Dielectric Response of a Thin-Layer Zero-Gap Semiconductor

It is shown that the dielectric response of a thin layer of α-Sn---type semiconductor is radically different than that of the bulk material. The q^-1 and ω^-1/2 singularities of the bulk polarizability are absent in the layer. Instead, the dielectric response and optical absorption of the layer are highly anisotropic, and the static dielectric constant is linearly dependent on layer thickness. In the random-phase approximation, the thin-layer energy-band structure is unconditionally stable against exciton formation.