Semiclassical theory of shot noise in disordered superconductor–normal-metal contacts

Nagaev, K. É.; Büttiker, Μ.

doi:10.1103/physrevb.63.081301

Cited by 54 publications

(72 citation statements)

References 23 publications

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“…Thus, in this process a charge transfer of 2e occurs, but with a reduced probability, since two particles have to tunnel. The shot noise is proportional to the charge of the elementary processes, and one thus naivly expects a doubling of the shot noise, which was indeed found theoretically [12,13] and experimentally [14,15] for diffusive conductors. It is remarkable that this doubling occurs for diffusive conductors, whereas it is not found for other conductors like, e. g., single-channel contacts [3,12,[16][17][18] , double tunnel junctions [19][20][21][22], or diffusive junctions with a tunneling barrier [23,24].…”

Section: Introductionmentioning

confidence: 88%

“…For an arbitrary geometry, the spectral conductance has to be found from the solution of a diffusion equation. Guided by the kinetic equation for the average transport, we may try to find the current noise by generalizing the Boltzmann-Langevin approach [13] to include the energy-and space-dependent conductivity. In fact, this task has already been performed.…”

Section: Energy-dependent Current Noisementioning

confidence: 99%

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Shot Noise in Mesoscopic Diffusive Andreev Wires

Belzig

2004

Molecular Nanowires and Other Quantum Objects

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We study shot noise in mesoscopic diffusive wires between a normal and a superconducting terminal. We particularly focus on the regime, in which the proximity-induced reentrance effect is important. We will examine the difference between a simple Boltzmann-Langevin description, which neglects induced correlations beyond the simple conductivity correction, and a full quantum calculation. In the latter approach, it turns out that two Andreev pairs propagating coherently into the normal metal are anti-correlated for E Ec, where Ec = D/L 2 is the Thouless energy. In a fork geometry the flux-sensitive suppression of the effective charge was confirmed experimentally.

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Section: Introductionmentioning

confidence: 88%

Section: Energy-dependent Current Noisementioning

confidence: 99%

Shot Noise in Mesoscopic Diffusive Andreev Wires

Belzig

2004

Molecular Nanowires and Other Quantum Objects

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“…7 Consider now the most intresting case of a strong coupling to the superconductors where r ≪ R. It is seen from Eqs. (11) and (12) that the noise measured at one of the normal ends of the cross is doubled with respect to a two-terminal normal-metal system, as it takes place in diffusive contacts where the transport current flows through an SN interface 2 .…”

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confidence: 99%

“…[4][5][6] Quite recently, it was shown that the doubled shot noise in diffusive NS contacts survives at finite voltages of the order of the energy gap. 7 Moreover, this noise does not require a phase coherence 8 and may be described in terms of a semiclassical Boltzmann -Langevin equation. 9 In this approach, the increased noise in NS systems is due to an excess heating of electron gas rather than to the doubling of the effective charge.…”

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confidence: 99%

Nonlocal effects in the shot noise of diffusive superconductor–normal-metal systems

Nagaev

2001

Phys. Rev. B

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A cross-shaped diffusive system with two superconducting and two normal electrodes is considered. A voltage eV < ∆ is applied between the normal leads. Even in the absence of average current through the superconducting electrodes their presence increases the shot noise at the normal electrodes and doubles it in the case of a strong coupling to the superconductors. The nonequilibrium noise at the superconducting electrodes remains finite even in the case of a vanishingly small transport current due to the absence of energy transfer into the superconductors. This noise is suppressed by electron-electron scattering at sufficiently high voltages.PACS numbers: 72.70.+m, 74.40+k, 74.50+r Recently, the noise properties of hybrid systems involving superconducting (S) and normal (N) metals became a subject of intensive studies. 1 A key effect in these properties is the Andreev reflection, in which electrons incident from the normal metal are reflected from the NS interface as holes. In particular, it was found that in the zero-voltage limit, the shot noise in diffusive NS contacts with phase-coherent transport is doubled with respect to its value in a normal contact with the same resistance. 2,3 This doubling was interpreted as an effective doubling of electron charge and has been experimentally confirmed in a number of papers. [4][5][6] Quite recently, it was shown that the doubled shot noise in diffusive NS contacts survives at finite voltages of the order of the energy gap. 7 Moreover, this noise does not require a phase coherence 8 and may be described in terms of a semiclassical Boltzmann -Langevin equation. 9 In this approach, the increased noise in NS systems is due to an excess heating of electron gas rather than to the doubling of the effective charge.Along with studying the shot noise in two-terminal systems, a considerable attention received the noise in multiterminal structures. It was found that the noise of normal-metal diffusive structures with more than two electrodes may exhibit exchange effects 10 and nonlocal effects. 11 The latter imply that the noise in the system is affected by a presence of open contacts even in the absence of average current flow through them.Several authors also calculated current correlations in single-channel multiterminal NS systems. 12-14 In particular, it was found that the noise measured at the two normal electrodes in a four-terminal system depends on the phase difference between the two superconducting electrodes. 12 A current noise was also calculated at a tip placed on a multimode quantum-coherent NS structure. 15 In this paper, we consider nonlocal effects in multiterminal mesoscopic diffusive SN systems using the semiclassical description of noise. In particular, we report on a semiclassical "proximity" effect in the noise where the current noise in a normal conductor is increased by its contact with a superconductor. Another finding is that under certain conditions, a large noise may be induced in an SNS structure even by a small transverse transport current.Consi...

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“…(18) where only the 2/3 and the integral terms survive. The first term is the semiclassical incoherent value [27], which also coincides with the fully coherent one [5]. The integral term singles out the interference contribution to the Fano factor.…”

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confidence: 99%

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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Semiclassical theory of shot noise in disordered superconductor–normal-metal contacts

Cited by 54 publications

References 23 publications

Shot Noise in Mesoscopic Diffusive Andreev Wires

Shot Noise in Mesoscopic Diffusive Andreev Wires

Nonlocal effects in the shot noise of diffusive superconductor–normal-metal systems

Energy Dependence of Current Noise in Superconducting/Normal Metal Junctions

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