Magnetic disorder induced Hall conductance fluctuation in the semi-magnetic topological insulator thin film

In this work, we investigate the effect of magnetic disorder on a magnetic topological insulator thin film that supports the semi-magnetic topological insulator, quantum anomalous Hall insulator, and axion insulator phases. Once the magnetic disorder is introduced, we find that the semi-magnetic topological insulator phase exhibits a significant fluctuation in the Hall conductance but its averaged value maintains the half-quantization. The scenario is distinct from that in the quantum anomalous Hall insulator and axion insulator phases, where the Hall conductance is stable and exhibits no fluctuation in the presence of weak magnetic disorder. We propose that the conductance fluctuation in the semi-magnetic topological insulator phase is attributed to the gapless surface state. The fluctuation arises because the system fluctuates between different quantized conductance plateaus, and its origin is different from the conventional conductance fluctuations caused by Anderson disorder.