Phase Structure of the Topological Anderson Insulator

TL;DR

This paper investigates the phase diagram and properties of the disordered topological Anderson insulator in two dimensions, revealing two distinct quantized conductance regimes and analyzing their characteristics and transitions.

Contribution

It provides the first detailed phase diagram of the 2D disordered topological Anderson insulator, identifying two scaling regions and analyzing their properties and boundaries.

Findings

Quantized conductance occurs without a bulk band gap.

Two distinct scaling regions: TAI-I with a bulk gap, TAI-II with localized bulk states.

No metallic phase at the transition between quantized and insulating phases.

Abstract

We study the disordered topological Anderson insulator in a 2-D (square not strip) geometry. We first report the phase diagram of finite systems and then study the evolution of phase boundaries when the system size is increased to a very large $1120 \times 1120$ area. We establish that conductance quantization can occur without a bulk band gap, and that there are two distinct scaling regions with quantized conductance: TAI-I with a bulk band gap, and TAI-II with localized bulk states. We show that there is no intervening insulating phase between the bulk conduction phase and the TAI-I and TAI-II scaling regions, and that there is no metallic phase at the transition between the quantized and insulating phases. Centered near the quantized-insulating transition there are very broad peaks in the eigenstate size and fractal dimension $d_2$; in a large portion of the conductance plateau eigenstates grow when the disorder strength is increased. The fractal dimension at the peak maximum is $d_2 \approx 1.5$. Effective medium theory (CPA, SCBA) predicts well the boundaries and interior of the gapped TAI-I scaling region, but fails to predict all boundaries save one of the ungapped TAI-II scaling region. We report conductance distributions near several phase transitions and compare them with critical conductance distributions for well-known models.