  Quantum anomalous Hall effect (QAH) is induced by substitution of a certain
portion, x, of Bi atoms in a BiTe-based insulating parent compound by magnetic
ions (Cr or V). We find the density of in-gap states, N(E), emerging as a
result of statistic fluctuations of the composition, x, in the vicinity of the
transition point, where the average gap, E_g, passes through zero. Local gap
follows the fluctuations of x. Using the instanton approach, we show that, near
the gap edges, the tails are exponential, ln N(E) \propto -(E_g-|E|), and the
tail states are due to small gap reduction. Our main finding is that, even when
the smearing magnitude exceeds the gap-width, there exists are semi-hard gap
around zero energy, where ln N(E) \propto -E_g/|E| (ln E_g/|E|). The states
responsible for N(E) originate from local gap reversals within narrow rings.
The consequence of semi-hard gap is the Arrhenius, rather than variable-range
hopping, temperature dependence of the diagonal conductivity at low
temperatures.
