Dielectric Singularity ofα−Sn

The wave-number-dependent dielectric function $\epsilon \mathrm{}\left(q\right)\mathrm{}$ for the zero-gap semiconductor $\alpha -\mathrm{S}\mathrm{n}$ has been calculated in the limit $q\to 0$. Because of the specific symmetry of the wave functions at the point of contact between the conduction and valence bands, $\epsilon \mathrm{}\left(q\right)\mathrm{}$ has a singularity of the form of $\frac{1}{q}$ in the long-wavelength limit. The screening of an impurity charge by this singular dielectric function is also discussed.