  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 $\Delta_z$.
