  We discuss the dynamical polarization, plasmon dispersion, relaxation time,
and the Friedel oscillation of screened potential of the two-dimension Dirac
and three-dimension 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 three-dimensions. 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. %The model for which the calculations based on is the
low-energy tight-binding model as presented in the Sec.2, %i.e., the results in
this paper is for the low-temperature and low-energy case %and it's thus
possible to carrying out a logarithmic self-energy correction to the relaxation
time as we discussed in the text. %The difference between the longitudinal
conductivity in serversal systems is also been discussed. Our results is
helpful to the application of the Dirac or Weyl systems as well as the study on
their low-temperature characters.
