  We report on a detailed study of the terahertz (THz) photoresistivity in a
strained HgTe three-dimensional topological insulator (3D TI) for all Fermi
level positions: inside the conduction and valence bands, and in the bulk gap.
In the presence of a magnetic field we detect a resonance corresponding to the
cyclotron resonance (CR) in the top surface Dirac fermions (DF) and examine the
nontrivial dependence of the surface state cyclotron mass on the Fermi level
position. We also detect additional resonant features at moderate electron
densities and demonstrate that they are caused by the mixing of surface DF and
bulk electrons. At high electron densities, we observe THz radiation induced
1/B-periodic low-field magneto-oscillations coupled to harmonics of the CR and
demonstrate that they have a common origin with microwave-induced resistance
oscillations (MIRO) previously observed in high mobility GaAs-based
heterostructures. This observation attests the superior quality of 2D electron
system formed by helical surface states in strained HgTe films.
