By solving a master equation in the Sierpinski lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P ~ L^(d_f-2-alpha), with an exponent depending on the fractal dimension d_f and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I, which implies that the Fano factor F=P/2eI is scale independent. We obtain a value F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.
We prove the universality of shot-noise in multiterminal diffusive conductors of arbitrary shape and dimension for purely elastic scattering as well as for hot electrons. Using a Boltzmann-Langevin approach we reduce the calculation of shot-noise correlators to the solution of a diffusion equation. We show that shot-noise in multiterminal conductors is a non-local quantity and that exchange effects can occur without quantum phase coherence even at zero electron temperature. Concrete numbers for shot-noise are given that can be tested experimentally.
We argue that the nearly 1/3 suppression of shot noise in nondegenerate diffusive contacts recently obtained by Gonzalez et al. (cond-mat/9803372) is due to the specific choice of the energy-independent elastic scattering time.
Shot noise is not normally evident in bulk solid-state conductors, since it is strongly attenuated by inelastic collisions. The ``anomalous'' emergence of macroscopic shot noise is discussed in G. Gomila and L. Reggiani, Phys. Rev. B 62, 8068 (2000). We remark on the consistency of this linear diffusive model at the large voltages and currents needed to see the effect.
Frequency-dependent nonequilibrium noise in quantum-coherent diffusive conductors is calculated with account taken of long-range Coulomb interaction. For long and narrow contacts with strong external screening the crossover between quantum and shot noise takes place at frequencies much smaller than the voltage drop across the contact. We also show that under certain frequency limitations, the semiclassical and quantum-coherent approaches to shot noise are mathematically equivalent.
Shot noise in diffusive mesoscopic conductors, at finite observation frequencies $ω$ (comparable to the reciprocal Thouless time $τ_T^{-1}$), is analyzed with an account of screening. At low frequencies, the well-known result $S_I(ω)=2eI/3$ is recovered. This result is valid at arbitrary $ωτ_T$ for wide conductors longer than the screening length. However, at least for two very different systems, namely, wide and short conductors, and thin conductors over a close ground plane, noise approaches a different fundamental level, $S_I(ω) = eI$, at $ωτ_T\gg 1$.
We present an experimental procedure for obtaining the conduction channels of low-dimensional conductors based on shot noise measurements. The transmission coefficient for each channel is determined numerically from the measured conductance and Fano factor. The channel analysis is demonstrated for atomic contacts of Ag, Au, Al and Pt, showing their channel evolution as a function of conductance and mechanical elongation. This approach can be readily applied to map the conduction channels in a wide range of nanoscale conductors under different conditions.
We describe a field-theoretic approach to calculate quantum shot noise in nanoscale conductors from first principles. Our starting point is the second-quantization field operator to calculate shot noise in terms of single quasi-particle wavefunctions obtained self-consistently within density functional theory. The approach is valid in both linear and nonlinear response and is particularly suitable in studying shot noise in atomic-scale conductors. As an example we study shot noise in Si atomic wires between metal electrodes. We find that shot noise is strongly nonlinear as a function of bias a…
New experiments that measure the low-frequency shot-noise spectrum at local tunneling contacts on mesoscopic structures are proposed. The current fluctuation spectrum at a single tunneling tip is determined by local partial densities of states. The current-correlation spectrum between two tunneling tips is sensitive to non-diagonal density of states elements which are expressed in terms of products of scattering states of the conductor. Thus such an experiment permits to investigate correlations of electronic wave functions. We present specific results for a clean wire with a single barrier an…
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 λ=d/L_D and the applied voltage qU/k_BT. The difference …
In this paper, we present a method to investigate the spin-current shot noise in mesoscopic conductors, by using scattering matrix theory and Green's function technique. We first derive a general expression for the spin-current noise at zero-frequency limit, and extract the shot-noise component by discussing it at zero-temperature limit. The expression indicates that the spin-current shot noise in one lead is caused by the transmissions to the spin-resolved states in this lead and the interferences of these transmissions. As an application, we simulate the spin-current shot noise in a spin tra…
There has been renewed interest in the physics of the so-called crossover for current fluctuations in mesoscopic conductors, most recently involving the possibility of its appearance in the passage to the macroscopic limit. Shot noise is normally absent from solid-state conductors in the large, and its anomalous resurgence there has been ascribed to a rich interplay of drift, diffusion, and Coulomb screening. We demonstrate that essentially the same rise in shot noise occurs in a much less complex system: the Boltzmann-Drude-Lorentz model of a macroscopic, uniform gas of strictly noninteractin…
Motivated by a recent experiment by L.-H. Reydellet et al., Phys. Rev. Lett. 90, 176803 (2003), we discuss an interpretation of photon-assisted shot noise in mesoscopic multiprobe conductors in terms of electron-hole pair excitations. AC-voltages are applied to the contacts of the sample. Of interest are correlations resulting from the fact that electrons and holes are generated in pairs. We show that with two out-of-phase ac-potentials of equal magnitude and frequency, applied to different contacts, it is possible to trace out the Hanbury Brown Twiss exchange interference correlations in a fo…
It is shown that measurements of zero-frequency shot-noise can provide information on electron-electron interaction, because the strong interaction results in the nonlinear voltage dependence of the shot noise in metallic wires. This is due to the fact that the Wiedemann-Franz law is no longer valid in the case of considerable electron-electron interaction. The deviations from this law increase the noise power and make it dependent strongly on the ratio of electron-electron and electron-impurity scattering rates.
