Long-range phase-coherent effects in the transport properties of mesoscopic superconductor–normal-metal structures

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Abstract
We present a theory of long-range phase-coherent effects in the transport properties of a normal-metal film contacting two superconductors. It is shown that the phase-coherent correction to the conductance exists even though the spacing between the two superconductors largely exceeds the coherence length and the critical Josephson current is exponentially small. This effect can appear as a Shapiro step or large conductance oscillation caused by the magnetic field. Moreover, it is shown that in the case of negligible Josephson coupling between superconductors, the Josephson effect can arise in the system if an additional current flows through the normal conductor and a dissipation takes place (dissipative Josephson effect). The amplitude of the phase-coherent correction part of the conductance is discussed from the viewpoint of temperature, bias voltage, magnetic field, and phase-breaking length dependence.