Energy Spectrum of the Valence Band in HgTe Quantum Wells on the Way from a Two- to Three-Dimensional Topological Insulator

The magnetic field and temperature dependences of longitudinal magnetoresistance and the Hall effect have been measured in order to determine the energy spectrum of the valence band in HgTe quantum wells with the width dQW = 20–200 nm. The comparison of hole densities determined from the period of Shubnikov–de Haas oscillations and the Hall effect shows that states at the top of the valence band are doubly degenerate in the entire dQW range, and the cyclotron mass 
 determined from the temperature dependence of the amplitude of Shubnikov–de Haas oscillation increases monotonically from 
 to 
 (
 is the mass of the free electron) with increasing hole density 
 from 
 to 
 cm–2. The determined dependence has been compared to theoretical dependences 
 calculated within the four-band kP model. These calculations predict an approximate stepwise increase in 
 owing to the pairwise merging of side extrema with increasing hole density, which should be observed at 
 and 4 × 1010 cm–2 for dQW = 20 and 200 nm, respectively. The experimental dependences are strongly inconsistent with this prediction. It has been shown that the inclusion of additional factors (electric field in the quantum well, strain) does not remove the contradiction between the experiment and theory. Consequently, it is doubtful that the mentioned kP calculations adequately describe the valence band at all dQW values.