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Recently, a quantum anomalous Hall insulator (QAHI)/superconductorheterostructure has been realized and shows half-quantized conductance plateausin two-terminal conductance measurements [Q. L. He \textit{et al.}, Science{\bf357}, 294 (2017)]. The half-quantized conductance plateaus are consideredas a solid evidence of chiral Majorana edge modes. However, there is a strongdebate over the origin of the half-quantized conductance plateaus. In thiswork, we propose a Josephson junction based on the QAHI/superconductorheterostructure to identify the existence of chiral Majorana edge modes. Wefind that the critical Josephson current dramatically increases to a peak valuewhen a half-quantized conductance plateau $\sigma_{12}=e^2/2h$ is showing upfor the $N=1$ chiral topological superconductor phase with a single chiralMajorana mode. Furthermore, we show that the critical Josephson current of the$N=1$ chiral topological superconductor exhibits an $h/e$-period oscillationand is robust to disorder, in contrast to the behaviors of conventionaltwo-dimensional electron gas systems. We also estimate experimentally relevantparameters and believe that the supercurrent can be observed in experiments.

Emergent Josephson current of $N=1$ chiral topological superconductor in quantum anomalous Hall insulator/superconductor heterostructures