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Topological insulators are ideally represented as having an insulating bulkwith topologically protected, spin-textured surface states. However, it isincreasingly becoming clear that these surface transport channels can beaccompanied by a finite conducting bulk, as well as additional topologicallytrivial surface states. To investigate these parallel conduction transportchannels, 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 lowermobility. We identify a clear Zeeman-split bulk contribution to theoscillations from a comparison between the charge-carrier densities extractedfrom the magnetoresistance and the oscillations. Furthermore, our analysesindicate the presence of a two-dimensional state and signatures of additionalstates the origin of which cannot be conclusively determined. Our findingsunderpin the necessity of theoretical studies on the origin of and theinterplay between these parallel conduction channels for a careful analysis ofthe material's performance.

Coexistence of bulk and surface states probed by Shubnikov-de Haas oscillations in Bi$_2$Se$_3$ with high charge-carrier density