Shot-noise suppression is investigated in nondegenerate diffusive conductors by means of an ensemble Monte Carlo simulator. The universal 1/3 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 longer 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 1/3 value in the low-frequency limit.
We investigate the injection of degenerate Fermi-Dirac electrons into a multimode ballistic conductor under the space-charge limited regime. The nonequilibrium current fluctuations were found to be suppressed by both Coulomb and Fermi correlations. We show that the Fermi shot-noise suppression factor is limited below by the value 2kT/epsilon_F, where T is the temperature and epsilon_F the Fermi energy of the injected electrons. The Coulomb noise suppression factor may attain much lower values epsilon_F/2qU, because of its dependence on the applied bias U >> kT/q. The asymptotic behaviour of th…
We investigate the correlations in the current fluctuations at different terminals of metallic diffusive conductors. We start from scattering matrix expressions for the shot noise and use the Fisher-Lee relation in combination with diagram technique to evaluate the noise correlations. Of particular interest are exchange (interference) effects analogous to the Hanbury Brown--Twiss effect in optics. We find that the exchange effect exists in the ensemble averaged current correlations. Depending on the geometry, it might have the same magnitude as the mean square current fluctuations of the shot …
A theory is presented for the universal reduction of shot noise by Coulomb repulsion, which was observed in computer simulations of a disordered non-degenerate electron gas by Gonzalez et al. (cond-mat/9803372). The universality of the reduction below the uncorrelated value is explained as a feature of the high-voltage regime of space-charge limited conduction. The reduction factor depends on the dimensionality d of the density of states, being close but not quite equal to 1/d in two and three dimensions.
We derive within a time-dependent scattering formalism expressions for both the current through ac-driven nanoscale conductors and its fluctuations. The results for the time-dependent current, its time average, and, above all, the driven shot noise properties assume an explicit and serviceable form by relating the propagator to a non-Hermitian Floquet theory. The driven noise cannot be expressed in terms of transmission probabilities. The results are valid for a driving of arbitrary strength and frequency. The connection with commonly known approximation schemes such as the Tien-Gordon approac…
We present a theoretical investigation of shot-noise suppression due to long-range Coulomb interaction in nondegenerate diffusive conductors. Calculations make use of an ensemble Monte Carlo simulator self-consistently coupled with a one-dimensional Poisson solver. We analyze the noise in a lightly doped active region surrounded by two contacts acting as thermal reservoirs. By taking the doping of the injecting contacts and the applied voltage as variable parameters, the influence of elastic and inelastic scattering in the active region is investigated. The transition from ballistic to diffusi…
We investigate the current injection into a ballistic conductor under the space-charge limited regime, when the distribution function of injected carriers is an arbitrary function of energy F_c(epsilon). The analysis of the coupled kinetic and Poisson equations shows that the injected current fluctuations may be essentially suppressed by Coulomb correlations, and the suppression level is determined by the shape of F_c(epsilon). This is in contrast to the time-averaged quantities: the mean current and the spatial profiles are shown to be insensitive to F_c(epsilon) in the leading-order terms at…
We investigate the noise properties of pump currents through molecular wires and coupled quantum dots. As a model we employ a two level system that is connected to electron reservoirs and is non-adiabatically driven. Concerning the electron-electron interaction, we focus on two limits: non-interacting electrons and strong Coulomb repulsion. While the former case is treated within a Floquet scattering formalism, we derive for the latter case a master equation formalism for the computation of the current and the zero-frequency noise. For a pump operated close to internal resonances, the differen…
We have derived a general formula describing current noise in multimode ballistic channels connecting source and drain electrodes with Fermi electron gas. In particular (at $eV\gg k_{B}T$), the expression describes the nonequilibrium ''shot'' noise, which may be suppressed by both Fermi correlations and space charge screening. The general formula has been applied to an approximate model of a 2D nanoscale, ballistic MOSFET. At large negative gate voltages, when the density of electrons in the channel is small, shot noise spectral density $S_{I}(0)$ approaches the Schottky value $2eI$, where $I$…
A short summary of the drift-diffusion-Langevin formalism for calculating finite-frequency shot noise in diffusive conductors is presented. Two new results are included in this presentation. First, we arrive at a simple (but accurate) phenomenological expression for the semiclassical distribution function of electrons in the presence of electron-electron scattering. Second, it is shown that in thin samples, low-frequency shot noise may be large even if the sample length is much larger than the electron-phonon relaxation length.
