Phase Structure of the Topological Anderson Insulator

We report the phase structure of disordered HgTe topological Anderson insulator in a 2-D geometry. We use exact diagonalization to calculate the spectrum and eigenstate structure, and recursive green's functions to calculate the conductance. All observables are measured at several system sizes, allowing us to determine phase transitions and two critical points. The quantized-conductance TAI phase contains two phases: TAI-I lying in a bulk band gap, and TAI-II where bulk states exist but are localized. We find that the TAI-II phase persists at disorder strengths where there is no bulk band gap; a bulk band gap is not necessary to obtain conductance quantization. In a previous work the weak-disorder edge of the TAI phase was explained as a transition into the bulk gap (TAI-I), but we find also a direct transition into the ungapped (TAI-II) quantized phase. Effective medium theory (SCBA) predicts well the boundaries and interior of the TAI-I phase, but fails at larger disorders including the interior of the TAI-II phase. When the system size is smaller than the bulk localization length, the quantized TAI region is bounded by either the bulk band edge or the localization length, but when the system size is large it is bounded by a transition of edge states.