We study disorder induced topological phase transitions in magnetically doped ${(\mathrm{Bi},\mathrm{Sb})}_2{\mathrm{Te}}_3$ thin films by using large scale transport simulations of the conductance through a disordered region coupled to reservoirs in the quantum spin Hall regime. Besides the disorder strength, the rich phase diagram also strongly depends on the magnetic exchange field, the Fermi level, and the initial topological state in the undoped and clean limit of the films. In an initially trivial system at nonzero exchange field, varying the disorder strength can induce a sequence of transitions from a normal insulating to a quantum anomalous Hall, then a spin-Chern insulating, and finally an Anderson insulating state. In contrast, for a system which is initially in the topological phase, a similar sequence can be induced by the disorder, but only starting from the quantum anomalous Hall phase that is also stabilized by the weak disorder. Varying the Fermi level we find a similarly rich phase diagram, including transitions from the quantum anomalous Hall to the spin-Chern insulating state via a state that behaves as a mixture of a quantum anomalous Hall and a metallic state, akin to recent experimental reports.

• Received 3 August 2020
• Accepted 3 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.201405