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 symmetry in fully relaxed magic-angle twisted bilayer graphene

Angeli, Mattia; Mandelli, Davide; Valli, Angelo; Amaricci, A.; Capone, Massimo; Tosatti, Erio; Fabrizio, Michele

doi:10.1103/physrevb.98.235137

Cited by 91 publications

(95 citation statements)

References 29 publications

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“…In this work we shall study in a holistic way both the effects of lattice deformation and the change in hopping due the change in alignment, which should be contrasted to related work in Refs. [40,41]. 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.…”

Section: Introductionsupporting

confidence: 60%

“…The twist angle is θ ≈ 1.05 • . Note that our approach is complementary to other studies, where one selects the angle which gives the narrowest bands near the neutrality point, and keeps the parametrization used fixed [26,40,51].…”

Section: Discussionmentioning

confidence: 95%

“…For this angle, the electronic properties depend on the choice of parameters used. In this respect, our analysis is rather different from those which select a given parametrization and modify the angle in order to obtain the narrowest band [26,40,51]. Note, finally, that experiments determine the twist angles mostly from measuring the electron density required to fill the bands in the Moiré superlattice.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionsupporting

confidence: 60%

Section: Discussionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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

2019

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“…We begin with an AB stacked bilayer graphene, then twist one of the layers around a point where the top and bottom lattice points overlap. At arbitrary twisting angle except when θ = nπ/3, the resulting structure, whether commensurate or incommensurate, always respects the chiral D 3 or D 6 group [20][21][22][23].…”

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confidence: 99%

Tunable Layer Circular Photogalvanic Effect in Twisted Bilayers

2020

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We develop a general theory of the layer circular photogalvanic effect (LCPGE) in quasi twodimensional chiral bilayers, which refers to the appearance of a polarization-dependent, out-of-plane dipole moment induced by circularly polarized light. We elucidate the geometric origin of the LCPGE as two types of interlayer coordinate shift weighted by the quantum metric tensor and the Berry curvature, respectively. As a concrete example, we calculate the LCPGE in twisted bilayer graphene, and find that it exhibits a resonance peak whose frequency can be tuned from visible to infrared as the twisting angle varies. The LCPGE thus provides a promising route towards frequency-sensitive, circularly-polarized light detection, particularly in the infrared range.

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“…Despite that, the Fourier transform of C(t), see Eq. (12), results in the density of states with typical van Hove peaks are shown in Ref. [7 and 36].…”

Section: Twisted Bilayer Graphenementioning

confidence: 99%

Time-evolution patterns of electrons in twisted bilayer graphene

Bercioux

2019

Phys. Rev. B

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We characterise the dynamics of electrons in twisted bilayer graphene by analysing the timeevolution of electron waves in the atomic lattice. We perform simulations based on a kernel polynomial technique using Chebyshev polynomials; this method does not requires any diagonalisation of the system Hamiltonian. Our simulations reveal that the inter-layer electronic coupling induces the exchange of waves between the two graphene layers. This wave transfer manifests as oscillations of the layer-integrated probability densities as a function of time. For the bilayer case, it also causes a difference in the wavefront dynamics compared to monolayer graphene. The intra-layer spreading of electron waves is irregular and progresses as a two-stage process. The first one characterised by a well-defined wavefront occurs in a short time -a wavefront forms instead during the second stage. The wavefront takes a hexagon-like shape with the vertices developing faster than the edges. Though the detail spreading form of waves depends on initial states, we observe localisation of waves in specific regions of the moiré zone. To characterise the electron dynamics, we also analyse the time auto-correlation functions. We show that these quantities shall exhibit the beating modulation when reducing the interlayer coupling. arXiv:1901.02794v3 [cond-mat.mes-hall]

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Emergent D6 symmetry in fully relaxed magic-angle twisted bilayer graphene

Cited by 91 publications

References 29 publications

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

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

Tunable Layer Circular Photogalvanic Effect in Twisted Bilayers

Time-evolution patterns of electrons in twisted bilayer graphene

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