Influence of Charge and Energy Imbalances on the Tunneling Current through a Superconductor-Normal Metal Junction

We consider quasiparticle charge and energy imbalances in a thin superconductor weakly coupled with two normal-metal electrodes via tunnel junctions at low temperatures. Charge and energy imbalances, which can be created by injecting quasiparticles at one junction, induce excess tunneling current Iex at the other junction. We numerically obtain Iex as a function of the bias voltage Vdet across the detection junction. We show that Iex at the zero bias voltage is purely determined by the charge imbalance, while the energy imbalance causes a nontrivial Vdet-dependence of Iex. The obtained voltage-current characteristics qualitatively agree with the experimental result by R. Yagi [Phys. Rev. B 73 (2006) 134507].