  By using the self-consistent Born approximation, we investigate disorder
effect induced by the short-range impurities on the band-gap in two-dimensional
Dirac systems with the higher order terms in momentum. Starting from the
Bernevig-Hughes-Zhang (BHZ) model, we calculate the density-of-states as a
function of the disorder strength. We show that due to quadratic corrections to
the Dirac Hamiltonian, the band-gap is always affected by the disorder even if
the system is gapless in the clean limit. Finally, we explore the disorder
effects by using an advanced effective Hamiltonian describing the side maxima
of the valence subband in HgTe~quantum wells. We show that the band-gap and
disorder-induced topological phase transition in the real structures may differ
significantly from those predicted within the BHZ model.
