Features of interband absorption in narrow-gap semiconductors
  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. 
L.A. Falkovsky