Abstract
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 ${R}_{\text{tot}}={R}_{Q}=h/4{e}^{2}$.
Highlights
Quantum phase transitions have long been at the forefront of condensed-matter theory
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
We expect a SC-normal crossover tuned by stiffnessas in Refs. 11 and 24͒, but in short wires, we expect a Schmid transition tuned by the total normal-part resistance
Summary
Quantum phase transitions have long been at the forefront of condensed-matter theory. Interesting are systems of reduced dimensionality and size, where fluctuations are enhanced, and ordering is illusive, and far from being explained by mean field theory. A first set of measurements on wires of various diameters and lengths 100 nmϽ L Ͻ 200 nm, showed a remarkable result: a transition when the total resistance of the wire was RQ = h / 4e2 = 6.45 k⍀,14 as if the entire wire was a single shunted junction. The nature of the breakdown of superconductivity in ultrathin MoGe nanowires remains an open question. We address this question and consider the general interplay between supercondcutivity and dissipation in such nanoscale superconductors
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