  Huang's experiment [Phys. Rev. Lett. $\bf 109$, 156802 (2012)] found, in the
quantum Hall bilayer of the Corbino geometry, the interlayer tunneling currents
at two edges are coupled to each other and one of two tunneling currents is
referred to as the compensating current of the other. Our another
work[arXiv:2006.15329] has explained this exotic coupling phenomenon as a
result of excitonic Josephson effect induced by interlayer tunneling current.
In this paper, we study the same setup -- excitonic Josephson junction -- but
in the weak Josephson coupling regime, which occurs for large junction length.
Interestingly, we find the compensating current drives the other edge to
undergo a nonequilibrium phase transition from a superfluid to resistive state,
which is signaled by an abrupt jump of the critical tunneling current. We also
identify the critical exponent and furthermore offer more experimental
prediction.
