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

TL;DR

This paper investigates how charge and energy imbalances in a superconductor affect tunneling currents in a superconductor-normal metal junction, revealing that charge imbalance influences zero-bias current and energy imbalance causes voltage-dependent effects.

Contribution

It provides a numerical analysis of excess tunneling current due to charge and energy imbalances, aligning with experimental observations and clarifying their distinct roles.

Findings

Zero bias excess current is determined by charge imbalance.

Energy imbalance causes nontrivial voltage dependence of excess current.

Results qualitatively agree with experimental data by Yagi.

Abstract

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].