Anderson localization induced by spin-flip disorder in large-Chern-number quantum anomalous Hall effect

Abstract

We numerically investigate the localization mechanisms of the quantum anomalous Hall effect (QAHE) with a large Chern number $\mathcal{C}$ in bilayer graphene and magnetic topological insulator thin films doped with nonmagnetic or spin-flip (magnetic) disorder. By calculating the modified Berry curvature in real space, we demonstrate that QAHEs in both systems turn into Anderson insulators when the disorder strength is large enough in the presence of nonmagnetic disorder. However, in the presence of spin-flip disorder, the localization mechanisms in the two systems are completely distinct. For ferromagnetic bilayer graphene with Rashba spin-orbit coupling, the QAHE with $\mathcal{C}=4$ first enters a metallic phase and then turns into an Anderson insulator with the increase of disorder strength, whereas for magnetic topological insulator thin films, the QAHE with $\mathcal{C}=\ensuremath{-}\mathcal{N}$ first enters a metallic phase, then turns into another QAHE with $\mathcal{C}=\ensuremath{-}(\mathcal{N}\ensuremath{-}1)$ as disorder strength increases, and finally turns into an Anderson insulator after $\mathcal{N}\ensuremath{-}1$ cycles between QAHE and metallic phases. The phase transitions in the two systems originate from the exchange of Berry curvature between conduction and valence bands. In the end, we provide a phenomenological picture related to the topological charges to help understand the underlying physical origins of the two different phase-transition mechanisms.