We present a theoretical investigation of shot-noise properties in nondegenerate elastic diffusive conductors. Both Monte Carlo simulations and analytical approaches are used. Two new phenomena are found: (i) the display of enhanced shot noise for given energy dependences of the scattering time, and (ii) the recovery of full shot noise for asymptotic high applied bias. The first phenomenon is associated with the onset of negative differential conductivity in energy space that drives the system towards a dynamical electrical instability in excellent agreement with analytical predictions. The en…
Using the 'drift-diffusion-Langevin' equation, we have quantitatively analyzed the effects of electron energy relaxation via their interaction with phonons, generally in presence of electron-electron interaction, on shot noise in diffusive conductors. We have found that the noise power $ S_I(ω)$ (both at low and high observation frequencies $ω$) drops to half of its 'mesoscopic' value only at $β\gtrsim 100,$ where $β$ is the ratio of the sample length $L$ to the energy relaxation length $l_{% {\rm ph}}$ (the latter may be much larger then the dephasing length). It means in particular that at l…
We study the noise properties of ballistic conductors with carriers satisfying fractional exclusion statistics. To test directly the nature of exclusion statistics we found that systems under weakly degenerate conditions should be considered. Typical of these systems is that the chemical potential, $μ$ is in the thermal range $|μ|<3k_{B}T$. In these conditions the noise properties under current saturation are found to depend upon the statistical parameter $g$, displaying suppressed shot noise for $1/2\leq g\leq 1$, and enhanced shot noise for $0<g<1/2$, according to the attractive or repulsive…
We consider a current-carrying, phase-coherent multi-probe conductor to which a small tunneling contact is attached. We treat the conductor and the tunneling contact as a phase-coherent entity and use a Green's function formulation of the scattering approach. We show that the average current and the current fluctuations at the tunneling contact are determined by an effective local non-equilibrium distribution function. This function characterizes the distribution of charge-carriers (or quasi-particles) inside the conductor. It is an exact quantum-mechanical expression and contains the phase-co…
We predict the existence of an anomalous crossover between thermal and shot noise in macroscopic diffusive conductors. We first show that, besides thermal noise, these systems may also exhibit shot noise due to fluctuations of the total number of carriers in the system. Then we show that at increasing currents the crossover between the two noise behaviors is anomalous, in the sense that the low frequency current spectral density displays a region with a superlinear dependence on the current up to a cubic law. The anomaly is due to the non-trivial coupling in the presence of the long range Coul…
We study the full probability distribution of the charge transmitted through a mesoscopic diffusive conductor during a measurement time T. We have considered a semi-classical model, with an exclusion principle in a discretized single-particle phase-space. In the large T limit, numerical simulations show a universal probability distribution which agrees very well with the quantum mechanical prediction of Lee, Levitov and Yakovets [PRB {51} 4079 (1995)] for the charge counting statistics. Special attention is given to its third cumulant, including an analysis of finite size effects and of some e…
Shot noise measurements are widely used for the characterization of nonequilibrium configurations in electronic conductors. The recently introduced quantum tomography approach was implemented for the studies of electronic wavefunctions of few-electron excitations created by periodic voltage pulses in phase-coherent ballistic conductors based on the high-quality GaAs two-dimensional electron gas. Still relying on the manifestation of Fermi correlations in noise, we focus on the simpler and more general approach beneficial for the local measurements of energy distribution (ED) in electronic syst…
We present a theory of conductance and noise in generic mesoscopic conductors connected in parallel, and we demonstrate that the additivity of conductance and of shot noise arises as a sole property of the junctions connecting the two (or more) conductors in parallel. Consequences on the functionality of devices based on the Aharonov-Bohm effect are also drawn.
