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

TL;DR

This paper investigates how a one-dimensional wire's conductance is affected by partial embedding in a superconductor, revealing interaction-dependent crossover behaviors influenced by temperature and wire length.

Contribution

It demonstrates that electron interactions determine whether the wire decouples or develops superconducting order when partly embedded in a superconductor.

Findings

Strong repulsion causes decoupling from the superconductor.

Weak/moderate repulsion induces superconducting order in the embedded segment.

Crossover temperature depends on the embedded length with a stretched exponential relation.

Abstract

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.