Theory of 2D crystals: graphene and beyond

Roldán, Rafael; Chirolli, Luca; Prada, Elsa; Silva-Guillén, Jose Ángel; San-José, Pablo; Guinea, F.

doi:10.1039/c7cs00210f

Cited by 140 publications

(104 citation statements)

References 58 publications

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“…Several plausible effects may explain the fact that Eqs. (25) and (26) give different results for a 2D layer fluctuating in 3 dimensions. One possibility is that the anharmonicity of the out-of-plane displacements is not correctly reproduced by the HLR analysis.…”

Section: Elastic Moduli From the Hlr Analysismentioning

confidence: 99%

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Phonon dispersion in two-dimensional solids from atomic probability distributions

Ramı́rez

Herrero

2019

The Journal of Chemical Physics

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We propose a harmonic linear response (HLR) method to calculate the phonon dispersion relations of two-dimensional (2D) layers from equilibrium simulations at finite temperature. This HLR approach is based on the linear response of the system, as derived from the analysis of its centroid density in equilibrium path integral simulations. In the classical limit, this approach is closely related to those methods that study vibrational properties by the diagonalization of the covariance matrix of atomic fluctuations. The validity of the method is tested in the calculation of the phonon dispersion relations of a graphene monolayer, a graphene bilayer, and graphane. Anharmonic effects in the phonon dispersion relations of graphene are demonstrated by the calculation of the temperature dependence of the following observables: the kinetic energy of the carbon atoms, the vibrational frequency of the optical E2g mode, and the elastic moduli of the layer.

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Section: Elastic Moduli From the Hlr Analysismentioning

confidence: 99%

“…(25) becomes different than that one in Eq. (26). Ripples depend on an additional elastic modulus, the bending stiffness, κ, that for an atom thick layer is a constant independent from the Lam coefficients, λ and µ.…”

Section: Elastic Moduli From the Hlr Analysismentioning

confidence: 99%

Phonon dispersion in two-dimensional solids from atomic probability distributions

Ramı́rez

Herrero

2019

The Journal of Chemical Physics

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“…3, where we assume a z−polarized emitter located at a distance of 1nm from free standing bilayer black phosphorus. Due to the large loss in the optical conductivity in the hyperbolic regions, a clear transition from the elliptical to hyperbolic regime [2] is not observed, as shown in Fig. 3 (a), (b), (c).…”

mentioning

confidence: 95%

“…Introduction. Semiconducting two dimensional (2D) crystals are excellent platforms for tuneable optoelectronics, thanks to their remarkable response to external electrical and mechanical stimuli [1,2]. In particular, atomically thin black phosphorus [3][4][5][6] (BP) has shown extraordinary tuneability of its optical and electronic properties by several methods [7], like electrostatic gating [8][9][10][11][12], chemical functionalization [13], quantum confinement (number of layers) [14], external strain [15] or high pressure [16,17].…”

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confidence: 99%

Tuning Two-Dimensional Hyperbolic Plasmons in Black Phosphorus

et al. 2019

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Black phosphorus presents a very anisotropic crystal structure, making it a potential candidate for hyperbolic plasmonics, characterized by a permittivity tensor where one of the principal components is metallic and the other dielectric. Here we demonstrate that atomically thin black phosphorus can be engineered to be a hyperbolic material operating in a broad range of the electromagnetic spectrum from the entire visible spectrum to ultraviolet. With the introduction of an optical gain, a new hyperbolic region emerges in the infrared. The character of this hyperbolic plasmon depends on the interplay between gain and loss along the two crystalline directions.

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“…The discovery of two-dimensional (2D) systems whose quasiparticles are described in terms of a Dirac theory 1 has been one of the major breakthroughs over the last two decades in condensed matter physics and has fuelled research in the area of 2D materials 2,3 . Graphene, that features gapless Dirac cones in the neighborhood of the Fermi energy 4 , is a paradigmatic example.…”

Section: Introductionmentioning

confidence: 99%

Optical orientation with linearly polarized light in transition metal dichalcogenides

et al. 2019

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We study the optical properties of semiconducting transition metal dichalcogenide monolayers under the influence of strong out-of-plane magnetic fields, using the effective massive Dirac model. We pay attention to the role of spin-orbit coupling effects, doping level and electron-electron interactions, treated at the Hartree-Fock level. We find that optically-induced valley and spin imbalance, commonly attained with circularly polarized light, can also be obtained with linearly polarized light in the doped regime. Additionally, we explore an exchange-driven mechanism to enhance the spinorbit splitting of the conduction band, in n-doped systems, controlling both the carrier density and the intensity of the applied magnetic field. arXiv:1811.04003v2 [cond-mat.mes-hall]

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Theory of 2D crystals: graphene and beyond

Cited by 140 publications

References 58 publications

Phonon dispersion in two-dimensional solids from atomic probability distributions

Phonon dispersion in two-dimensional solids from atomic probability distributions

Tuning Two-Dimensional Hyperbolic Plasmons in Black Phosphorus

Optical orientation with linearly polarized light in transition metal dichalcogenides

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