  Topological insulators are ideally represented as having an insulating bulk
with topologically protected, spin-textured surface states. However, it is
increasingly becoming clear that these surface transport channels can be
accompanied by a finite conducting bulk, as well as additional topologically
trivial surface states. To investigate these parallel conduction transport
channels, we studied Shubnikov-de Haas oscillations in Bi$_2$Se$_3$ thin films,
in high magnetic fields up to 30 T so as to access channels with a lower
mobility. We identify a clear Zeeman-split bulk contribution to the
oscillations from a comparison between the charge-carrier densities extracted
from the magnetoresistance and the oscillations. Furthermore, our analyses
indicate the presence of a two-dimensional state and signatures of additional
states the origin of which cannot be conclusively determined. Our findings
underpin the necessity of theoretical studies on the origin of and the
interplay between these parallel conduction channels for a careful analysis of
the material's performance.
