Edge dependence of the Josephson current in the quantum Hall regime

The observation of Josephson current in the quantum Hall regime has attracted considerable attention, revealing the coexistence of two seemingly incompatible phases: the quantum Hall and superconducting states. However, the mechanism underlying the Josephson current remains unclear because of the observed h/2e magnetic interference period and the lack of precisely quantized Hall plateaus. To address this issue, we investigate the edge dependence of the Josephson current in graphene Josephson junctions operating in the quantum Hall regime. By systematically comparing devices with native, etched, edge-free, and gate-defined edges, we demonstrate that the Josephson current is confined to the physical edges and is highly sensitive to specific edge configurations. Our findings provide direct evidence that counter-propagating quantum Hall edge states mediate Andreev bound states, enabling Josephson coupling. These results clarify the underlying mechanism of Josephson current in the quantum Hall regime and offer new strategies for engineering superconducting hybrid devices.