Influence of magnetic impurities on charge transport in diffusive-normal-metal/superconductor junctions

Yokoyama, Takehito; Tanaka, Yukio; Golubov, Alexandre Avraamovitch; Inoue, Jun; Asano, Yasuhiro

doi:10.1103/physrevb.71.094506

Cited by 20 publications

(14 citation statements)

References 52 publications

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“…9. As seen from the plots, the influence of uniaxial spin-flip scattering is a gradual suppression of the proximity-induced features in the DOS, consistent with previous results 66,67,68,69,70 . The effect of isotropic spinflip scattering is virtually identical to the uniaxial case.…”

Section: Minigap and Spin-orbit Scatteringsupporting

confidence: 91%

Role of interface transparency and spin-dependent scattering in diffusive ferromagnet/superconductor heterostructures

2008

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We present a numerical study of the density of states in a ferromagnet/superconductor junction and the Josephson current in a superconductor/ferromagnet/superconductor junction in the diffusive limit by solving the Usadel equation with Nazarov's boundary conditions. Our calculations are valid for an arbitrary interface transparency and arbitrary spin-dependent scattering rate, which allows us to explore the entire proximity-effect regime. We first investigate how the proximity-induced anomalous Green's function affects the density of states in the ferromagnet for three magnitudes of the exchange field h compared to the superconducting gapIn each case, we consider the effect of the barrier transparency and allow for various concentrations of magnetic impurities. We clarify features that may be expected in the various parameter regimes accessible for the ferromagnetic film, with regard to thickness and exchange field. In particular, we address how the zero-energy peak and minigap observed in experiments may be understood in terms of the interplay between the singlet and triplet anomalous Green's function and their dependence on the concentration of magnetic impurities. Our results should serve as a useful tool for quantitative analysis of experimental data. We also investigate the role of the barrier transparency and spin-flip scattering in a superconductor/ferromagnet/superconductor junction. We suggest that such diffusive Josephson junctions with large residual values of the supercurrent at the 0-π transition, where the first harmonic term in the current vanishes, may be used as efficient supercurrentswitching devices. We numerically solve for the Josephson current in such a junction to clarify to what extent this idea may be realized in an experimental setup. It is also found that uniaxial spin-flip scattering has very different effect on the 0-π transition points depending on whether one regards the width-or temperaturedependence of the current. Our theory takes into account vital elements that are necessary to obtain quantitative predictions of the supercurrent in such junctions.

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Section: Minigap and Spin-orbit Scatteringsupporting

confidence: 91%

Role of interface transparency and spin-dependent scattering in diffusive ferromagnet/superconductor heterostructures

2008

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“…As expected the density of states increases when we move away from the interface. For large spin-flip scattering rates, the elliptic solution (14) saturates to the normal state bulk value θ(x) = 0, everywhere except in a thin domain close to the S-N interface (rigid boundary at x = 0).…”

mentioning

confidence: 99%

“…For the case of a junction with L = 1.1 ξ (corresponding to the Thouless energy of the order of ∆), they find that the minigap closes when Γ sf ≈ 0.4 ∆. Other works 13,14 have analyzed the effect of magnetic impurities in the transport properties of S-N junctions, finding that the Thouless energy is the scale which controls the effect of spin flip scattering on the proximity effect. Due to the self-consistent treatment and the non-linearity of the Usadel equations the complete numerical solution of the problem is difficult.…”

