Weak quantization of noninteracting topological Anderson insulator

We study the transition between the two-dimensional topological insulator\n(TI) featuring quantized edge conductance and the trivial Anderson insulator\n(AI) induced by strong disorder. We discover a distinct scaling behavior of TI\nnear the phase transition where the longitudinal conductance approaches the\nquantized value by a power law with system size, instead of an exponential law\nin clean TI. This region is thus called the weak quantization topological\ninsulator (WQTI). By using the self-consistent Born approximation, we associate\nthe emergence of the weak quantization with the imaginary part of the effective\nself-energy acquiring a finite value at strong disorder. We use our analytical\ntheory, supported by direct numerical simulations, to study the effect of\ndisorder range on the topological Anderson insulator. Interestingly, while this\nphase is quite generic for uncorrelated or short-range disorder, it is strongly\nsuppressed by long-range disorder, perhaps explaining why it has never been\nseen in solid state systems.\n