Transformation of energy spectrum and wave functions on the way from a 2D-to-3D topological insulator in HgTe quantum wells

Abstract

A magnetotransport and quantum capacitance of the two-dimensional (2D) electron gas in $\mathrm{HgTe}/{\mathrm{Cd}}_{x}{\mathrm{Hg}}_{1\ensuremath{-}x}\mathrm{Te}$ quantum wells of a width $(20.2--46.0)$ nm are experimentally investigated. It is shown that the first energy subband of spatial quantization is split due to the spin-orbit interaction and the split branches are single spin, therewith the splitting strength increases with the increase of the quantum well width. The electron effective masses in the branches are close to each other within the actual density range. Magnetointersubband oscillations (MISO) observed in the structures under study exhibit the growing amplitude with the increasing electron density that contradicts to the expected decrease of wave-function overlap for the rectangular quantum well. To interpret the data obtained, we have used a self-consistent approach to calculate the electron energy spectrum and the wave function within framework of the $kP$ model. It has been, in particular, shown that the MISO amplitude increase results from the increasing overlap of the wave functions due to their shift from the gate electrode with the gate voltage increase known as a phenomenon of the negative electron polarizability. The results obtained from the transport experiments are supported by quantum capacitance measurements.