The contact conductance of a one-dimensional wire partly embedded in a superconductor

The conductance through a semi-infinite one-dimensional wire, partly embedded in a superconducting bulk electrode, is studied. When the electron-electron interactions within the wire are strongly repulsive, the wire effectively decouples from the superconductor. If they are moderately or weakly repulsive, the proximity of the superconductor induces superconducting order in the segment of the wire embedded in it. In this case it is shown that the conductance exhibits a crossover from conductive to insulating behavior as the temperature is lowered down. The characteristic crossover temperature of this transition has a stretched exponential dependence on the length of the part of the wire embedded in the superconductor. The amount of this stretch is determined by the nature of the electron interactions within the wire.