Quantum Hall effect and Landau levels in the three-dimensional topological insulator HgTe

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 (nondegenerate), 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) We found a similar though less pronounced behavior 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 nonquantized 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 surfaces) 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.