A virtually exact Hall resistance quantization to a value reliant only on the Planck constant h and electron charge in two-dimensional systems under strong magnetic fields not only demonstrated the role of topology in condensed matter physics but also played a crucial role in redefining S.I. units in terms of constants of nature in 2019. Furthermore, the accuracy of metrological relevance has also been achieved in the case of the quantum anomalous Hall effect (QAHE), allowing fabrication of resistance standards operating without any external magnetic field.


Inspired by experimental results accumulated by researchers at the Würzburg University and two Warsaw IRA centres: MagTop/IFPAN and CENTERA/Unipress, Tomasz Dietl has elucidated the origin of poor quantization precision in the case of the third member of the quantum Hall effects’ trio: the quantum spin Hall effect (QSHE). On a microscopic level, in quantum Hall systems, the electric current flows along edge one-dimensional channels. A topological protection of these states against backscattering  leads to resistance quantization in the units of h/e2. In the case of QSHE, two time-reversal Kramers partners (helical states) form edge conducting channels, as shown in Figure. In contrast, time-reversal breaking by a strong magnetic field or ferromagnetically ordered Cr or V spins results in the presence of channels with different velocity directions on the opposite sample edges in the QHE and QAHE regime, respectively.


Tomasz Dietl has considered the role of residual impurities present in any materials and whose concentration is known from the gate-voltage width corresponding to the bandgap region. By determining impurity ionization energies and spin-dependent coupling between edge electrons and acceptor holes in a non-perturbative way, it has been possible to explain the magnitude of an average length electron travels without backscattering in topological HgTe quantum wells and WTe2 monolayers, typically of the order of 10 and 0.1 µm, respectively, several orders of magnitude shorter than in the case of QHE and QAHE. However, the quantization precision can be restored by paramagnetic impurities, such as Mn. The latter looks surprising, but quantitative evaluation demonstrates that Mn spins form ferromagnetic clouds around acceptors (i.e., bound magnetic polarons), diminishing coupling between electrons and holes and, thus, reducing the backscattering rate at low temperatures.



  1. Dietl, “Effects of charge dopants in quantum spin Hall materials” https://link.aps.org/doi/10.1103/PhysRevLett.130.086202
  2. Dietl, “Quantitative theory of backscattering in topological HgTe and (Hg,Mn)Te quantum wells: Acceptor states, Kondo effect, precessional dephasing, and bound magnetic polaron” https://link.aps.org/doi/10.1103/PhysRevB.107.085421 (Editors’Suggestion)