Study of the nonequilibrium state of superconductors by large quasiparticle injection from an external current source

We have studied the nonequilibrium state of superconductors by injecting large numbers of quasiparticles from an external current source into a superconducting film of a tunnel junction with low tunnel resistance (typically 0.1-1 Ω for junction area ≃ ${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^2$). It was observed that there was a critical tunnel current density at which a voltage appeared locally in the part of a superconducting film confined to the junction area. Its values ranged from ${10}^2$ to ${10}^3$ A/${\mathrm{cm}}^2$ for bath temperatures well below $T_c$. Followed by this voltage onset, a transition region corresponding to the nonequilibrium intermediate resistive state was also observed. For further increase of the tunnel current, the local film resistance developed beyond the value of its normal resistance, suggesting that the nonequilibrium state extends far beyond the voltage onset point. A theory based on the modified Rothwarf-Taylor equations and Parker's $T^{*}$ model is presented to compare with the experimental results. The calculated critical current density yielded almost the same order of magnitude as those found experimentally. The detailed behavior, however, deviates from the theoretical predictions although the film makes a second-order transition in the broad range of temperatures. It is also shown using four-terminal analysis that our observations and those by Wong, Yeh, and Langenberg are essentially the same.