Dynamical Polarization Function, Plasmons and Screening in Silicene and Other Buckled Honeycomb Lattices

We explore the dielectric properties of graphene-like two-dimensional Kane-Mele topological insulators manifest in buckled honeycomb lattices (ex. silicene, germanene, etc.). The effect of an onsite potential difference ($\Delta_z$) between sublattices is given particular attention. We present the results for the real and imaginary parts of the dynamical polarization function. We show that these results display features of three regimes (topological insulator, valley-spin polarized metal, and trivial band insulator) and may be used to extract information on the strength of the intrinsic spin-orbit coupling. We study the inverse dielectric function and provide numerical results for the plasmon branch. We discuss the behaviour of the plasmon as a function of sublattice potential difference and show that the behaviour of the plasmon branch as $\Delta_z$ is varied is dependent on the location of the chemical potential with respect to the gaps. The static polarization is discussed and numerical results for the screening of a charged impurity are provided. We observe a beating phenomenon in the effective potential which is dependent on $\Delta_z$.