Charge Transfer Statistics Research Articles

Stub model for charge transport through a quantum dot connected to noncollinear ferromagnets

A stub model is introduced to describe the charge transport properties of a system consisting of an arbitrary number of noncollinear ferromagnetic or normal reservoirs coupled nonideally to a normal metal chaotic cavity. We characterize the contacts by a reduced set of parameters which can be used to express the average value of any charge-transfer cumulant. Explicit expressions of this set of parameters are given for the cases of ideal ballistic contacts and tunnel junctions. The average conductance and shot-noise power of a two terminal FNF device with noncollinear ferromagnetic reservoirs are calculated analytically via an extended diagrammatic method which allows for the importation of all diagrams of the corresponding NNN system. We observe that the Fano factor exhibits a transition between monotonic and nonmonotonic behaviors as a function of the reservoir's relative magnetization angle. A diagram of this transition in the plane of the polarization parameters is shown. With straightforward modifications, our scheme paves the way for efficient calculations of the average value of an arbitrary cumulant of the charge-transfer statistics in hybrid devices along with its quantum corrections.

Charge transfer statistics in symmetric fractional edge-state Mach-Zehnder interferometer

We have studied the zero-temperature statistics of charge transfer between the two edges of Quantum Hall liquids with filling factors $\nu_{0,1}=1/(2 m_{0,1}+1)$ forming Mach-Zehnder interferometer. The known Bethe ansatz solution for symmetric interferometer is used to obtain the cumulant-generating function of charge at constant voltage $V$ between the edges. Its low-$V$ behavior can be interpreted in terms of electron tunneling, while its large-$V$ asymptotics reproduces the $m$-state dynamics ($m\equiv 1+m_{0}+m_{1}$) of quasiparticles with fractional (for $m>1$) charge and statistics. We also analyze the transition region between electrons and quasiparticles.

Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedom

We analyze the full counting statistics of a single-site quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electron-phonon coupling. We identify explicitly the contributions due to quasielastic and inelastic transport processes in the cumulant generating function and discuss their influence on the transport properties of the dot. We find that in the low-energy sector, i.e., for bias voltage and phonon frequency much smaller than the dot-electrode contact transparency, the inelastic term causes a sign change in the shot noise correction at certain universal values of the transmission. Furthermore, we show that when the correction to the current due to inelastic processes vanishes, all the odd order cumulants vanish as well.

Elementary charge-transfer processes in mesoscopic conductors

We determine charge-transfer statistics in a quantum conductor driven by a time-dependent voltage and identify the elementary transport processes. At zero temperature unidirectional and bidirectional single-charge transfers occur. The unidirectional processes involve electrons injected from the source terminal due to excess dc bias voltage. The bidirectional processes involve electron-hole pairs created by time-dependent voltage bias. This interpretation is further supported by the charge-transfer statistics in a multiterminal beam-splitter geometry in which injected electrons and holes can be partitioned into different outgoing terminals. The probabilities of elementary processes can be probed by noise measurements: the unidirectional processes set the dc noise level, while bidirectional ones give rise to the excess noise. For ac voltage drive, the noise oscillates with increasing the driving amplitude. The decomposition of the noise into the contributions of elementary processes reveals the origin of these oscillations: the number of electron-hole pairs generated per cycle increases with increasing the amplitude. The decomposition of the noise into elementary processes is studied for different time-dependent voltages. The method we use is also suitable for systematic calculation of higher-order current correlators at finite temperature. We obtain current noise power and the third cumulant in the presence of time-dependent voltage drive. The charge-transfer statistics at finite temperature can be interpreted in terms of multiple-charge transfers with probabilities which depend on energy and temperature.

Statistics of charge transfer through impurities in strongly correlated 1D metals*

AbstractWe review recent advances in the field of full counting statistics (FCS) of charge transfer through impurities imbedded into strongly correlated one‐dimensional metallic systems, modelled by Tomonaga‐Luttinger liquids (TLLs). We concentrate on the exact analytic solutions for the cumulant generating function, which became available recently and apply these methods in order to obtain the FCS of a non‐trivial contact between two crossed TLL.

Statistics of charge transfer through impurities in strongly correlated 1D metals

We study the counting statistics of charge transport in the Anderson impurity model (AIM) employing both Keldysh perturbation theory in a Fermi liquid picture and the Bethe ansatz. In the Fermi liquid approach, the object of our principal interest is the generating function for the cumulants of the charge current distribution. We derive an exact analytic formula relating the full counting statistic (FCS) generating function to the self-energy of the system in the presence of a measuring field. We first check that our approach reproduces correctly known results in simple limits, like the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM perturbatively in the Coulomb interaction. By comparing this perturbative analysis with a strong coupling expansion, we arrive at a conjecture for an expression for the FCS generating function at 𝒪(V3) (V is the voltage across the impurity) valid at all orders in the interaction. In the second part of the article, we examine a Bethe ansatz analysis of the current noise for the AIM. Unlike the Fermi liquid approach, here the goal is to obtain qualitative, not quantitative, results for a wider range of voltages both in and out of a magnetic field. Particularly notable are finite field results showing a double peaked structure in the current noise for voltages satisfying eV ∼ μB H. This double peaked structure is the “smoking gun” of Kondo physics in the current noise and is directly analogous to the single peak structure predicted in the differential conductance of the AIM.

