Recently, a quantum anomalous Hall insulator (QAHI)/superconductor heterostructure has been realized and shows half-quantized conductance plateaus in two-terminal conductance measurements [Q. L. He et al., Science 357, 294 (2017)]. The half-quantized conductance plateaus are considered as a solid evidence of chiral Majorana edge modes. However, there is a strong debate over the origin of the half-quantized conductance plateaus. In this work, we propose a Josephson junction based on the QAHI/superconductor heterostructure to identify the existence of chiral Majorana edge modes. We find that the critical Josephson current dramatically increases to a peak value when a half-quantized conductance plateau ${\sigma }_{12}=e^2/2h$ is showing up for the $N=1$ chiral topological superconductor phase with a single chiral Majorana mode. Furthermore, we show that the critical Josephson current of the $N=1$ chiral topological superconductor exhibits an $h/e$-period oscillation and is robust to disorder, in contrast to the behaviors of conventional two-dimensional electron gas systems. We also estimate experimentally relevant parameters and believe that the supercurrent can be observed in experiments.

• Received 4 July 2018
• Revised 9 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.165439