Localization and mobility gap in the topological Anderson insulator

It has been proposed that disorder may lead to a new type of topological insulator, called the topological Anderson insulator (TAI). Here we examine the physical origin of this phenomenon. We calculate the topological invariants and density of states of the disordered model in a supercell of a two-dimensional HgTe/CdTe quantum well. The topologically nontrivial 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 nontrivial subgaps separated by almost flat and localized bands.