Phase-coherent conductance of a superconductor-normal-metal quantum interferometer

A theory of the subgap conductance of a hybrid superconductor-normal-metal ($\frac{S}{N}$) quantum interferometer consisting of two tunnel junctions ($\frac{S}{N}$) in contact with an $N$ layer is developed. The oscillatory dependence of the conductance of the system $G$ on the phase difference between superconductors $\varphi$ is shown to be due to the proximity effect, i.e., to the penetration of the condensate into the $N$ region. The $G\left(\varphi \right)$ dependence is found for the cases of both weak and strong proximity effects. This dependence can radically change its shape form qualitatively when the voltage is varied. The amplitude of the conductance oscillations appears to be large in the case of strong proximity effect. Different layouts are considered including the cases when there is the third tunnel junction or point contact between the $N$ conductor and the $N$ electrode.