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We investigate the interband and intraband transition of the monolayer andAB-stacked bilayer silicene in low-energy tight-binding model under theelectric field, where we focus on the dynamical polarization function,screening due to the charged impurity, and the plasmon dispersion. We obtainthe logarithmically divergen polarization function within therandom-phase-approximation (RPA) whose logarithmic singularities corresponds tothe discontinuities of the first derivative which is at the momentum ${\bfq}=2{\bf k}_{F}$ in static case and indicate the topological phase transitionpoint from the gapless semimetal to the gapped band insulator. We also obtainthe power-law-dependent Friedel oscillation which can be enhanced by increasingthe Rashba-coupling, that can contribute to the screened potential of thecharged impurity which scale as $\sim r^{-1/2}$ in the short distance from theimpurity and scale as $\sim r^{-1/3}$ in the long distance from the impurity.In the single-particle excitation regime with the electron-hole continuum, theinterband and intraband transition happen, and the plasmon dispersion, which wemainly focus on the optical plasmon (which $\sim\sqrt{{\bf q}}$ inlong-wavelength limit) in this paper, start to damped into the electron-holepairs due to the nonzero imaginary part of the polarization function.

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