  Under certain conditions, Hg(Cd)Te quantum wells (QWs) are known to realize a
time-reversal symmetric, two-dimensional topological insulator phase. Its
low-energy excitations are well-described by the phenomenological
Bernevig-Hughes-Zhang (BHZ) model that interpolates between Schr\"odinger and
Dirac fermion physics. We study the polarization function of this model in
random phase approximation (RPA) in the intrinsic limit and at finite doping.
While the polarization properties in RPA of Dirac and Schr\"odinger particles
are two comprehensively studied problems, our analysis of the BHZ model bridges
the gap between these two limits, shedding light on systems with intermediate
properties. We gain insight into the screening properties of the system and on
its characteristic plasma oscillations. Interestingly, we discover two
different kinds of plasmons that are related to the presence of intra- and
interband excitations. Observable signatures of these plasmons are carefully
analyzed in a variety of distinct parameter regimes, including the
experimentally relevant ones for Hg(Cd)Te QWs. We conclude that the discovered
plasmons are observable by Raman or electron loss spectroscopy.