Circuit theory and full counting statistics of charge transfer through mesoscopic systems: A random-matrix approach

We introduce a random-matrix description of full counting statistics of charge transfer through a quantum mesoscopic system at finite temperature in the presence two nonideal contacts. Using the exact map between random-matrix theory and the supersymmetric nonlinear $\ensuremath{\sigma}$ model, we demonstrate, via explicit calculations, that the saddle-point equation, derived by applying the variational principle to the supersymmetric action, can be cast in the form of the two-terminal version of Nazarov's circuit theory, thus giving it the status of a controlled approximation. For the case in which the mesoscopic system is a quantum dot at zero temperature, this circuit theory has recently been shown [A. L. R. Barbosa and A. M. S. Mac\^edo, Phys. Rev. B 71, 235307 (2005)] to reproduce exactly the asymptotic semiclassical limit of the Poisson kernel in perfect agreement with a diagrammatic approach for averaging over the unitary group. We report applications of our formalism to the description of charge transfer through a quantum dot, a quantum chain, and a quantum wire. We also discuss the role of different symmetry classes (orthogonal, unitary, and symplectic) and show how to use known exact connections between the supersymmetric nonlinear $\ensuremath{\sigma}$ model and random scattering matrix theories to perform both perturbative and nonperturbative calculations. We believe that our results will help unify the various approaches being currently used in mesoscopic physics of hybrid devices within a single physically sound and mathematically rigorous theoretical scheme.

Hanbury Brown–Twiss Correlations and Noise in the Charge Transfer Statistics through a Multiterminal Kondo Dot

We analyze the charge transfer statistics through a quantum dot in the Kondo regime, when coupled to an arbitrary number of terminals N. Special attention is paid to current cross correlations between concurring transport channels, which show distinct Hanbury Brown-Twiss antibunching for N>2 reflecting the fermionic nature of charge carriers. While this effect weakens as one moves away from the Kondo fixed point, a new type of correlations between nonconcurring channels emerges which are due entirely to the virtual polarization of the Kondo singlet. As these are not obscured by the background from fixed-point correlations they provide a promising means for extracting information on the parameters of the underlying Fermi-liquid model from the experimental data.

Frequency-dependent current correlation functions from scattering theory

We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal with arbitrary correlation functions. Our formalism might be useful in view of recent developments in full counting statistics of charge transfer, where detecting schemes have been proposed for measurement of frequency dependent spectra of higher moments. Some of these schemes are different from the well-known fictitious spin-detector and therefore generally involve calculation of non-Keldysh-contour-ordered correlation functions. As an illustration of our method we consider various third order correlation functions of current, including the usual third cumulant of current statistics. We investigate the frequency dependence of these correlation functions explicitly in the case of energy-independent scattering. The results can easily be generalized to the calculation of arbitrary n-th order correlation functions, or to include the effect of interactions.

Full Counting Statistics of Chiral Luttinger Liquids with Impurities

We study the statistics of charge transfer through an impurity in a chiral Luttinger liquid (realized experimentally as a quantum point contact in a fractional quantum Hall edge state device). Taking advantage of the integrability we present a procedure for obtaining the cumulant generating function of the probability distribution to transfer a fixed amount of charge through the constriction. Using this approach we analyze in detail the behavior of the third cumulant C3 as a function of applied voltage, temperature, and barrier height. We predict that C3 can be used to measure the fractional charge at temperatures, which are several orders of magnitude higher than those needed to extract the fractional charge from the measurement of the second cumulant. Moreover, we identify the component of C3, which carries the information about the fractional charge.

Statistics of charge transfer in a tunnel junction coupled to an oscillator

The charge transfer statistics of a tunnel junction coupled to a quantum object is studied using the charge projection technique. The joint dynamics of the quantum object and the number of charges transferred through the junction is described by the charge specific density matrix. The method allows evaluating the joint probability distribution of the state of the quantum object and the charge state of the junction.The statistical properties of the junction current are derived from the charge transfer statistics using the master equation for the charge specific density matrix. The theory is applied to a nanoelectromechanical system, and the influence on the average current and the current noise of the junction is obtained for coupling to a harmonic oscillator.

