Charge imbalance and Josephson effects in superconductor-normal metal mesoscopic structures

TL;DR

This paper analyzes how charge imbalance from normal metal reservoirs influences the Josephson effect in superconductor-normal metal structures, revealing increased critical current, characteristic peaks, and shifted Shapiro steps near the critical temperature.

Contribution

It introduces a detailed calculation of the effective critical current and resistance in a superconductor-normal metal Josephson junction considering charge imbalance effects.

Findings

Charge imbalance significantly alters the junction's characteristics.

Effective critical current exceeds the standard critical current and depends on the charge imbalance relaxation length.

Peaks in the I-V characteristics are due to Carlson-Goldman mode excitation.

Abstract

We consider a $SBS$ Josephson junction the superconducting electrodes $S$ of which are in contact with normal metal reservoirs ($B$ means a barrier). For temperatures near $T_{c}$ we calculate an effective critical current $% I_{c}^{\ast}$ and the resistance of the system at the currents $I<$ $% I_{c}^{\ast}$ and $I>>I_{c}^{\ast}$. It is found that the charge imbalance, which arises due to injection of quasiparticles from the $N$ reservoirs into the $S$ wire, affects essentially the characteristics of the structure. The effective critical current $I_{c}^{\ast}$ is always larger than the critical current $I_{c}$ in the absence of the normal reservoirs and increases with decreasing the ratio of the length of the $S$ wire $2L$ to the charge imbalance relaxation length $l_{Q}$. It is shown that a series of peaks arises on the $I-V$ characteristics due to excitation of the Carlson-Goldman collective modes. We find the position of Shapiro steps which deviates from that given by the Josephson relation.