  We study a two-terminal graphene Josephson junction with contacts shaped to
form a narrow constriction, less than 100nm in length. The contacts are made
from type II superconducting contacts and able to withstand magnetic fields
high enough to reach the quantum Hall (QH) regime in graphene. In this regime,
the device conductance is determined by edge states, plus the contribution from
the constricted region. In particular, the constriction area can support
supercurrents up to fields of ~2.5T. Moreover, enhanced conductance is observed
through a wide range of magnetic fields and gate voltages. This additional
conductance and the appearance of supercurrent is attributed to the tunneling
between counter-propagating quantum Hall edge states along opposite
superconducting contacts.
