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

Abstract

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 𝜎 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 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 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.

Transformation of an energy spectrum and wave functions in the crossover from two- to three-dimensional topological insulator in HgTe quantum wells: long and thorny way

“…A possible reason is the difference of dielectric susceptibility of think layer forming the quantum well from that of the parent bulk material as discussed in Refs. [34,38,51,52]. We are not aware of papers in which this was considered for such a complicated spectrum as HgTe/Hg 1−x Cd x Te QWs.…”

“…In almost all the experimental studies of the magnetotransport in wide QWs (d > 15 − 20 nm), structures with the gate were studied, and the results were analyzed using an "intuitive model" in which it is assumed that near each of the walls there are single-spin states at a some distance from the wall of a some width L z , which are independent of V g and shift only in the energy by applied gate voltage [21,37,38]. The accuracy of this approach, especially for sufficiently wide QWs, remains unclear.…”

Bilinear magnetoresistance in HgTe topological insulator: opposite signs at opposite surfaces demonstrated by gate control

“…Interpretation of BMR with opposite contributions from opposite surfaces We developed a model on the basis of the theory of the BMR in TIs by Dyrdal et al [18,19], the filling of the bottom surface is here weakly dependent on the gate voltage. [13].…”

Thermoelectric Transport in a Three-Dimensional HgTe Topological Insulator

“…Remarkably, the spin of surface Dirac electrons is locked perpendicular to the wave vector k in the 2D plane, which leads to the suppression of the electron scattering on impurities. The wide strain HgTe films are among of the best host 3DTI materials [5,6] because, in such a system, a very high mobility of 2D surface electrons µ~100 m 2 /V•s is achieved [7][8][9][10].…”