Full counting statistics of Cooper pair shuttling

The Cooper pair shuttle is a simple model system that combines features of coherent and incoherent transport. We evaluate the full counting statistics (FCS) of charge transfer via the shuttle in the incoherent regime. We describe two limiting cases when the FCS allows for classical interpretation. Generally, the classical interpretation fails, yielding negative and imaginary ``probabilities.'' This signals that superconducting coherence survives even in the incoherent regime. We evaluate the current noise in some detail.

Dc transport in superconducting point contacts: A full-counting-statistics view

We present a comprehensive theoretical analysis of the dc transport properties of superconducting point contacts. We determine the full counting statistics for these junctions, which allows us to calculate not only the current or the noise, but all the cumulants of the current distribution. We show how the knowledge of the statistics of charge transfer provides an unprecedented level of understanding of the different transport properties for a great variety of situations. We illustrate our results with the analysis of junctions between BCS superconductors, contacts between superconductors with pair-breaking mechanisms and short diffusive bridges. We also discuss the temperature dependence of the different cumulants and show the differences with normal contacts.

Full counting statistics of a charge shuttle

We study the charge transfer in a small grain oscillating between two leads. Coulomb blockade restricts the charge fluctuations in such a way that only zero or one additional electrons can sit on the grain. The system thus acts as a charge shuttle. We obtain the full counting statistics of charge transfer and discuss its behavior. For large oscillation amplitude the probability of transferring electrons per cycle is strongly peaked around one. The peak is asymmetric since its form is controlled by different parameters for and . Under certain conditions the systems behaves as if the effective charge is of the elementary one. Knowledge of the counting statistics gives a new insight on the mechanism of charge transfer.

Shot noise of spin-polarized electrons

The shot noise of spin polarized electrons is shown to be generically dependent upon spin-flip processes. Such a situation represents perhaps the simplest instance where the two-particle character of current fluctuations out of equilibrium is explicit, leading to trinomial statistics of charge transfer in a single channel model. We calculate the effect of spin-orbit coupling, magnetic impurities, and precession in an external magnetic field on the noise in the experimentally relevant cases of diffusive wires and lateral semiconductor dots, finding dramatic enhancements of the Fano factor. The possibility of using the shot noise to measure the spin-relaxation time in an open mesoscopic system is raised.

Full Counting Statistics of Multiple Andreev Reflection

We derive the full counting statistics of charge transfer through a voltage biased superconducting junction. We find that, for measurement times much longer than the inverse Josephson frequency, the counting statistics describes a correlated transfer of quanta of multiple electron charges, each quantum associated with the transfer of a single quasiparticle. An expression for the counting statistics in terms of the quasiparticle scattering amplitudes is derived.

Interaction Effects on Counting Statistics and the Transmission Distribution

We investigate the effect of weak interactions on the full counting statistics of charge transfer through an arbitrary mesoscopic conductor. We show that the main effect can be incorporated into an energy dependence of the transmission eigenvalues and study this dependence in a nonperturbative approach. An unexpected result is that all mesoscopic conductors behave at low energies such as either a single or a double tunnel junction, which divides them into two broad classes.

Full counting statistics of charge transfer in Coulomb blockade systems

Full counting statistics (FCS) of charge transfer in mesoscopic systems has recently become a subject of significant interest, since it proves to reveal an important information about the system which can be hardly assessed by other means. While the previous research mostly addressed the FCS of noninteracting systems, the present paper deals with the FCS in the limit of strong interaction. In this Coulomb blockade limit the electron dynamics is known to be governed by a master equation. We develop a general scheme to evaluate the FCS in such case, this being the main result of the work presented. We illustrate the scheme, by applying it to concrete systems. For generic case of a single resonant level we establish the equivalence of scattering and master equation approach to FCS. Further we study a single Coulomb blockade island with two and three leads attached and compare the FCS in this case with our recent results concerning an open dot either with two and three terminals. We demonstrate that Coulomb interaction suppresses the relative probabilities of large current fluctuations.

Superconductive proximity effect in interacting disordered conductors

We present a general theory of the superconductive proximity effect in disordered normal--superconducting (N-S) structures, based on the recently developed Keldysh action approach. In the case of the absence of interaction in the normal conductor we reproduce known results for the Andreev conductance G_A at arbitrary relation between the interface resistance R_T and the diffusive resistance R_D. In two-dimensional N-S systems, electron-electron interaction in the Cooper channel of normal conductor is shown to strongly affect the value of G_A as well as its dependence on temperature, voltage and magnetic field. In particular, an unusual maximum of G_A as a function of temperature and/or magnetic field is predicted for some range of parameters R_D and R_T. The Keldysh action approach makes it possible to calculate the full statistics of charge transfer in such structures. As an application of this method, we calculate the noise power of an N-S contact as a function of voltage, temperature, magnetic field and frequency for arbitrary Cooper repulsion in the normal metal and arbitrary values of the ratio R_D/R_T.