  The universal value of Faraday rotation angle close to the fine structure
constant is experimentally observed in thin HgTe quantum wells with thickness
on the border between trivial insulating and the topologically non-trivial
Dirac phases. The quantized value of the Faraday angle remains robust in the
broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of
the hole-like carriers extracted from the analysis of the transmission data
shows theoretically predicted universal value of consistent with the doubly
degenerate Dirac state. On shifting the Fermi level by the gate voltage the
effective sign of the charge carriers changes from positive (holes) to negative
(electrons). The electron-like part of the dynamic response does not show
quantum plateaus and is well described within the classical Drude model.
