  In this study, we examine multiple encapsulated graphene Josephson junctions
to determine which mechanisms may be responsible for the supercurrent observed
in the quantum Hall (QH) regime. Rectangular junctions with various widths and
lengths were studied to identify which parameters affect the occurrence of QH
supercurrent. We also studied additional samples where the graphene region is
extended beyond the contacts on one side, making that edge of the mesa
significantly longer than the opposite edge. This is done in order to
distinguish two potential mechanisms: a) supercurrents independently flowing
along both non-contacted edges of graphene mesa, and b) opposite sides of the
mesa being coupled by hybrid electron-hole modes flowing along the
superconductor/graphene boundary. The supercurrent appears suppressed in
extended junctions, suggesting the latter mechanism.
