Interband and intraband transition, dynamical polarization and screening of the monolayer and bilayer silicene in low-energy tight-binding model

Abstract

We investigate the interband and intraband transition of the monolayer and AB-stacked bilayer silicene in low-energy tight-binding model under the electric field, where we focus on the dynamical polarization function, screening due to the charged impurity, and the plasmon dispersion. We obtain the logarithmically divergen polarization function within the random-phase-approximation (RPA) whose logarithmic singularities corresponds to the discontinuities of the first derivative which is at the momentum q = 2kF in static case and indicate the topological phase transition point from the gapless semimetal to the gapped band insulator. We also obtain the power-law-dependent Friedel oscillation which can be enhanced by increasing the Rashba-coupling, that can contribute to the screened potential of the charged impurity which scale as ∼ r −1/2 in the short distance from the impurity and scale as ∼ r −1/3 in the long distance from the impurity. In the single-particle excitation regime with the electron-hole continuum, the interband and intraband transition happen, and the plasmon dispersion, which we mainly focus on the optical plasmon (which ∼ √ q in long-wavelength limit) in this paper, start to damped into the electron-hole pairs due to the nonzero imaginary part of the polarization function. In low-frequency regime where the collective behavior and optical properties of the Dirac material relys more on the frequency than the fine structure constant, the intraband transition is dominate and it's found that completely undamped in the static case (ω = 0), which is due to the absence of the imaginary dynamic polarization. We also observe the linear (weakly damped) plasmon model for the classical bilayer silicene which is similar to the high-energy π-plasmon or the case of conducting substrate which with strong metallic screening in the bulk semiconductor. For the large carrier density, we find the plasmon diapersion has ωp ∼ n 1/2 which consistent with the quadratic dispersion around the Dirac-point like the bilayer silicene with the effective mass about the interlayer hopping (esperially when taking the Rashba-coupling and exchange field into consider) or the normal two-dimension electron gas, while in the little concentration limit, ωp ∼ n 1/4 which consistent with the linear dispersion like the monolayer silicene. Under the nonmagnetic impurity scattering, the Thomas-Fermi decay and Friedel oscillation can easily be observed due to the strong spin-orbit couopling of the bilayer silicene even we don't take the Rashba-coupling into consider. *

Electronic properties of the parabolic Dirac system

“…where the scattering momentum q here is usually at the Fermi surface (i.e., q = 2k F ) where the scattering the dominant, and it's also similar to the results about the Friedel oscillation of the screened potential [51,53,29,22,52] as well as the long range spin susceptibility [54]. In Fig.10, we show the RKKY range function for the casees of T = 1 and T = 2, where we set the momentum cutoff as k c = 4.8 eV.…”

Dynamical current–current correlation in two-dimensional parabolic Dirac systems

“…Since most of the 2D Dirac system is unlike the QED, which, in non-relativistic case, the momentum integral is ultraviolet convergent and doesn't need the cutoff, the most of the 2D Dirac systems as we discussed need the ultraviolet cutoff Λ (i.e., the Fourier transform of the Λ r ), and we estimate the ultraviolet curoff as the bandwidth of the silicene, which is about 4.8 eV, and such estimation is valid and enough for our computation in this article [21,22,20]. While for the effective mass m which is related to both the interlayer and intralayer hopping, we use the typical value of bilayer silicene which is m = 0.298m 0 [23,24,25,26,27], while for the bilayer graphene, our results are applicable after replace the effective mass as m = 0.033m 0 [28] or m = 0.029m 0 [29]. For the 3D Dirac or Weyl system, the longitudinal susceptibility as well as the current-current correlation function is needed to taking the chiral anomaly and the monopole formed by the Weyl nodes into account. )…”

Electronic transport and dynamical polarization in bilayer silicene-like systems

“…For the dynamical polarization of the monolayer silicene, we have discussed in the Refs. [13,9,16,17], while for the bilayer silicene which is a parabolic system the interlayer hopping t ⊥ need to be taken into account. The kink of the bilayer silicene we discuss here is the AB-stacked one which is generally more stable than the AA-stacked one [65], and the parameters are setted as: The nearest-neighbor (NN) interlayer hopping is t ⊥ = 2 eV which is much larger than the next-nearest-neighbor (NNN) interlayer one [65] and thus we consider only the NN interlayer hopping here.…”

“…For band structure of moolayer silicene, the symmetry between the conduction band and the valence band will be broken in silicene by the next-nearest-neighbor (NNN) Rashba-coupling (induced by the applied perpendicular electric field) (see Refs. [9,10,11]). We found that, the static polarization of bilayer silicene could be nearly temperature-independent in adiabatically case with the large band gap.…”

“…At low-temperature, the carrier transport and the relaxation rate of the bilayer silicene is discussed in the presence of randomly charged impurity and the dominant elastic back scattering, we also compare the results to the case of three-dimension Weyl semimetal. The electronic transport in the presence of screened Coulomb potential also affects the dc conductivity [15] as well as the Friedel oscillation [9,13,16,17,18] of the silicene. At finite temperature, the the electron-phonon interaction is calculated and the acoustic phonon model of silicene is obtained by the DFT study and compared to the MoS 2 .…”