  We study the interplay between Dirac and Schr\"odinger fermions in the
polarization properties of a two-dimensional electron gas (2DEG). Specifically,
we analyze the low-energy sector of narrow-gap semiconductors described by a
two-band Kane model. In the context of quantum spin Hall insulators,
particularly, in Hg(Cd)Te quantum wells, this model is named
Bernevig-Hughes-Zhang model. Interestingly, it describes electrons with
intermediate properties between Dirac and Schr\"odinger fermions. We calculate
the dynamical dielectric function of such a model at zero temperature within
random phase approximation. Surprisingly, plasmon resonances are found in the
intrinsic (undoped) limit, whereas they are absent - in that limit - in
graphene as well as ordinary 2DEGs. Additionally, we demonstrate that the
optical conductivity offers a quantitative way to identify the topological
phase of Hg(Cd)Te quantum wells from a bulk measurement.
