Three-dimensional phase diagram of disordered HgTe/CdTe quantum spin-Hall wells

We compute the phase diagram of HgTe/CdTe quantum wells in the three-dimensional parameter space of Dirac mass, Fermi level, and disorder strength. The phase diagram reveals the quantum spin-Hall, the metallic, and the normal insulating phases. The phase boundary of the quantum spin-Hall state is shown to be strongly deformed by the disorder. Taking specific cuts into this three-dimensional phase diagram, we recover the so-called topological Anderson insulator (TAI) phase, but now we can demonstrate explicitly that the TAI is not a distinct phase; instead, it is part of the quantum spin-Hall phase. Calculations are performed with Sₙ-conserving and Sₙ-nonconserving Hamiltonians.