Effective Dirac Hamiltonian for anisotropic honeycomb lattices: Optical properties

Oliva-Leyva, M.; Naumis, Gerardo G.

doi:10.1103/physrevb.93.035439

Cited by 38 publications

(34 citation statements)

References 63 publications

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“…A tight binding-model of 8 − P mmn borophene has been recently developed [12,13] and an effective low-energy Hamiltonian in the vicinity of Dirac points was proposed on symmetry consideration. Pseudomagnetic fields were also predicted similar to those in strained graphene [4,[14][15][16][17] and its relationship with electronic [18,19] and optical conductivity [20,21].…”

Section: Introductionmentioning

confidence: 85%

Metal-insulator transition in 8−Pmmn borophene under normal incidence of electromagnetic radiation

Espinosa-Champo

Naumis

2019

Phys. Rev. B

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The energy spectrum for the problem of 8−P mmn borophene's electronic carriers under perpendicular incidence of electromagnetic waves is studied without the use of any perturbative technique.This allows to study the effects of very strong fields. To obtain the spectrum and wavefunctions, the time-dependent Dirac equation is solved by using a frame moving with the space-time cone of the wave, i.e., by transforming the equation into an ordinary differential equation in terms of the wave-phase, leading to an electron-wave quasiparticle. The limiting case of strong fields is thus analyzed.The resulting eigenfunctions obey a generalized Mathieu equation,i.e., of a classical parametric pendulum. The energy spectrum presents bands, and a gap at the Fermi energy. The gaps are due to the space-time diffraction of electrons in phase with the electromagnetic field, i.e., electrons in borophene acquire an effective mass under strong electromagnetic radiation

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Section: Introductionmentioning

confidence: 85%

Metal-insulator transition in 8−Pmmn borophene under normal incidence of electromagnetic radiation

Espinosa-Champo

Naumis

2019

Phys. Rev. B

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“…where γ = t 1 2 + t 2 2 + t 3 2 and, equation (66) is valid for any anisotropic honeycomb lattice [163]. Typical contour plots resulting from the energy dispersion given by equation (65) are shown in figure 13(a) for unstrained graphene, and in figures 13(b), 13(c) and 13(d) for other representative types of strain.…”

Section: Uniformly Strained Graphenementioning

confidence: 99%

Electronic and optical properties of strained graphene and other strained 2D materials: a review

et al. 2017

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Abstract. This review presents the state of the art in strain and rippleinduced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed DiracSchrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide-and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

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“…The light blue straight lines are the section of the Dirac cone cut by the k x = 0 plane and the solid gray lines are the quasi-energy spectrum in the approximation r = √ a. The blue, orange, green and red lines correspond to the different bands arising from the exact expression of the quasi-energy (33). We readily confirm that both, the exact and the approximated quasi-energy spectrum lines, asymptotically come close to the Dirac cone.…”

Section: B Quasi-energy Spectrummentioning

confidence: 99%

Dynamical band gap tuning in anisotropic tilted Dirac semimetals by intense elliptically polarized normal illumination and its application to8−Pmmnborophene

et al. 2019

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The Dynamical-gap formation in Weyl semimetals modulated by intense elliptically polarized light is addressed through the solution of the time-dependent Schrödinger equation for the Weyl Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasi-energy spectrum of the two-dimensional Weyl Hamiltonian under normal incidence of elliptically polarized electromagnetic waves are obtained using a non-perturbative approach. In it, the Weyl equation is reduced to an ordinary second-order differential Mathieu equation. It is shown that the stability conditions of the Mathieu functions are directly inherited by the wave function resulting in a quasiparticle spectrum consisting of bands and gaps determined by dynamical diffraction and resonance conditions between the electron and the electromagnetic wave. Estimations of the electromagnetic field intensity and frequency, as well as the magnitude of the generated gap are obtained for the 8 − P mmn phase of borophene. We provide with a simple method that enables to predict the formation of dynamical-gaps of unstable wave functions and their magnitudes. This method can readily be adapted to other Weyl semimetals.

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Effective Dirac Hamiltonian for anisotropic honeycomb lattices: Optical properties

Cited by 38 publications

References 63 publications

Metal-insulator transition in 8−Pmmn borophene under normal incidence of electromagnetic radiation

Metal-insulator transition in 8−Pmmn borophene under normal incidence of electromagnetic radiation

Electronic and optical properties of strained graphene and other strained 2D materials: a review

Dynamical band gap tuning in anisotropic tilted Dirac semimetals by intense elliptically polarized normal illumination and its application to8−Pmmnborophene

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