mentioning

confidence: 99%

Minigap in a superconductor–normal metal junction with paramagnetic impurities

Crouzy¹,

Bascones²,

Иванов³

2005

Phys. Rev. B

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We study the effect of spin-flip scattering on the density of states in a long diffusive S-N junction with transparent interface. We calculate the critical value of the spin-flip scattering rate at which the minigap closes and give the dependence of the minigap on the spin-flip rate. For the system we consider, the minigap and the critical spin-flip rate have the scale of the Thouless energy, and not of the superconducting gap.Proximity structures made of superconducting and non-superconducting elements in contact with each other is a topic of current theoretical and experimental interest. Most of the experimental applications concern diffusive materials for which an appropriate formalism has been derived.1 In the diffusive regime the motion of the electrons is governed by frequent scattering on impurity atoms: the elastic mean free path l e is much smaller than the relevant length scales of the system, namely the superconducting coherence length ξ and the dimension of the normal (N) and superconducting (S) electrodes. As a consequence of Andreev reflection and its interplay with disorder, a gap is opened in the spectrum of the N-region (see for example 2,3,4,5 and references therein). This minigap does not depend on the position in the junction and is of the order of magnitude of the Thoulessis the diffusion constant and L is the length of the normal wire. Here and in the following, we use the units withh = 1.Elastic scattering on impurities is not harmful for isotropic superconductivity and is directly connected to the appearance of the minigap. On the contrary, scattering on magnetic impurities leads to the destruction of singlet superconductivity. The exchange interaction between the spin of the electrons and the magnetic impurities breaks the time reversal symmetry between the electrons in Cooper pairs and reduces the superconducting correlations. Scattering on magnetic impurities can be described in terms of a spin-flip scattering rate Γ sf . In the Born approximation 6,7 Γ sf is proportional to the impurity concentration. The energy gap E g in the electron density of states (DoS) of a bulk superconductor is lowered by spin-flip scatteringand closes for the critical concentration of magnetic impuritiesHere, the order parameter ∆ itself depends on Γ sf .In the "dirty" limit, the equations of motion for the quasiclassical matrix Green function (averaged over the fast Fermi oscillations and the momentum directions) can be reduced to the Usadel equations.1,9 Usadel equations have been very useful in the analysis of position dependent problems like proximity effect. Spin-flip and inelastic scattering processes can be included in the Usadel equations through the corresponding scattering rates Γ sf , respectively Γ in . 10The impact of spin-flip scattering on the proximity effect and the minigap can be controlled by selectively doping the normal and/or superconducting regions with magnetic impurities or applying a magnetic field to a thin film or wire.7,11 Belzig et al 12 have numerically shown that the minigap i...

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“…28 By applying the VZK theory, a number of authors investigated theoretically charge transport in various proximity structures. [28][29][30][31][32][33][34][35][36][37][38][39] This work was based on the boundary conditions for the KeldyshNambu Green's function at the DN/S interface derived by Kupriyanov and Lukichev ͑KL͒ 40 from Zaitsev's boundary condition 41 in the isotropic limit. The KL boundary conditions were recently extended by Nazarov within the circuit theory 42 and applied by Tanaka et al 43 to the study of charge transport in N/S junctions with arbitrary interface transparency in order to investigate more complex structures.…”

Section: Introductionmentioning

confidence: 99%

Theory of thermal and charge transport in diffusive normal metal/superconductor junctions

et al. 2005

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Thermal and charge transport in diffusive normal metal ͑DN͒/insulator/s-, d-, and p-wave superconductor junctions are studied based on the Usadel equation with the Nazarov's generalized boundary condition. We derive a general expression of the thermal conductance in unconventional superconducting junctions. Thermal conductance, electric conductance of junctions and their Lorentz ratio are calculated as a function of resistance in DN, the Thouless energy, magnetic scattering rate in DN and transparency of the insulating barrier. We also discuss transport properties for various orientation angles between the normal to the interface and the crystal axis of superconductors. It is demonstrated that the proximity effect does not influence the thermal conductance while the midgap Andreev resonant states suppress it. Dependencies of the electrical and thermal conductance on temperature are sensitive to pairing symmetries and orientation angles. The results imply a possibility to distinguish one pairing symmetry from another based on the results of experimental observations.

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Influence of magnetic impurities on charge transport in diffusive-normal-metal/superconductor junctions

Cited by 20 publications

References 52 publications

Role of interface transparency and spin-dependent scattering in diffusive ferromagnet/superconductor heterostructures

Role of interface transparency and spin-dependent scattering in diffusive ferromagnet/superconductor heterostructures

Minigap in a superconductor–normal metal junction with paramagnetic impurities

Theory of thermal and charge transport in diffusive normal metal/superconductor junctions

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