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

Role of the compensating current in the weak Josphson coupling regime: An extended study on excitonic Josephson junctions