  For semiconductors and semimetals possessing a narrow gap between bands with
different parity, the dispersion of the dielectric function is explicitly
evaluated in the infrared region. The imaginary part of the dielectric function
has a plateau above the absorption threshold for the interband electron
transitions. The real part of the dielectric function has a logarithmic
singularity at the threshold. This results in the large contribution into the
dielectric constant for pure semiconductors at low frequencies. For samples
with degenerate carriers, the real part of the dielectric function is divergent
at the absorption threshold. This divergence is smeared with the temperature or
the collision rate.
