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