Electronic structure and optical properties of twisted bilayer graphene calculated via time evolution of states in real space

Le, H. Anh; Do, V. Nam

doi:10.1103/physrevb.97.125136

Cited by 39 publications

(34 citation statements)

References 32 publications

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“…The rotation angle can be expressed in terms of the integers n, m as 2 cos θ = (m 2 + n 2 + 4mn)/(m 2 + n 2 + mn). The magic angle θ = 1.08 • corresponds to (n, m) = (31,30), with the number of atoms in the unit cell given by N = 4 |(L 1 × L 2 )|/|(a 1 × a 2 )| = 11164. As n = m + 1, the lattice constant L = |L 1 | = |L 2 | = a|m − n|/ [2 sin(θ/2)] ∼ 12.78 nm is coincident in this case with the Moiré pattern period L M = a/ [2 sin(θ/2)].…”

Section: Appendix A: Lattice Geometry and Reciprocal Spacementioning

confidence: 99%

Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle θ∼1.08∘

et al. 2019

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We combine state-of-the-art large-scale first principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle θ =1.08 • . We show that the energy width of the flat band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes.

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Section: Appendix A: Lattice Geometry and Reciprocal Spacementioning

confidence: 99%

Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle θ∼1.08∘

et al. 2019

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“…We implemented this procedure for the first time in Ref. [36], and results for extremely tiny twist configuration of TBG were in agreement with the approach of continuum models. 7…”

Section: A the Empirical Tight-binding Hamiltonianmentioning

confidence: 53%

“…In the tight-binding representation with the initial states chosen as a localised at a particular lattice node |ψ(0) = |i , the time auto-correlation C i (t) = i|ψ(t) = g i (t), i.e., equal to the local probability amplitude at the node i. Its power spectrum, defined as the Fourier transform of C i (t), is the local density of states of electron in the considered system: 35,36…”

Section: A the Empirical Tight-binding Hamiltonianmentioning

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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“…(19) it yields C i (t) = i|ψ(t) = g i (t), i.e., equal to the local probability amplitude at the node i. Its power spectrum, defined as the Fourier transform of C i (t), is identified as the density of states of an electron at the lattice node i, i.e., the local density of states [20,27]:…”

Section: Ii3 Sampling Of Localized States and Local Density Of Statesmentioning

confidence: 99%

“…Partial knowledge on the energy spectrum, however, can be obtained by interpolating/extrapolating data of the energy spectrum of commensurate TBG configurations for that of the incommensurate ones. This scheme is guaranteed by a demonstration of the continuous variation of the energy spectrum versus the twist angle [20]. Effective continuum models can be also constructed to study the electronic structure of TBG configurations of tiny twist angles [3,5,7,15,[21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Real-Space Approach for the Electronic Calculation of Twisted Bilayer Graphene Using the Orthogonal Polynomial Technique

Nguyen²,

Nguyen³

et al. 2019

Comm. in Phys.

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We discuss technical issues involving the implementation of a computational method for the electronic structure of material systems of arbitrary atomic arrangement. The method is based on the analysis of time evolution of electron states in the real lattice space. The Chebyshev polynomials of the first kind are used to approximate the time evolution operator. We demonstrate that the developed method is powerful and efficient since the computational scaling law is linear. We invoked the method to study the electronic properties of special twisted bilayer graphene whose atomic structure is quasi-crystalline. We show the density of states of an electron in this graphene system as well as the variation of the associated time auto-correlation function. We find the fluctuation of electron density on the lattice nodes forming a typical pattern closely related to the typical atomic pattern of the quasi-crystalline bilayer graphene configuration.

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Electronic structure and optical properties of twisted bilayer graphene calculated via time evolution of states in real space

Cited by 39 publications

References 32 publications

Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle θ∼1.08∘

Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle θ∼1.08∘

Time-evolution patterns of electrons in twisted bilayer graphene

Real-Space Approach for the Electronic Calculation of Twisted Bilayer Graphene Using the Orthogonal Polynomial Technique

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