Quantum shot noise in a normal-metal–superconductor point contact

Muzykantskiǐ, B. A.; Khmelnitskii, D. E.

doi:10.1103/physrevb.50.3982

Cited by 149 publications

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“…He also investigated the finite temperature case and derived the Nyquist noise. The results were rederived within the scattering approach by Muzykantskii and Khmelnitskii [169]. The general case was studied by de Jong and Beenakker [170] in the framework of the scattering approach; we followed their work in the course of the above derivation.…”

Section: A Shot Noise Of Normal-superconductor Interfacesmentioning

confidence: 99%

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Shot noise in mesoscopic conductors

2000

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Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and BoltzmannLangevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.

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Section: A Shot Noise Of Normal-superconductor Interfacesmentioning

confidence: 99%

“…(A9) can be also obtained classically [347], using the generalization of the minimal correlation approach. Muzykantskii and Khmelnitskii [169] investigate the counting statistics for the NS interface and find…”

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confidence: 99%

Shot noise in mesoscopic conductors

2000

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“…Several methods have been used in finding this quantity. Originally, quantum mechanical methods based on scattering theory [2,3], the Keldysh approach put forth by Nazarov [4] or sigma-models [5] have been advanced and have been successfully applied to a number of problems among which we mention only multiterminal structures [6], normal-superconducting samples [7], combined photon/electron statistics [8], and conductors which are current (instead of voltage) biased [9].…”

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Stochastic Path Integral Formulation of Full Counting Statistics

et al. 2003

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We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semi-classical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.PACS numbers: 72.70.+m, 76.36.Kv Noise properties of electrical conductors are interesting because they reveal additional information beyond linear response [1]. In the pioneering work of Levitov and Lesovik [2], the optics concept of full counting statistics (FCS) for photons was introduced for electrons in the context of mesoscopic physics. FCS gives the probability of counting a certain number of particles at a measurement apparatus in a certain amount of time and finds not only conductance and shot noise, but all higher current cumulants as well. Several methods have been used in finding this quantity. Originally, quantum mechanical methods based on scattering theory [2,3], the Keldysh approach put forth by Nazarov [4] or sigma-models [5] have been advanced and have been successfully applied to a number of problems among which we mention only multiterminal structures [6], normal-superconducting samples [7], combined photon/electron statistics [8], and conductors which are current (instead of voltage) biased [9].A quantum mechanical treatment of transport shows that the leading contribution to current cumulants is of the order of the channel number N . For many conductors or circuits of interest, this leading order is a semi-classical quantity [10]. Weak localization or universal conductance fluctuations provide only a small correction of order 1. Clearly, it is desirable to have a purely semi-classical theory to calculate semi-classical results. To provide such a derivation of FCS is the main purpose of this work.That a purely classical theory should be developed was realized by de Jong [11] who put forth a discussion for problems which can be described with the help of master equations. A more general approach, leading to a set of rules for a cascade of higher order cumulants, was recently invented by Nagaev [12] and applied to chaotic cavities [13]. The work presented here aims at providing a foundation for the cascade approach by deriving a functional integral from which FCS, but also dynamical quantities such as correlation functions, can be obtained.The approach provided here applies to an arbitrary mesoscopic network. Its semi-classical nature does not allow the treatment of weak localization corrections nor is it applicable to macroscopic quantum effects like the 25 50Full counting statistics of a chaotic cavity at zero temperature: Comparison between hot (thick lines) and...

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“…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.…”

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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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Quantum shot noise in a normal-metal–superconductor point contact

Cited by 149 publications

References 5 publications

Shot noise in mesoscopic conductors

Shot noise in mesoscopic conductors

Stochastic Path Integral Formulation of Full Counting Statistics

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

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