Stress-Dependent Dielectric Constant of a Zero-Gap Semiconductor

For a symmetry-induced zero-gap semiconductor, such as gray tin, under uniaxial stress, the static dielectric constant at infinite wavelength and zero temperature is shown to contain a term of the form of $\delta _0^{}{}_{}{}^{\frac{-1\mathrm{}}{2}}$, where $2{\delta }_0$ is the stress splitting of the energy band at the band edge. The measured stress dependence of electron mobility of a degenerate $n$-type sample of gray tin at low temperature is explained in terms of this anomaloous screening.