Algebraic and geometric mean density of states in topological Anderson insulators

Algebraic and geometric mean density of states in disordered systems may reveal properties of electronic localization. In order to understand the topological phases with disorder in two dimensions, we present the calculated density of states for the disordered Bernevig-Hughes-Zhang model. The topological phase is characterized by a perfectly quantized conducting plateau, carried by helical edge states, in a two-terminal setup. In the presence of disorder, the bulk of the topological phase is either a band insulator or an Anderson insulator. Both of them can protect edge states from backscattering. The topological phases are explicitly distinguished as a topological band insulator or a topological Anderson insulator from the ratio of the algebraic mean density of states to the geometric mean density of states. The calculation reveals that the topological Anderson insulator can be induced by disorders from either a topologically trivial band insulator or a topologically nontrivial band insulator.