We investigate the charge and heat electronic noise in a generic two-terminal mesoscopic conductor in the absence of the corresponding charge and heat currents. Despite these currents being zero, shot noise is generated in the system. We show that, irrespective of the conductor's details and the specific nonequilibrium conditions, the charge shot noise never exceeds its thermal counterpart, thus establishing a general bound. Such a bound does not exist in the case of heat noise, which reveals a fundamental difference between charge and heat transport under zero-current conditions.
We calculate the low-frequency current noise for AC biased mesoscopic chaotic cavities and diffusive wires. Contrary to what happens for the admittance, the frequency dispersion is not dominated by the electric response time (the "RC" time of the circuit), but by the time that electrons need to diffuse through the structure (dwell time or diffusion time). Frequency dispersion of noise stems from fluctuations of the Fermi distribution function that preserve charge neutrality. Our predictions can be verified with present experimental technology.
We demonstrate a close relation between Coulomb effects in non-local electron transport and non-local shot noise in three-terminal metallic conductors. Provided the whole structure is normal, cross-correlations in shot noise are negative and Coulomb interaction tends to suppress both local and non-local conductances of the system. The behavior of normal-superconducting-normal structures at subgap energies is entirely different. In the tunneling limit non-local differential conductance of such systems are found to have an S-like shape and can turn negative at non-zero bias. At high transmission…
Using the 'drift-diffusion-Langevin' equation we show that, at least in one geometry, finite-frequency shot noise is of the order of the 'full' shot noise $2eI$ provided the sample is either short or long enough, $L > L_0(ω)$. Here $L_0(ω) = D'/\lph ω$ with $D'$ the effective diffusion coefficient, $\lph$ the electron-phonon energy relaxation length with energy transfer $eV$, and $ω$ the observation frequency. For example, in a typical 'zero frequency' experiment, actually performed at 10 KHz, shot noise may be large for $L$ larger than a few centimeters. At 100 MHz shot noise may be large for…
Diffusive molecules share the 1/3 shot noise suppression of quantum conductors
The University of Tokyo（东京大学）；Institute of Industrial Science, The University of Tokyo（东京大学产业科学研究所）；LAAS-CNRS（法国国家科学研究中心 LAAS 实验室）；Aix Marseille Univ（艾克斯-马赛大学）；Université de Toulon（土伦大学）；CNRS（法国国家科学研究中心）；NTT Basic Research Laboratories（NTT 基础研究实验室）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；ITODYS-CNRS（法国国家科学研究中心 ITODYS 研究所）
When subjected to electromagnetic radiation, the fluctuation of the electronic current across a quantum conductor increases. This additional noise, called photon-assisted shot noise, arises from the generation and subsequent partition of electron-hole pairs in the conductor. The physics of photon-assisted shot noise has been thoroughly investigated at microwave frequencies up to 20 GHz, and its robustness suggests that it could be extended to the Terahertz (THz) range. Here, we present measurements of the quantum shot noise generated in a graphene nanoribbon subjected to a THz radiation. Our r…
We study noise and transport in multiterminal diffusive conductors. Using a Boltzmann-Langevin equation approach we reduce the calculation of shot-noise correlators to the solution of diffusion equations. Within this approach we prove the universality of shot-noise in multiterminal diffusive conductors of arbitrary shape and dimension for purely elastic scattering as well as for hot electrons. We show that shot-noise in multiterminal conductors is a non-local quantity and that exchange effects can occur in the absence of quantum phase coherence even at zero electron temperature. It is also sho…
In the hot electron regime, electron-electron scattering strongly modifies not only the shot noise but also the full counting statistics. We employ a method based on a stochastic path integral to calculate the counting statistics of two systems in which noise in the hot electron regime has been experimentally measured. We give an analytical expression for the counting statistics of a chaotic cavity and find that heating due to electron-electron scattering renders the distribution of transmitted charge symmetric in the shot noise limit. We also discuss the frequency dispersion of the third orde…
We analyze current fluctuations in mesoscopic coherent conductors in the presence of electron-electron interactions. In a wide range of parameters we obtain explicit universal dependencies of the current noise on temperature, voltage and frequency. We demonstrate that Coulomb interaction decreases the Nyquist noise. In this case the interaction correction to the noise spectrum is governed by the combination $\sum_nT_n(T_n-1)$, where $T_n$ is the transmission of the $n$-th conducting mode. The effect of electron-electron interactions on the shot noise is more complicated. At sufficiently large …
A general formula for current noise in a two-terminal ballistic nondegenerate conductor under the action of long-range Coulomb correlations has been derived. The noise reduction factor (in respect to the uncorrelated value) is obtained for biases ranging from thermal to shot noise limits, and it is related to spatial variations in transport characteristics. The contributions of different energy groups of carriers to the noise are found, that leads us to suggest an electron energy spectroscopy experiment to probe the Coulomb correlations in ballistic conductors.
