Magnetic field and contact resistance dependence of non-local charge imbalance

Kleine, Andreas; Baumgärtner, A.; Trbovic, Jelena; Golubev, Dmitri S.; Zaikin, Andrei D.; Schönenberger, Christian

doi:10.1088/0957-4484/21/27/274002

Cited by 27 publications

(29 citation statements)

References 23 publications

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“…The wave functions ϕ n (x), appearing in Eq. (19) are the eigenfunctions of a single electron Hamiltonian of the superconducting lead with eigenenergies ξ n , i.e. they are the solutions of the Schrödinger equation…”

Section: Cumulant Generating Functionmentioning

confidence: 99%

Cross-correlated shot noise in three-terminal superconducting hybrid nanostructures

Golubev

Zaikin

2019

Phys. Rev. B

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We work out a unified theory describing both non-local electron transport and cross-correlated shot noise in a three-terminal normal-superconducting-normal (NSN) hybrid nanostructure. We describe noise cross correlations both for subgap and overgap bias voltages and for arbitrary distribution of channel transmissions in NS contacts. We specifically address a physically important situation of diffusive contacts and demonstrate a non-trivial behavior of non-local shot noise exhibiting both positive and negative cross correlations depending on the bias voltages. For this case, we derive a relatively simple analytical expression for cross-correlated noise power which contains only experimentally accessible parameters. NSN structures with low transparency contacts 6 .One possible way to discriminate between CAR and EC processes is to investigate fluctuations of the currents I 1 and I 2 . It is well known that in normal (i.e. arXiv:1902.05476v2 [cond-mat.supr-con]

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Section: Cumulant Generating Functionmentioning

confidence: 99%

Cross-correlated shot noise in three-terminal superconducting hybrid nanostructures

Golubev

Zaikin

2019

Phys. Rev. B

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“…and Ref. [29] for details) yields a charge relaxation time of τ Q = 3±1ps<< τ S1 . Figure 4a shows nonlocal resistance as a function of local voltage over a larger range of magnetic fields and summarises our main results: the asymmetric (red and blue) spin signal grows with magnetic field then diminishes and becomes narrower in V as the superconducting gap decreases.…”

mentioning

confidence: 90%

“…To compare τ S1 to the charge relaxation time τ Q , we measure the charge imbalance signal at high bias voltage (V=430µV) as the magnetic field is increased. R C initially decreases due to the fieldinduced pair-breaking [27,28] then diverges at the critical field H C  6kG as the superconducting gap goes to zero before dropping abruptly to zero in the normal state [29]. A theoretical fit ( Figure 4b, green line, see Supp.…”

mentioning

confidence: 96%

Spin imbalance and spin-charge separation in a mesoscopic superconductor

et al. 2013

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What happens to spin-polarized electrons when they enter a superconductor? Superconductors at equilibrium and at finite temperature contain both paired particles (of opposite spin) in the condensate phase as well as unpaired, spin-randomized quasiparticles. Injecting spin-polarized electrons into a superconductor (and removing pairs) thus creates both spin and charge imbalances 1-7 , which must relax when the injection stops, but not necessarily over the same time (or length) scale. These different relaxation times can be probed by creating a dynamic equilibrium between continuous injection and relaxation; this leads to constant-in-time spin and charge imbalances, which scale with their respective relaxation times and with the injection current. Whereas charge imbalances in superconductors have been studied in great detail both theoretically 8 and experimentally 9 , spin imbalances have not received much experimental attention 6,10,11 despite intriguing theoretical predictions of spin-charge separation effects 12,13 . Here we present evidence for an almost-chargeless spin imbalance in a mesoscopic superconductor.A pure spin imbalance in a superconductor can be understood in the following manner: imagine injecting spin-randomized electrons continuously into a small superconducting volume and taking out Cooper pairs. The number of electron-like quasiparticles increases, that is, their chemical potential µ QP rises whereas that of the Cooper pairs µ P drops by the same amount to conserve particle number. This charge imbalance was first observed in a pioneering experiment, where µ QP − µ P was measured 1,2,14 . (Hereafter µ P ≡ 0, that is, all chemical potentials are measured with respect to that of the condensate.) If the injected electrons are (or become) spin-polarized, in general µ QP↑ = µ QP↓ = µ P , we can define a charge imbalance µ C ≡ (µ QP↑ + µ QP↓ )/2 and spin imbalance µ S ≡ (µ QP↑ − µ QP↓ )/2 (ref. 13). If charge relaxes faster than spin, a situation may arise in which µ C = 0 while µ S = 0. This is our chargeless spin imbalance. (See Supplementary Information for more details.) In the experiment, µ QP↑ − µ P and µ QP↓ − µ P are measured as a voltage drop between a spin-sensitive electrode and the superconductor.We implement a mesoscopic version of an experiment proposed in refs 12,13; this offers two practical advantages: the detector can be placed within a spin relaxation length λ S of the injection point and all out-of-equilibrium signals are enhanced by the small injection volume. In diffusive transport, λ S = (Dτ S2 ) 1/2 , where τ S2 is the spin relaxation time and D the diffusion constant (∼5 × 10 −3 m 2 s −1 in our samples 15 ). Our samples are FISIF lateral spin valves 16 , where the F are ferromagnets (Co), the I are insulators (Al 2 O 3 ) and S is the superconductor (Al), as shown in Fig. 1a. The SIF junctions have sheet resistances of ∼1.6 × 10 −6 cm 2 (corresponding to a barrier transparency T ∼ 5 × 10 −5 ) and tunnelling is the main transport mechanism through the insulator. By sweeping an...

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“…and ∆(T ′ ) denotes the standard BCS temperature dependence of the superconducting gap. Equations (15), (16) and (22) constitute a complete system which allows one to determine the temperatures T inj , T det and T S as functions of the bias voltages. This system of equations was resolved numerically by iterations.…”

Section: Non-local Conductance and Heating: Theoretical Modelmentioning

confidence: 99%

Nonlocal transport and heating in superconductors under dual-bias conditions

et al. 2013

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We report on an experimental and theoretical study of nonlocal transport in superconductor hybrid structures, where two normal-metal leads are attached to a central superconducting wire. As a function of voltage bias applied to both normal-metal electrodes, we find surprisingly large nonlocal conductance signals, almost of the same magnitude as the local conductance. We demonstrate that these signals are the result of strong heating of the superconducting wire and that under symmetric bias conditions, heating mimics the effect of Cooper pair splitting.

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Magnetic field and contact resistance dependence of non-local charge imbalance

Cited by 27 publications

References 23 publications

Cross-correlated shot noise in three-terminal superconducting hybrid nanostructures

Cross-correlated shot noise in three-terminal superconducting hybrid nanostructures

Spin imbalance and spin-charge separation in a mesoscopic superconductor

Nonlocal transport and heating in superconductors under dual-bias conditions

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