Resistance of superconducting nanowires connected to normal-metal leads

Boogaard, G. R.; Verbruggen, A. H.; Belzig, Wolfgang; Klapwijk, T. M.

doi:10.1103/physrevb.69.220503

Cited by 62 publications

(68 citation statements)

References 14 publications

(16 reference statements)

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“…The second peak corresponds to the first to second exited state transition, which corresponds to the (dressed) anharmonicity, a rough approximation of E c /h = 370 MHz. the conversion of a supercurrent into a normal current at the interface between MoRe and the graphite [40].…”

Section: Resultsmentioning

confidence: 99%

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

et al. 2017

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In this experiment, we couple a superconducting transmon qubit to a high-impedance 645 microwave resonator. Doing so leads to a large qubit-resonator coupling rate g, measured through a large vacuum Rabi splitting of 2g 910 MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies ω, placing our system close to the ultrastrong coupling regime (ḡ = g/ω = 0.071 on resonance). Combining this setup with a vacuum-gap transmon architecture shows the potential of reaching deep into the ultrastrong couplingḡ ∼ 0.45 with transmon qubits.

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Section: Resultsmentioning

confidence: 99%

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

et al. 2017

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“…2) can now be calculated with the equations described above. In a previous analysis a finite differential conductance was found at zero bias employing a linear response calculation [8]. With the approach introduced here, the full current-voltage relation can be obtained.…”

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confidence: 99%

Critical Voltage of a Mesoscopic Superconductor

et al. 2006

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We study the influence of a voltage-driven nonequilibrium of quasiparticles on the properties of short mesoscopic superconducting wires. We employ a numerical calculation based upon the Usadel equation. Going beyond linear response, we find a nonthermal energy distribution of the quasiparticles caused by the applied bias voltage. It is demonstrated that this nonequilibrium drives the system from the superconducting state to the normal state, at a current density far below the critical depairing current density. DOI: 10.1103/PhysRevLett.96.147002 PACS numbers: 74.78.Na, 74.20.Fg, 74.25.Bt, 74.25.Sv The energy distribution function of quasiparticles in a normal metal is under equilibrium conditions given by the Fermi-Dirac distribution f 0 . In recent years it has been demonstrated that in a voltage (V)-biased mesoscopic wire (length L) a two-step nonequilibrium distribution develops [1] with additional rounding by quasiparticle scattering due to spin-flip and/or Coulomb interactions [2]. Figure 1(a) shows the distribution, which resembles two shifted FermiDirac functions:with " the quasiparticle energy and x the coordinate along the wire. For strong enough relaxation (L L , with L the phase coherence length) and/or high temperatures (k B T eV) the distribution returns to a Fermi-Dirac distribution with a local effective temperature.The questions we address here are how the distribution function is modified when the normal wire is replaced by a superconducting wire [for a typical result see Fig. 1(b)] and how this affects observable properties such as the currentvoltage characteristics of the system and the breakdown of the superconducting state. The static nonequilibrium distribution leads to the occurrence of a resistance of the superconductor. Another source of voltage might potentially develop due to phase-slip events, either thermally activated or as quantum phase slips [3,4]. The problem that we study focuses on wires which are wide enough to ignore the contribution of quantum phase slips-but still more narrow than the superconducting phase coherence length 0 -to the resistance and are also far enough below the critical temperature T c to ignore the thermally assisted contribution. Within these constraints we relate the distribution function to observable quantities. To do this, it is convenient to separate the part of f which is symmetric in particle-hole space, f L (energy mode), from the asymmetric part, f T (charge mode), since they each have a different spatial and spectral form [ Figs. 1(c) and 1(d)]. In particular, we will show that the breakdown is characterized by a voltage rather than by a current; in other words, the system cannot be trivially treated as two resistors modelling the normal current to supercurrent conversion, with a superconducting element characterized by its depairing current in between.The transport and spectral properties of dirty superconducting systems (' e 0 , with ' e the elastic mean free path) are described by the quasiclassical Green functions obeying the Usadel equat...

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“…We will consider quasi-one dimensional nanowires with a large number of transverse channels (so that the electronic localization length is much larger than the mean free path (ℓ)) which can model numerous recent experiments [5,6,7,8,9,10,11,12,13]. We will describe universal deviations in the value of W from L 0 , which can serve as sensitive tests of the theory in future experiments.…”

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Universal thermal and electrical transport near the superconductor-metal quantum phase transition in nanowires

et al. 2008

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We describe the thermal (κ) and electrical (σ) conductivities of quasi-one dimensional wires, across a quantum phase transition from a superconductor to a metal induced by pairbreaking perturbations. Fluctuation corrections to BCS theory motivate a field theory for quantum criticality. We describe deviations in the Wiedemann-Franz ratio κ/σT (where T is the temperature) from the Lorenz number (π 2 /3)(kB/e) 2 , which can act as sensitive tests of the theory. We also describe the crossovers out of the quantum critical region into the metallic and superconducting phases.The Wiedemann-Franz law relates the low temperature (T ) limit of the ratio W ≡ κ/(σT ) of the thermal (κ) and electrical (σ) conductivities of metals to the universal Lorenz number L 0 = (π 2 /3)(k B /e) 2 . This remarkable relationship is independent of the strength of the interactions between the electrons, relates macroscopic transport properties to fundamental constants of nature, and depends only upon the Fermi statistics and charge of the elementary quasiparticle excitations of the metal. It has been experimentally verified to high precision in a wide range of metals [1], and realizes a sensitive macroscopic test of the quantum statistics of the charge carriers.It is interesting to note the value of the WiedemannFranz ratio in some other important strongly interacting quantum systems. In superconductors, which have low energy bosonic quasiparticle excitations, σ is infinite for a range of T > 0, while κ is finite in the presence of impurities [2], and so W = 0. At quantum phase transitions described by relativistic field theories, such as the superfluid-insulator transition in the Bose Hubbard model, the low energy excitations are strongly coupled and quasiparticles are not well defined; in such theories the conservation of the relativistic stress-energy tensor implies that κ is infinite, and so W = ∞ [3]. Li and Orignac [4] computed W in disordered Luttinger liquids, and found deviations from L 0 , and found a non-zero universal value for W at the metal-insulator transition for spinless fermions.The present paper will focus on the quantum phase transition between a superconductor and a metal (a SMT). We will consider quasi-one dimensional nanowires with a large number of transverse channels (so that the electronic localization length is much larger than the mean free path (ℓ)) which can model numerous recent experiments [5,6,7,8,9,10,11,12,13]. We will describe universal deviations in the value of W from L 0 , which can serve as sensitive tests of the theory in future experiments.The mean-field theory for the SMT goes back to the early work [14] of Abrikosov and Gorkov (AG): in one of the earliest discussions of a quantum phase transition, they showed that a large enough concentration of magnetic impurities could induce a SMT at T = 0. It has since been shown that such a theory applies in a large variety of situations with 'pair-breaking' perturbations: anisotropic superconductors with non-magnetic impurities [15], lower-dimensional superco...

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Resistance of superconducting nanowires connected to normal-metal leads

Cited by 62 publications

References 14 publications

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

Critical Voltage of a Mesoscopic Superconductor

Universal thermal and electrical transport near the superconductor-metal quantum phase transition in nanowires

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