Understanding the Quantum Spin Hall Effect
Tomasz Dietl
(International Research Centre MagTop, Institute of Physics,
Polish Academy of Sciences, Warsaw, Poland)
Inspired by experimental results for HgTe and (Hg,Mn)Te topological quantum wells accumulated in Würzburg and also by CETRERA/MagTop collaboration in Warsaw [1], theory of the quantum spin Hall effect was developed [2]. It was demonstrated that (i) the presence of dopants is necessary to pin the Fermi energy in the topological gap; (ii) scattering of edge electrons by acceptor holes explains quantitatively and without adjustable parameters a short magnitude of the topological protection length, provided that non-scalar terms in the electron-hole exchange and the Kondo and Luttinger effects are taken into account [2]. Realizing that also in the case of the quantum anomalous effects, hoping conductivity between impurity states deteriorates the quantization precision at above 0.1 K, we address here the question how to improve quantization accuracy in the case of those two quantum Hall effects. In this context the role of bound magnetic and lattice polarons, negative U centers, and co-doping will be discussed.
[1] I. Yahniuk et al., npj Quant. Mater. 4 (2019) 13; arXiv:2111.07581 (2021).
[2] T. Dietl, Phys. Rev. Lett. 130 (2023) 086202; Phys. Rev. B 107 (2023) 085421.