Superconductor to normal-metal transition in finite-length nanowires: Phenomenological model

In this paper we discuss the interplay of quantum fluctuations and dissipation in uniform superconducting nanowires. We consider a phenomenological model with superconducting and normal components and a finite equilibration rate between these two fluids. We find that phase-slip dipoles proliferate in the wire and decouple the two fluids within its bulk. This implies that the normal fluid only couples to the superconductor fluid through the leads at the edges of the wire, and the local dissipation is unimportant. Therefore, while long wires have a superconductor-metal transition tuned by local properties of the superconducting fluid, short wires have a transition when the total resistance is Rtot=RQ=h /4e2.