  We review low and high field magnetotransport in 80 nm-thick strained HgTe, a
material that belongs to the class of strong three-dimensional topological
insulators. Utilizing a top gate, the Fermi level can be tuned from the valence
band via the Dirac surface states into the conduction band and allows studying
Landau quantization in situations where different species of charge carriers
contribute to magnetotransport. Landau fan charts, mapping the conductivity $
\sigma_{xx}(V_g, B) $ in the whole magnetic field - gate voltage range, can be
divided into six areas, depending on the state of the participating carrier
species. Key findings are: (i) the interplay of bulk holes (spin-degenerate)
and Dirac surface electrons (non-degenerate), coexisting for $ E_F $ in the
valence band, leads to a periodic switching between odd and even filling
factors and thus odd and even quantized Hall voltage values. (ii) A similar
though less pronounced behavior we found for coexisting Dirac surface and
conduction band electrons. (iii) In the bulk gap, quantized Dirac electrons on
the top-surface coexist at lower B with non-quantized ones on the bottom side,
giving rise to quantum Hall plateau values depending - for a given filling
factor - on the magnetic field strength. In stronger $ B $ fields, Landau level
separation increases, charge transfer between different carrier species becomes
energetically favorable and leads to the formation of a global (i.e. involving
top and bottom surface) quantum Hall state. Simulations using the simplest
possible theoretical approach are in line with the basic experimental findings,
describing correctly the central features of the transitions from classical to
quantum transport in the respective areas of our multicomponent charge carrier
system.