Photo-assisted transport through a mesoscopic conductor occurs when an oscillatory (AC) voltage is superposed to the constant (DC) bias which is imposed on this conductor. Of particular interest is the photo assisted shot noise, which has been investigated theoretically and experimentally for several types of samples. For DC biased conductors, a detection scheme for finite frequency noise using a dissipative resonant circuit, which is inductively coupled to the mesoscopic device, was developped recently. We argue that the detection of the finite frequency photo-assisted shot noise can be achie…
We present the most complete scattering theory for noise in noninteracting case. The exact formula for spectral density of current fluctuations at finite frequency is presented in terms of scattering matrix for a coherent quantum conductor. We show that the shot noise at finite frequency in an ideally conducting contact is finite and the spectral density of the noise has a singularity at the "Josephson" frequency $ω=eV/\hbar $, set by the voltage. We also discuss fluctuations of charge in an ideal conductor.
The quantum excitations of the collective magnetization dynamics in a ferromagnet (F) - magnons - enable spin transport without an associated charge current. This pure spin current can be transferred to electrons in an adjacent non-magnetic conductor (N). We evaluate the finite temperature noise of the magnon-mediated spin current injected into N by an adjacent F driven by a coherent microwave field. We find that the dipolar interaction leads to squeezing of the magnon modes giving them wavevector dependent non-integral spin, which directly manifests itself in the shot noise. For temperatures …
We study fluctuations of spin-polarized currents in a three-terminal spin-valve system consisting of a diffusive normal metal wire connected by tunnel junctions to three ferromagnetic terminals. Based on a spin-dependent Boltzmann-Langevin equation, we develop a semiclassical theory of charge and spin currents and the correlations of the currents fluctuations. In the three terminal system, we show that current fluctuations are strongly affected by the spin-flip scattering in the normal metal and the spin polarizations of the terminals, which may point in different directions. We analyze the de…
We report on a quantum form of electronic flicker noise in nanoscale conductors that contains valuable information on quantum transport. This noise is experimentally identified in atomic and molecular junctions, and theoretically analyzed by considering quantum interference due to fluctuating scatterers. Using conductance, shot noise, and flicker noise measurements, we show that the revealed quantum flicker noise uniquely depends on the distribution of transmission channels, a key characteristic of quantum conductors. This dependence opens the door for the application of flicker noise as a dia…
A theory of non-equilibrium (``shot'') noise and high frequency conductance in diffusive mesoscopic conductors with screening is presented. Detailed results are obtained for two simple geometries, for both large and short electron-electron scattering length $l_{ee}$, at frequencies of the order of the inverse Thouless time $1/τ_T$. The conductance and the noise are found to exhibit significant frequency dependence. For $L \ll l_{ee}$, the high-frequency ($ωτ_T \gg 1$) shot noise spectral density $S_I(ω)$ approaches a finite value between $2eI/3$ and $2eI$, depending on the screening properties…
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…
In these notes we discuss the origin of shot noise ('Schroteffekt') of vacuum tubes in detail. It will be shown that shot noise observed in vacuum tubes and first described by W. Schottky in 1918 is a purely classical phenomenon. This is in pronounced contrast to shot noise investigated in mesoscopic conductors which is due to quantum mechanical diffraction of electron waves.
