  We report on transport and capacitance spectroscopy study of two kinds of
quantum wells, namely Cd$_{0.02}$Hg$_{0.98}$Te and Cd$_{0.06}$Hg$_{0.94}$Te
with the thicknesses of 7.4 and 11.5 nm, accordingly. The fraction of Cd was
chosen in a way that the both quantum wells are expected to have gapless band
structure typical for a Dirac fermions system. We have established that the
first quantum well exhibits a massless Dirac fermions system with a quality
slightly better then in conventional HgTe quantum wells of critical thickness.
Second quantum well exhibits a high-quality two-dimensional topological
insulator state with the energy gap of around 10 meV and well-defined edge
transport making it as a good candidate for further study and applications of
topological insulators.
