Effects of random domains on the zero Hall plateau in quantum anomalous Hall effect

Recently, a zero Hall conductance plateau with random domains is experimentally observed in quantum anomalous Hall (QAH) effect. We study the effects of random domains on the zero Hall plateau in QAH insulators. We find the structure inversion symmetry determines the scaling property of the zero Hall plateau transition in the QAH systems. In the presence of structure inversion symmetry, the zero Hall plateau state shows a quantum-Hall-type critical point, originating from the two decoupled subsystems with opposite Chern numbers. However, the absence of structure inversion symmetry leads to mixture between these two subsystems, gives rise to a line of critical points, and dramatically changes the scaling behavior. Hereinto, we predict a Berezinskii-Kosterlitz-Thouless-type transition during the Hall conductance plateau switching in the QAH insulators. Our results are instructive for both theoretic understanding of the zero Hall plateau transition and future transport experiments in the QAH insulators.