Cascade approach to current fluctuations in a chaotic cavity

Nagaev, K. É.; Samuelsson, Peter; Pilgram, Sebastian

doi:10.1103/physrevb.66.195318

Cited by 81 publications

(150 citation statements)

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“…The theory [11,13,14] resulting from the σ-model (3), reduced to the subspace (5), accounts for real fluctuations in agreement with the cascade idea of Nagaev [17]. Below we use a similar ideology, "projecting" the σ-model on the subspace appropriate for the ZBA problem.…”

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confidence: 99%

Nonequilibrium Zero-Bias Anomaly in Disordered Metals

2008

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The non-equilibrium zero bias anomaly (ZBA) in the tunneling density of states of a diffusive metallic film is studied. An effective action describing virtual fluctuations out-of-equilibrium is derived. The singular behavior of the equilibrium ZBA is smoothed out by real processes of inelastic scattering.PACS numbers: 73.40.Gk, 73.50.Td The suppression of tunneling current at low bias due to electron-electron interaction is known as the zero bias anomaly (ZBA). The theory of ZBA for disordered metals at thermal equilibrium has been developed, on a perturbative level, by Altshuler and Aronov [1,2]. The nonperturbative generalization of this theory was achieved by Finkelstein [3]. Measurements of the tunneling density of states (DOS) in biased quasi-one-dimensional wires [4] call for an extension of the theory to non-equilibrium setups. In this work we study the ZBA for disordered metallic films out of equilibrium, in both the perturbative and the non-perturbative (in interaction) limits.Besides the experimental motivation, the problem of ZBA in a non-equilibrium system is of fundamental theoretical interest. At equilibrium, the distribution of electrons in phase space has a single edge at the Fermi surface. The Coulomb interaction between the tunneling electron and the electrons in the Fermi sea excites virtual particle-hole pairs around the Fermi edge, leading to the suppression of the tunneling DOS, similarly to the Debye-Waller factor. The suppression gets stronger when the electron energy approaches the Fermi energy. Out of equilibrium, the distribution of particles may have several sharp edges rather than a single one at the Fermi surface, which poses important questions addressed in this work: How will the excitation of electron-hole pairs in this situation affect the tunneling DOS? Will there be an interpaly between the two edges? We show that the two edges are not independent: one edge affects the ZBA near the other via real interaction-induced scattering processes governing the dephasing of electrons in the non-equlibrium regime. From this point of view the problem we are considering is a representive of a class of phenomena that involve renormalization away from thermal equilibrium, such as the Fermi edge singularity [5] and the Kondo effect [6].What makes the ZBA particularly interesting is its deep connection to various conceptually important phenomenological ideas. At equilibrium, the nonperturbative results [3] have been reproduced by quantum hydrodynamical methods [7], and, within the framework of the theory of dissipation [8], by methods that rely on the fluctuation-dissipation theorem. Our work

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confidence: 99%

Nonequilibrium Zero-Bias Anomaly in Disordered Metals

2008

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“…Surprisingly, the stationary point is given by λ C = 0 and f C = 1/2 independent of γ, implying the absence of cascade corrections [21] to the FCS. Evaluating Eq.…”

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confidence: 99%

Quantum-to-Classical Crossover in Full Counting Statistics

Sukhorukov

Bulashenko

2005

Phys. Rev. Lett.

