  Using THz spectroscopy in external magnetic fields we investigate the
low-temperature charge dynamics of strained HgTe, a three dimensional
topological insulator. From the Faraday rotation angle and ellipticity a
complete characterization of the charge carriers is obtained, including the 2D
density, the scattering rate and the Fermi velocity. The obtained value of the
Fermi velocity provides further evidence for the Dirac character of the
carriers in the sample. In resonator experiments, we observe quantum Hall
oscillations at THz frequencies. The 2D density estimated from the period of
these oscillations agrees well with direct transport experiments on the
topological surface state. Our findings open new avenues for the studies of the
finite-frequency quantum Hall effect in topological insulators.
