Spatio-temporal chaos is predicted to occur in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Under dc voltage bias, undamped time-dependent oscillations of the current (due to the motion and recycling of electric field domain walls) have been observed in recent experiments. Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal.Comment: 3 pages, LaTex, RevTex, 3 uuencoded figures (1.2M) are available upon request from oleg@arwen.uc3m.es, to appear in Phys.Rev.

Shot-noise suppression is investigated in nondegenerate diffusive conductors by means of an ensemble Monte Carlo simulator. The universal 1͞3 suppression value is obtained when transport occurs under elastic collision regime provided the following conditions are satisfied: (i) The applied voltage is much larger than the thermal value; (ii) the length of the device is much greater than both the elastic mean free path and the Debye length. By fully suppressing carrier-number fluctuations, long-range Coulomb interaction is essential to obtain the 1͞3 value in the low-frequency limit.[ S0031-9007(98)05732-9] PACS numbers: 72.70. + m, 73.23.Ad, 73.50.Td In recent years kinetic phenomena in mesoscopic structures are offering a fascinating scenario for fundamental research [1]. One of the most up-to-date subjects is shotnoise suppression in disordered conductors. Here, the excess noise power has been predicted to comprise exactly one-third of the full shot-noise value S I 2eI. This result has been credited to different theoretical approaches as applied to several microscopic models of disordered conductors. For a phase-coherent model Beenakker and Büttiker [2] obtained the result using a bimodal distribution of transmission eigenvalues with the help of random matrix theory to calculate averages. For a semiclassical 1D model which includes Pauli principle Nagaev [3] found the same result using a Boltzmann kinetic approach within an elastic and energy independent relaxation-time approximation. For a semiclassical sequential tunneling model de Jong and Beenakker [4] obtained the 1͞3 value within a Boltzmann-Langevin approach in the limit of an infinite number of equal barriers and independently from the value of their transmission coefficient. Compatible results have been found by Liu et al.[5] from a semiclassical implementation of a Monte Carlo simulation which includes Pauli principle. For a phase-coherent model Nazarov [6] has proven the universality of this result in the diffusive limit for arbitrary shape and resistivity distribution of the conductor as long as its length is greater than the carrier mean free path. Experimental evidence of the reduced shot-noise level close to the predicted 1͞3 value in diffusive mesoscopic conductors has been provided in [7][8][9].From the above it is argued that the 1͞3 value of the suppression factor g S I ͞2eI is a universal phenomenon whose physical meaning should lay beyond classical or quantum mechanics and originate from some unifying concept. The aim of this Letter is to address this issue. We conjecture that discreteness of charge transport is at the basis of such a concept, and that a transport dominated by elastic interactions is ultimately the physical reason for the 1͞3 suppression independently from the quantum or classical approach used. Both the (apparently unrelated) coherent [2] and semiclassical [3] contexts where the reduction factor 1͞3 has appeared assume a degenerate Fermi gas, and the noise reduction comes from the regulation of electron motion by the ...

We present a microscopic analysis of shot-noise suppression due to long-range Coulomb interaction in semiconductor devices under ballistic transport conditions. An ensemble Monte Carlo simulator selfconsistently coupled with a Poisson solver is used for the calculations. A wide range of injection-rate densities leading to different degrees of suppression is investigated. A sharp tendency of noise suppression at increasing injection densities is found to scale with a dimensionless Debye length related to the importance of spacecharge effects in the structure. ͓S0163-1829͑97͒09735-X͔The phenomenon of shot noise, associated with the randomness in the flux of carriers crossing the active region of a device, has become a fundamental issue in the study of electron transport through mesoscopic devices. In particular, the possibility of shot-noise suppression has recently attracted a lot of attention, both theoretically and experimentally.1 At low frequency ͑small compared to the inverse transit time through the active region͒ the power spectral density of shot noise is given by S I ϭ␥2qI, where I is the dc current, q is the electron charge, and ␥ is the suppression factor. When the carriers crossing the active region are uncorrelated, full shot noise with ␥ϭ1 ͑Poisson statistics͒ is observed. However, correlations between carriers can reduce the shot-noise value, giving ␥Ͻ1. In real mesoscopic devices different types of mechanisms resulting in shot-noise suppression can be distinguished: ͑i͒ statistical correlations due to the Pauli exclusion principle ͑important for degenerate materials obeying Fermi statistics͒, ͑ii͒ short-range Coulomb interaction ͑electron-electron scattering͒, and ͑iii͒ long-range Coulomb interaction ͑by means of the self-consistent electric potential͒. While the first two mechanisms have been extensively discussed in solid-state literature, 1 the last one has received less attention, 2 although its role in shot-noise suppression has been known for a long time in vacuum-tube devices.3 The only exception that should be mentioned is the Coulomb blockade in resonant-tunneling devices, which can be also referred to as the last mechanism of suppression. The blockade is provided by a built-in charge inside a quantum well which redistributes the chemical potential, and prevents the incoming carriers from passing through the well, thereby resulting in carrier correlation and shot-noise suppression ͑see the experimental evidence 4 ͒. The Coulomb blockade is a consequence of long-range Coulomb interaction, and it acts under the sequential tunneling regime of carrier transport.The main objective of the present paper is to prove the importance of long-range Coulomb interaction between the carriers on the shot-noise power spectrum under the ballistic regime of electron transport. The ballistic regime is now accessible in modern mesoscopic devices like electron waveguides, quantum point contacts, etc., which have characteristic lengths of the order, or smaller, than the carrier mean free path. The current exist...

A self-consistent theory of shot noise in ballistic two-terminal conductors under the action of long-range Coulomb correlations is presented. Analytical formulas for the electron distribution function and its fluctuation along the conductor, which account for the Coulomb correlations, have been derived. Based upon these formulas, the current-noise reduction factor has been obtained for biases ranging from thermal to shot-noise limits as dependent on two parameters: the ratio between the length of the sample and the Debye screening length ϭd/L D and the applied voltage qU/k B T. The difference with the formulas for a vacuum diode is discussed.

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 ...

We present a numerical simulation of shot-noise suppression due to long-range Coulomb interaction in nondegenerate ballistic transport. Calculations make use of an ensemble Monte Carlo simulator self-consistently coupled with a one-dimensional Poisson solver, and are applied to a ballistic semiconductor structure formed of a lightly doped active region surrounded by two contacts acting as reservoirs. The doping of the injecting contacts and the applied voltage are taken as variable parameters. At increasing voltages the transition from thermal to shot-noise conditions is analysed. Space-charge is found to be responsible for an important suppression of shot noise even in the presence of linear current-voltage characteristics. At increasing injection rates we have found a strong tendency towards shot-noise suppression which scales with a dimensionless Debye length. The statistical properties of the electron flow along the structure are modified by Coulomb interaction, evidencing a sub-Poissonian behaviour. The frequency dependence of the fluctuations is also analysed. The spectral density of current fluctuations exhibits structures related to the different characteristic times involved in the carrier transport.

Within a Monte Carlo simulation, we investigate the statistical properties of an electron flow injected with a Poissonian distribution and transmitted under ballistic regime in the presence of long-range Coulomb interaction. Electrons are shown to exhibit a motional squeezing which tends to space them more regularly rather than strictly at random, and to evidence a sub-Poissonian statistics with a substantially reduced Fano factor F n Ӷ1. The temporal ͑anti͒correlation among carriers is demonstrated to be a collective effect which persists over the transit of several successive electrons, and results in a considerable ͑more than one order of magnitude͒ shot-noise suppression. ͓S0163-1829͑98͒03903-4͔

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low-and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnol'd tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac ϩdc driving.