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Theoretically, the quantum anomalous Hall effect is characterized by aquantized Hall conductance. However, many experiments only reported thequantization of the Hall resistance, which is accompanied by a non-vanishinglongitudinal resistance, resulting in a non-quantized Hall conductance.Meanwhile, the non-vanishing longitudinal resistance features a universalexponential decay with the increase in magnetic field. Such a discrepancyobviously challenges the understanding of the quantum anomalous Hall effect. Tothis end, we propose that the coupling of chiral edge states, which has notbeen properly evaluated in the previous theories, hinders the quantization ofthe Hall conductance, while it maintains the quantization of the Hallresistance. The coupling between the chiral edges states along the oppositeboundaries can be assisted by magnetic domains or defects inside the samplebulk, which has been already identified in recent experiments. We demonstratethat the chiral edge state coupling theory works rather well to explain theexperimental results in both magnetic topological insulator and moir\'esuperlattice systems.

Chiral edge state coupling theory of transport in quantum anomalous Hall insulators