Absence of supercurrent in edge-free Corbino graphene Josephson junction in the quantum Hall regime

The first observation of the supercurrent in graphene Josephson junction in the quantum Hall regime has attracted considerable attention, which demonstrated the hybridization of two seemingly incompatible phases: quantum Hall state and superconducting state. However, the mechanism of the quantum Hall supercurrent is still controversial due to not exactly quantized resistance at quantum hall plateau. This suggests that the supercurrent may flow through not perfectly insulating bulk state instead of quantum Hall edge states. In order to specify this issue, we fabricated and measured graphene Josephson junction both in conventional rectangular geometry with edges and Corbino geometry without any edge. Highly transparent molybdenum/rhenium superconducting contacts are realized to achieve Josephson coupling as high as  at zero magnetic field in both rectangular and Corbino geometry. In the quantum Hall regime, supercurrent was observed in rectangular graphene Josephson junction with edges, however, supercurrent was absent in edge-free Corbino graphene Josephson junction. Our results strongly support that the supercurrent observed in quantum Hall regime flows along the edges of graphene.