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

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 tot = R Q = h / 4e 2 .

Superconductor–insulator transition in nanowires and nanowire arrays

“…In this work we will explore the analogies, in fact the duality, between weak superconducting nanowires and Josephson junctions and chains or arrays built of them. Our emphasis differs from earlier theoretical studies of the superconducting transition in wires or films when the transition is driven by dissipation [12][13][14][15][16]. QPS can also occur in chains of Josephson junctions [17].…”

Coulomb blockade due to quantum phase slips illustrated with devices

“…Even if this is not the case, it has been shown 23 that, for a finite wire embedded into an external circuit, the Schmid transition should be governed by the external impedance of the circuit rather than the wave impedance of the wire. There were recent attempts 27 to modify the traditional renormalization schemes to take into account finite l and possible normal excitations not captured by the hydrodynamic action. More experiments and more detailed comparison of experiment and theory are required to resolve the issue.…”

Flux–charge duality and topological quantum phase fluctuations in quasi-one-dimensional superconductors

“…Finally, in section 7, we suggest an alternative explanation for the observed destruction of superconductivity when R n R Q [50]. Whereas most previous attempts to understand this apparent insulating behavior as T → 0 have been built on the idea of a dissipative phase transition [56][57][58][59], we hypothesize instead a disorder-driven transition, with virtual type II phase slip-antiphase slip pairs as the fundamental quantum excitation. This picture is analogous to the so-called 'dirty Boson' model for quantum vortex-antivortex pair unbinding in quasi-2D superconductors [21], which has been used to explain an apparent superconductor-toinsulator transition (SIT) in highly disordered thin films [22,23,86].…”

“…It has been identified [61,98] with the'rate' of QPS estimated by Giordano [37], and later calculated by several authors using time-dependent GL theory [51,92,93], and by GZ using microscopic theory [45,46]. In one form or another, it is the essential input parameter to all subsequent theoretical work aimed at deducing the effects of QPS, appearing as the dual of the Josephson energy in lumped-element treatments [55,61,98,115], and in more recent theories in terms of the so-called 'QPS fugacity' f ≡ e −S 0 [56][57][58][59]. In all of these cases it is either left as an unknown input parameter, or taken from the results of GZ or earlier authors.…”

“…However, none can obviously explain the observed T = 0 transition at R n ∼ R Q in a low-Z electromagnetic environment. In all of these theories the predicted transition relies on the presence of a form of dissipation which somehow remains even as T → 0, such as anomalous excited quasiparticles [59], a resistive shunt [56], continuum plasmon modes [45,46,56] or the QPSs themselves [58]. Our discussion suggests a possible alternative view, in which a T = 0 SIT may be driven by disorder-induced quantum phase fluctuations, analogous to the SIT observed in some quasi-2D systems [22,23] when the sheet resistance R R Q .…”