Theory of charge transport in diffusive normal metal/conventional superconductor point contacts

Tanaka, Yukio; Golubov, Alexandre Avraamovitch; Kashiwaya, Satoshi

doi:10.1103/physrevb.68.054513

Cited by 47 publications

(74 citation statements)

References 77 publications

(67 reference statements)

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“…It was shown in Ref. 43 that a zero bias conductance peak ͑ZBCP͒ in low transparent N/S junctions transforms to a zero bias conductance dip ͑ZBCD͒ with increasing the interface transparency.…”

Section: Introductionmentioning

confidence: 99%

“…[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. The Nazarov's boundary conditions coincide with the KL boundary conditions when transmission coefficients are sufficiently low, while the BTK theory 10 is reproduced in the ballistic regime.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2005

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“…Note that we assume a weak ferromagnet and neglect the difference of the Fermi velocities of the majority and minority spin subbands. Further we shall apply the Nazarov's boundary condition 24,25 for θ(x) at both interfaces. At the DF/N interface it has the following form:…”

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Resonant peak in the density of states in normal-metal/diffusive-ferromagnet/superconductor junctions

2005

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The conditions for the formation of zero-energy peak in the density of states (DOS) in the normal metal / insulator / diffusive ferromagnet / insulator / s-wave superconductor (N/I/DF/I/S) junctions are studied by solving the Usadel equations. The DOS of the DF is calculated in various regimes for different magnitudes of the resistance, Thouless energy and the exchange field of the DF, as well as for various resistances of the insulating barriers. The conditions for the DOS peak are formulated for the cases of weak proximity effect (large resistance of the DF/S interface) and strong proximity effect (small resistance of the DF/S interface).In ferromagnet/superconductor (F/S) junctions Cooper pairs penetrating into the F layer from the S layer have a nonzero momentum due to the influence of exchange field 1,2,3 . This results in oscillating behavior of the pair amplitude or a π-phase shift of the order parameter in the ferromagnet. A negative sign of the real part of the order parameter may occur when the thickness of the F layer is larger than the coherence length of the F layer. The occurrence of the π-phase shift makes it possible to realize the SFS π -junctions 1 , as was confirmed experimentally 4,5,6,7,8 . The order parameter oscillations also lead to nonmonotonous dependence of T c in SF bilayers on the F-layer thickness 9,10,11,12,13 . Effects of resonant transmission in conductivity of SF structures were discussed in Ref 14,15,16 .Another interesting consequence of the oscillations of the pair amplitude is the spatially damped oscillating behavior of the density of states (DOS) in a ferromagnet predicted theoretically 17,18,19,20 in various regimes. The energy dependent DOS calculated in the clean 18 and the dirty 21 limits exhibits rich structures. Experimentally DOS in F/S bilayers was measured by Kontos et al. who found a broad DOS peak around zero energy when the π-phase shift occurs 22 . In diffusive ferromagnet/superconductor (DF/S) junctions the zeroenergy DOS may have a sharp peak 21 . However the conditions for the appearance of such anomaly have not been studied systematically so far.The purpose of the present paper is to calculate DOS in N/DF/S junctions and to formulate the conditions for the zero-energy DOS peak in two regimes corresponding to the weak proximity effect (large DF/S interface resistance) and strong proximity effect (small DF/S interface resistance). We will show that in the former case the condition is equivalent to the one of Ref. 21 , while in the latter case the new condition is found. The calculation will be performed in the zero-temperature regime by varying the interface resistances as well as the resistance, the exchange field and the Thouless energy of the DF layer.We consider a junction consisting of normal and superconducting reservoirs connected by a quasi-onedimensional diffusive ferromagnet conductor (DF) with a resistance R d and a length L much larger than the mean free path. The DF/N interface located at x = 0 has the resistance R ′ b , while the DF/S interface...

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“…(18) is the central result of the paper. Once the problem for the conductance has been solved and θ(x) and f T (x) are known [2,18], we provide a simple and efficient way to calculate the noise. It suffices to solve the linear differential equation (15) with the given boundary conditions, and substitute the result into Eq.…”

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“…It suffices to solve the linear differential equation (15) with the given boundary conditions, and substitute the result into Eq. (18). This program has to be followed numerically in most situations, but its implementation is straightforward and allows to obtain quantitative predictions for a wide range of realizable experiments.…”

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Energy Dependence of Current Noise in Superconducting/Normal Metal Junctions

Houzet¹,

Pistolesi

NATO Science Series

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Interference of electronic waves undergoing Andreev reflection in diffusive conductors determines the energy profile of the conductance on the scale of the Thouless energy. A similar dependence exists in the current noise, but its behavior is known only in few limiting cases. We consider a metallic diffusive wire connected to a superconducting reservoir through an interface characterized by an arbitrary distribution of channel transparencies. Within the quasiclassical theory for current fluctuations we provide a general expression for the energy dependence of the current noise.PACS numbers: 74.45.+c,74.40.+k,72.70.+m Interference of electronic waves in metallic disordered conductors is responsible for weak localization corrections to the conductance [1]. If these are neglected, the probability of transferring an electron through the diffusive medium is given by the sum of the modulus squared of the quantum probability amplitudes for crossing the sample along all possible paths. This probability is denoted as semiclassical, since quantum mechanics is necessary only for establishing the probability for following each path independently of the phases of the quantum amplitudes. In superconducting/normal metal hybrid structures, interference contributions are not corrections, they may actually dominate the above defined semiclassical result for temperatures and voltages smaller than the superconducting gap. This is seen experimentally as an energy dependence of the conductance on the scale of the Thouless energy. Indeed, the energy dependence comes from the small wavevector mismatch, linear in the energy of the excitations, between the electron and the Andreev reflected hole. This is responsible for the phase difference in the amplitudes for two different paths leading to interference. The effect is well known and explicit predictions and measurements exist for a number of systems [2,3,5].Interference strongly affects the current noise too [6]. The largest effects are expected in the tunneling limit, when the transparency of the barrier is small and its resistance is much larger than the resistance of the diffusive normal region. Then, the conductance has a strong non linear dependence at low bias (reflectionless tunneling) [2,3]. This is actually the case, but the zero-temperature noise (or shot noise) does not give any additional information on the system since it is simply proportional to the current, as shown numerically in a specific example in Ref.[4] and quite generally in Ref. [7]. The double tunnel barrier system has been considered in Ref. [8]. In the case of a diffusive metal wire in contact with a superconductor through an interface of conductance G B much larger than the wire conductance G D , Belzig and Nazarov [9] found that the differential shot noise, dS/dV , shows a reentrant behavior, as a function of the voltage bias, similar, but not identical, to the conductance one. (The extension of the Boltzman-Langevin approach to the coherent regime in Ref.[10] neglects this difference.) In order to comp...

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Theory of charge transport in diffusive normal metal/conventional superconductor point contacts

Cited by 47 publications

References 77 publications

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

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

Resonant peak in the density of states in normal-metal/diffusive-ferromagnet/superconductor junctions

Energy Dependence of Current Noise in Superconducting/Normal Metal Junctions

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