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The reduction of quantum scattering leads to the suppression of shot noise. In the present paper, we analyze the crossover from the quantum transport regime with universal shot noise, to the classical regime where noise vanishes. By making use of the stochastic path integral approach, we find the statistics of transport and the transmission properties of a chaotic cavity as a function of a system parameter controlling the crossover. We identify three different scenarios of the crossover.PACS numbers: 05.45.Mt, 73.50 Td, 74.40.+k Random transfer of charge in electrical conductors leads to time-dependent fluctuations of the current, a phenomenon called shot noise. In recent years, the shot noise has been extensively studied in mesoscopic conductors [1], small degenerate electron systems of a size comparable to the coherence length of electrons. In contrast to the classical shot noise in vacuum tubes, which was explained by Schottky already in 1918 [2], the shot noise in mesoscopic conductors originates from the quantum-mechanical scattering of electrons. Consequently, in a noninteracting mesoscopic conductor biased by the chemical potential difference ∆µ, the average current I = ∆µ n T n [3] (setting electron charge and the Planck constant e = h = 1), the noise power S ≡ I 2 = ∆µ n T n (1 − T n ) at zero temperature [1], and in general the higher cumulants of current I m [4], are determined by the transmission matrixt, namely by the eigenvalues T n , n = 1, . . . , N , oft †t . The current cumulants I m = ∆µN C m can be expressed via the cumulant generating function (CGF) C m = ∂ m H(λ)/∂λ m | λ=0 . In the semiclassical limit, N ≫ 1, the CGF is given by [5]:where ρ(T ) = N −1 n δ(T − T n ) is the transmission eigenvalue distribution. Eq. (1) generalizes the binomial statistics, and together with the inverse formula (12), provides a connection between the full counting statistics (FCS) and the scattering properties of a mesoscopic system to leading order in 1/N .The quantum origin of shot noise in mesoscopic conductors implies that regardless of the character of disorder, current can flow without noise if quantum scattering is suppressed [6]. Therefore, in the classical limit the noise should vanish even in a chaotic system, such as a mesoscopic cavity, where the transport in quantum regime is universally described by Random Matrix Theory (RMT) [7]. It has been predicted [8] that in a mesoscopic cavity with long-range disorder that models chaotic dynamics the noise power shows an exponential crossover S = S RMT exp(−τ E /τ D ) as a function of the ratio of the Ehrenfest (diffraction) time τ E to the average dwell time of electrons τ D . Ref. [9] suggested that this crossover results from a sharp cut-off introduced by the Ehrenfest time in the exponential distribution P(t) = τ −1 D exp(−t/τ D ) of the dwell times of classical trajectories. Recent numerical analysis [10] has demonstrated that the cut-off leads to a complete separation of the cavity's phase space into the quantum universal part of relative volume ...

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“…The appeal of this approach is its intuitive transparency, yet traditionally it was constructed to describe pair correlation functions, hence was limited to finding the second current cumulant. In a recent insightful work Nagaev [10] has proposed a generalization of the KTF, expressing higher order cumulants in terms of pair correlators. Using this idea (which was termed the "cascade approach"), Nagaev calculated the third and the fourth cumulants of the current.…”

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confidence: 99%

Kinetic theory of fluctuations in conducting systems

2005

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We propose an effective field theory describing the time dependent fluctuations of electrons in conducting systems, generalizing the well known kinetic theory of fluctuations. We apply then the theory to analyze the effects of strong electron-electron and electron-phonon scattering on the statistics of current fluctuations. We find that if the electron-electron scattering length is much shorter than the transport mean free path the higher cumulants of current are parametrically enhanced.Fluctuations of electric current in time have been the subject of fundamental and applied research since the time of Schottky. They have been a centerpiece in the study of systems ranging from vacuum tubes to quantum Hall bars (for a review see [1]). More recently noise has been recognized as an important diagnostic probe for the nature of disorder and interactions. Traditionally the number of electrons taking part in transport in macroscopic systems is large; for that reason current fluctuations obey nearly Gaussian statistics. Under such circumstances it is the power spectrum which is the object of primary interest when addressing the fluctuations. However, as the sample size shrinks down from a vacuum tube to a nanojunction, and the currents involved become correspondingly smaller, the central limit theorem does not apply any more, and information concerning higher current cumulants may be needed. Various techniques have been applied to address this issue [1,2,3,4,5,6].There is an interesting and relevant class of systems out of equilibrium in which the effect of quantum interference on transport quantities is negligible. Transport through such systems is often described by classical kinetic equations (e.g. the Boltzmann equation). The intensity of the noise spectrum can then found employing a related approach, known as the kinetic theory of fluctuations (KTF) [7,8,9]. The appeal of this approach is its intuitive transparency, yet traditionally it was constructed to describe pair correlation functions, hence was limited to finding the second current cumulant. In a recent insightful work Nagaev [10] has proposed a generalization of the KTF, expressing higher order cumulants in terms of pair correlators. Using this idea (which was termed the "cascade approach"), Nagaev calculated the third and the fourth cumulants of the current. While this approach was shown to successfully address a number of problems, its (quantum-mechanical) microscopic foundations, as well as its formulation in terms of an effective field theory (which would allow for further generalization, such as including interactions or calculating the full counting statistics (FCS)) were not fully understood. An important step in the latter direction was an introduction of a stochastic path integral by Pilgram, Jordan, Sukhorukov, and Büttiker [11].In the present paper we propose a phenomenological effective field theory describing the time dependent fluctuations in phase space of electrons in conducting systems. This is a field-theoretical implementation of the Nagae...

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Cascade approach to current fluctuations in a chaotic cavity

Cited by 81 publications

References 20 publications

Nonequilibrium Zero-Bias Anomaly in Disordered Metals

Nonequilibrium Zero-Bias Anomaly in Disordered Metals

Quantum-to-Classical Crossover in Full Counting Statistics

Kinetic theory of fluctuations in conducting systems

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