Temperature Dependence of the Static Dielectric Constant of a Symmetry-Induced Zero-Gap Semiconductor

It is shown that the random-phase approximation static dielectric constant of a semiconductor with a ${\Gamma }_8$ conduction—valence-band degeneracy is nondivergent at zero momentum transfer for any concentration of ionized impurities (including the intrinsic material) so long as $T\ne 0$. The temperature dependence of the dielectric constant is calculated. It is shown that in the nondegenerate limit the dependence of the interband polarization is pure $T^{-\frac{1}{2}}$. Illustrative calculations are presented for $\alpha -\mathrm{S}\mathrm{n}$.