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

TL;DR

This study investigates the energy spectrum and wave functions in HgTe quantum wells during the transition from two- to three-dimensional topological insulators, revealing spin-orbit splitting, wave function overlap effects, and the role of electron polarizability.

Contribution

It provides a detailed experimental and theoretical analysis of the energy spectrum transformation and wave function behavior in HgTe quantum wells across the topological transition.

Findings

Spin-orbit splitting increases with quantum well width.

Magneto-intersubband oscillations grow with electron density.

Wave function overlap increases due to negative electron polarizability.

Abstract

A magnetotransport and quantum capacitance of the two-dimensional electron gas in HgTe/Cd$_x$Hg$_{1-x}$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. Magneto-intersubband 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 \emph{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 phenomenon of the negative electron polarizability. The results obtained from the transport experiments are supported by quantum capacitance measurements.