Edge dependence of the supercurrent in the quantum Hall regime

The authors show here that the supercurrent in graphene Josephson junctions under quantum Hall conditions is strictly mediated by physical edges. By comparing native, etched, edge-free, and gate-defined geometries, they find that the Josephson coupling disappears without edges and reemerges only when edge conduction is restored. This demonstrates that the supercurrent originates from Andreev bound states formed by paired upstream and downstream modes along the edges, highlighting edge engineering as a key strategy for realizing hybrid topological superconductivity in quantum Hall systems.