  Semiconductors' sensitivity to electrostatic gating and doping accounts for
their widespread use in information communication and new energy technologies.
It is demonstrated quantitatively and with no adjustable parameters that the
presence of paramagnetic acceptor dopants elucidates a variety of hitherto
puzzling properties of two-dimensional topological semiconductors at the
topological phase transition and in the regime of the quantum spin Hall effect.
The concepts of charge correlation, Coulomb gap, exchange interaction between
conducting electrons and holes localized on acceptors, strong coupling limit of
the Kondo effect, and bound magnetic polaron explain a short topological
protection length, high hole mobilities compared with electron mobilities, and
different temperature dependence of the spin Hall resistance in HgTe and
(Hg,Mn)Te quantum wells.
