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Integer quantum Hall conductivity and longitudinal conductivity in silicene under the electric field and magnetic field
We investigate the integer Hall conductivity and longitudinal conductivity of
silicene under the magnetic field, electric field, and exchange field in this
letter. We focus not only on the low-temperature and -function
impurities (i.e., independent of the scattering momentum) case, which only
exist the intra-Landau level transition, but also on the case of inter-Landau
level transition which also with the non-elastic scattering. The resulting
longitudinal conductivity is very different with the intra-Landau level one at
low-temperature. The exprssions of the Hall conductivity, longitudinal
conductivity, valley contributed Hall conductivity, and the spin or valley Hall
conductivity, are deduced in this letter. We also compute the dynamical
polarization under the magnetic field which is a important quantity and has
many exciting and novel properties, and with the screened scattering due to the
charged impurities. The polarization function here is also related to the
Landau level index under the magnetic field, and shows step-like feature rather
than the logarithmically divergenas which appears for the zero-magnetic field
case, and it's also naturally related to the conductivity in silicene. The
generalized Laguerre polynomial is used in both the longitudinal conductivity
and dynamical polarization function under magnetic field
Dynamical polarization and the optical response of silicene and related materials
We discuss the dynamical polarization, optical response in low-frequency
regime under in-plane polarized driving field of the silicene. The dynamical
polarization, dielectric function, and absorption of radiation in infrared
region are obtained and shown in the space, and they are
distinguishing for the cases of chemical potential larger than the band gap and
smaller than the band gap. The optical properties of silicene and the related
group-V and group-VI materials: MoS and black phosphorus are explored
through the first-principle study. The plasmon which damped into the
electron-hole pair in the single-particle excitation regime is also mentioned.
The spin/valley polarized electron-hole pairs can be formed through that way,
especially for the high-energy -plasmon which begin to damp at the small
-limit. The anisotropic effects induced by the warping structure or
charged impurity, and the anisotropic polarization induced by the polarized
incident light are also discussed. Our result exhibits the great potential in
the optoelectronic applications of the materials we discussed
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