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

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 $I_c^{*}$ and the resistance of the system at the currents $I<I_c^{*}$ and $I⪢I_c^{*}$. 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 $I_c^{*}$ 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 $I\text{−}V$ 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.

Figure 1

Schematic view of the system under consideration.

Figure 2

The normalized effective critical current as a function of $\theta =L∕l_Q$ for $b=R_B∕R_Q=0.2$ (curve 1), $b=2$ (curve 2), and $b=5$ (curve 3).

Figure 3

The resistance of the system at currents less than the effective critical current as a function of $\theta$ for $b=0.2$ (curve 1), $b=2$ (curve 2), and $b=5$ (curve 3).

Figure 4

Correction to the $I\text{−}V$ characteristics for ${\omega }_{\gamma }=0.1$ (curve 1) and ${\omega }_{\gamma }=0.5$ (curve 2).