Frequency-Dependent Dielectric Function of a Zero-Gap Semiconductor

The frequency-dependent dielectric function $\epsilon \left(\omega \right)$ of an inherently zero-gap semiconductor, such as grey tin, has unusual properties at low temperatures. In undoped samples $\epsilon \left(\omega \right)\sim {\omega }^{-\frac{1}{2}}$; in doped samples interband effects considerably modify the coefficient of the additional ${\omega }^{-2\mathrm{}}$ term from its free-carrier value, the sign being reversed for $p$-type impurities. These properties should be observable in reflectance measurements.