Dynamical polarization, plasmon model, and the Friedel oscillation of the screened potential in doped Dirac and Weyl system

Abstract

We discuss the dynamical polarization, plasmon dispersion, relaxation time, and the Friedel oscillation of screened potential of the two-dimension Dirac and threedimension Weyl system (which are gapped) in the low-energy tigh-binding model. The results, like the Fermi wavevector, Thomas-Fermi wavevector, and longitudinal conductivity are obtained in different dimensions. Some important conclusions are detailedly discussed in this paper, including the screening character under short or long range Coulomb interaction, and the longitudinal conductivity in two-or threedimensions. The longitudinal conductivity in optical limit is distinguishing for the case of two-dimension system and three-dimension system. The density-dependence (including the carrier density and the impurity concentration) of the Fermi wavevector, dc conductivity, and the relaxation time are discussed. Specially, for the doped Weyl system, the pumped carrier density due to the chiral anomaly origin from electromagnetic response is controlled by the internode relaxation time which has also been analyzed. Our results is helpful to the application of the Dirac or Weyl systems as well as the study on their low-temperature characters.

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.…”

Two-dimensional parabolic Dirac system in the presence of non-magnetic and magnetic impurities

“…in asymptotic approximation. For the more general cases that the q is comparable with the m D , the static polarization function can be written at zero-temperature as [38,39,40,47,48,33] Π…”

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.…”

“…We have clarified the density-dependence (carriers or the impurities) of the Fermi wave vector, Thomas-Fermi wave vector, plasmon dispersion, and the density of states (DOS) at Fermi level in Ref. [17] for the 2D Dirac system and the 3D Dirac or Weyl system, here we use the results we obtained in Ref. [17] for further discussion.…”

“…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 .…”