We calculate current (shot) noise in a metallic diffusive conductor generated by spin imbalance in the absence of a net electric current. This situation is modeled in an idealized three-terminal setup with two biased ferromagnetic leads (F-leads) and one normal lead (N-lead). Parallel magnetization of the F-leads gives rise in spin-imbalance and finite shot noise at the N-lead. Finite spin relaxation results in an increase of the shot noise, which depends on the ratio of the length of the conductor ($L$) and the spin relaxation length ($l_s$). For $L\gg l_s$ the shot noise increases by a facto…
We show that the density matrix for a finite conductor attached to reservoirs obtained by Keldysh formalism is of MacLennan-Zubarev form. On the basis of the fact that the density matrix is the invariant part proposed by Zubarev, it is shown that Keldysh formalism may describe the irreversible processes and steady-state feature of the system. An important consequence of the MacLennan-Zubarev form of the density matrix is a generalization of the Kubo formula in a nonequilibrium case. On the basis of the result, we propose the formula of shot noise and a nonequilibrium identity between different…
Fluctuations of electric current in a spin valve consisting of a diffusive conductor connected to ferromagnetic leads and operated in the giant magnetoresistance regime are studied. It is shown that a new source of fluctuations due to spin-flip scattering enhances strongly shot noise up to a point where the Fano factor approaches the full Poissonian value.
We investigate current fluctuations in non-degenerate semiconductors, on length scales intermediate between the elastic and inelastic mean free paths. We present an exact solution of the non-linear kinetic equations in the regime of space-charge limited conduction, without resorting to the drift approximation of previous work. By including the effects of a finite voltage and carrier density in the contact region, a quantitative agreement is obtained with Monte Carlo simulations by Gonz{á}lez et al., for a model of an energy-independent elastic scattering rate. The shot-noise power $P$ is suppr…
Quantum pumping processes are accompanied by considerable quantum noise. We investigated the pumped shot noise (PSN) properties in adiabatically modulated graphene-based double-barrier structures. General expressions for adiabatically PSN in phase-coherent mesoscopic conductors are derived based on the scattering approach. It is found that comparing with the Poisson processes, the PSN is dramatically enhanced where the dc pumped current changes flow direction, which demonstrates the effect of the Klein paradox.
A theory is presented for the photodetection statistics of radiation produced by current fluctuations in a phase-coherent conductor. Deviations are found from the Poisson statistics that would result from a classical current. For detection in a narrow frequency interval, the photocount distribution has the negative-binomial form of black-body radiation if this frequency interval is less than the mean current in the conductor. When electronic localization sets in, a different type of super-Poissonian photon statistics results.
The charge fluctuations of two nearby mesoscopic conductors coupled only via the long range Coulomb force are discussed and used to find the dephasing rate which one conductor exerts on the other. The discussion is based on a formulation of the scattering approach for charge densities and the density response to a fluctuating potential. Coupling to the Poisson equation results in an electrically self-consistent description of charge fluctuations. At equilibrium the low-frequency noise power can be expressed with the help of a charge relaxation resistance (which together with the capacitance de…
In the presence of shot noise the charge on a mesoscopic conductor fluctuates. We are interested in the charge fluctuations which arise if the conductor is in the proximity of a gate to which it is coupled by long range Coulomb forces only. Specifically we consider a gate coupled to the edge of a Hall bar subject to a quantizing magnetic field which contains a quantum point contact. The gate is located away from the quantum point contact. We evaluate the charge relaxation resistance for this geometry. The charge relaxation resistance determines the current fluctuations and potential fluctuatio…
We formulate a general path integral approach which describes statistics of current fluctuations in mesoscopic coherent conductors at arbitrary frequencies and in the presence of interactions. Applying this approach to the non-interacting case, we analyze the frequency dispersion of the third cumulant of the current operator ${\cal S}_3$ at frequencies well below both the inverse charge relaxation time and the inverse electron dwell time. This dispersion turns out to be important in the frequency range comparable to applied voltages. For comparatively transparent conductors it may lead to the …
We investigate the shot noise of nonequilibrium carriers injected into a ballistic conductor and interacting via long-range Coulomb forces. Coulomb interactions are shown to act as an energy analyzer of the profile of injected electrons by means of the fluctuations of the potential barrier at the emitter contact. We show that the details in the energy profile can be extracted from shot-noise measurements in the Coulomb interaction regime, but cannot be obtained from time-averaged quantities or shot-noise measurements in the absence of interactions.
