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 $I_{\rm ex}$ at the other junction. We numerically obtain $I_{\rm ex}$ as a function of the bias voltage $V_{\rm det}$ across the detection junction. We show that $I_{\rm ex}$ at the zero bias voltage is purely determined by the charge imbalance, while the energy imbalance causes a nontrivial $V_{\rm det}$-dependence of $I_{\rm ex}$. The obtained voltage-current characteristics qualitatively agree with the experimental result by R. Yagi [Phys. Rev. B {\bf 73} (2006) 134507].