Quantum spin-valley effect: Dynamical polarization and optical properties of silicene

We present a theoretical realization of the dynamical polarization and optical absorption coefficient of the semiconductor silicene under the influence of a perpendicular electric field. Using Green’s function theory, we derive the dynamical polarization function and, through the Ehrenreich–Cohen model, we obtain the dynamical dielectric function when a perpendicular electric field is applied to the system. Our analytical calculations reveal that silicene has a small energy gap, which can be controlled by the perpendicular electric field. We find that there is a significant difference in the spin-valley polarization of the polarization function for the spin-up and spin-down states. In particular, the optical absorption results show that the absorption of silicene is low, around 50 meV, and the external electric field and temperature play a crucial role in determining the optical absorption peaks. Compared with ab initio calculations, we discuss the validity of the methods used in the literature. The detailed results of the dynamical polarization function and the spin-valley optical absorption coefficient of silicene are presented.