  It has been proposed that disorder may lead to a new type of topological
insulator, called topological Anderson insulator (TAI). Here we examine the
physical origin of this phenomenon. We calculate the topological invariants and
density of states of disordered model in a super-cell of 2-dimensional
HgTe/CdTe quantum well. The topologically non-trivial phase is triggered by a
band touching as the disorder strength increases. The TAI is protected by a
mobility gap, in contrast to the band gap in conventional quantum spin Hall
systems. The mobility gap in the TAI consists of a cluster of non-trivial
subgaps separated by almost flat and localized bands.
