Role of magnetic doping in topological HgTe and application of the Gram-Schmidt method for computing impurity states in quantum wells

TL;DR

This paper investigates the effects of magnetic doping in HgTe quantum wells on the quantum spin Hall effect, introducing a Gram-Schmidt orthogonalization method to accurately compute impurity states and their localization, impacting understanding of magnetic polarons.

Contribution

It proposes a novel application of the Gram-Schmidt method for impurity state calculations in quantum wells, improving accuracy over traditional eigenvalue approaches.

Findings

Determined impurity level energies and localization radii in HgTe quantum wells.

Analyzed the formation and energy of magnetic polarons in doped quantum wells.

Discussed implications for band transport and quantum Hall effects.

Abstract

The quantum spin Hall effect in non-magnetic and Mn-doped HgTe quantum well is strongly affected by Kondo scattering of edge electrons by holes localized on acceptors. A generalized eigenvalue method is usually employed for determining impurity binding energies from the multiband Kohn-Luttinger Hamiltonians in bulk samples and semiconductor quantum structures. Such an approach provides accurate values of the level positions but its applicability for determining the impurity localization radius can be questioned. As an alternative method we propose here the Gram-Schmidt ortogonalization procedure allowing to employ the standard eigenvalue algorithms and, thus, to determine both impurity level energies and the set of normalized eigenvectors. We apply this approach to singly-ionized acceptor states in HgTe quantum wells and obtain impurity level energies and localization radiuses even for states degenerate with the continuum of band states. Such information allows us to assess the energy of bound magnetic polarons in quantum wells doped with magnetic ions. We determine the polaron energies and discuss consequences of the resonant polaron formation on band transport in the bulk samples and quantum wells in the regimes of quantum Hall effects.