On the zero-field quantization of the anomalous quantum Hall effect in two-dimensional moiré layers

In recent breakthrough experiments, twisted moir\'e layers of transition-metal dichalcogenides are found to manifest both integer and fractional quantum anomalous Hall effects in zero applied magnetic field because of the underlying flat-band topology and spontaneous breaking of the time-reversal invariance. In the current Letter, we critically analyze the experimental values of the quantized conductance in each case to emphasize the role of disorder in the problem, pointing out that obtaining accurate quantized conductance in future experiments would necessitate better contacts and lower disorder.