  We discuss the optical conductivity of several non-interacting
two-dimensional (2D) semiconducting systems focusing on gapped Dirac and
Schr\"odinger fermions as well as on a system mixing these two types. Close to
the band-gap, we can define a universal optical conductivity quantum of
$\sigma_0=\frac{1}{16}\frac{e^2}{\hbar}$ for the pure systems. The effective
optical conductivity then depends on the degeneracy factors $g_s$ (spin) and
$g_v$ (valley) and on the curvature around the band-gap $\nu$, i.e., it
generally reads $\sigma=g_sg_v\nu\sigma_0$. For a system composed of both types
of carriers, the optical conductivity becomes non-universal.
