Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0411019 · Physical Review Letters

Full Counting Statistics for the Kondo Dot

A. Komnik, Alexander O. Gogolin

Published Jun 2, 2005• 45 citations
arXivHTMLPDF

Abstract

The generating function for the cumulants of charge current distribution is calculated for two generalized Majorana resonant level models: the Kondo dot at the Toulouse point and the resonant level embedded in a Luttinger liquid with the interaction parameter g=1/2. We find that the low-temperature nonequilibrium transport in the Kondo case occurs via tunneling of physical electrons as well as by coherent transmission of electron pairs. We calculate the third cumulant ("skewness") explicitly and analyze it for different couplings, temperatures, and magnetic fields. For the g=1/2 setup the statistics simplifies and is given by a modified version of the Levitov-Lesovik formula.

DOI
10.1103/physrevlett.94.216601

Related papers

Towards full counting statistics for the Anderson impurity model

Alexander O. Gogolin, A. Komnik

We analyze the full counting statistics (FCS) of the charge transport through the Anderson impurity model (AIM) and similar systems with a single conducting channel. The object of principal interest is the generating function for the cumulants of charge current distribution. We derive an exact analytic formula relating the FCS generating function to the self energy of the system in the presence of the measuring field. We first check that our approach reproduces correctly known results in simple limits, such as the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM both perturbatively in the Coulomb interaction and in the Kondo regime at the Toulouse point (we also study a related model of a spinless single-site quantum dot coupled to two half-infinite metallic leads in the Luttinger liquid phase at a special interaction strength). At zero temperature the FCS turns out to be binomial for small voltages. For the generic case of arbitrary energy scales the FCS is shown to be captured very well by generalizations of the Levitov-Lesovik type formula. Surprisingly, the FCS for the AIM indicates a presence of coherent electron pair tunnelling in addition to conventional single-particle processes. By means of perturbative expansions around the Toulouse point we succeeded in showing the universality of the binomial FCS at zero temperature in linear response. Based on our general formula for the FCS we then argue for a more general binomial theorem stating that the linear response zero-temperature FCS for any interacting single-channel setup is always binomial.

arXiv:cond-mat/0512174•Physical Review B•May 1, 2006•136 citations

Transient dynamics of the nonequilibrium Majorana resonant level model

A. Komnik

The Majorana resonant level model describes the universality class of the two-channel/terminal Kondo model at the Toulouse point as well as of a resonant level between two half-infinite Tomonaga-Luttinger liquids. We analyze the time evolution of the electric current and of the population function after an instantaneous switching on of the tunneling coupling. We find that the only time scale, which governs the relaxation of the initial dot preparation is the inverse contact transparency $\ensuremath{\Gamma}$, whatever the dot offset energy $\ensuremath{\Delta}$, applied bias voltage, or temperature. The voltage alone determines the superimposed oscillatory behavior of the observables for weak detuning $|\ensuremath{\Delta}|<\ensuremath{\Gamma}/2$. In the opposite case of strong detuning $|\ensuremath{\Delta}|>\ensuremath{\Gamma}/2$ a beating pattern emerges. For the current the finite temperature plays the similar role as the hybridization. The dot population function dynamics approaches that of a resonant $(\ensuremath{\Delta}=0)$ setup upon increasing the voltage or/and temperature.

arXiv:0903.3344•Physical Review B•Jun 1, 2009•28 citations

Current statistics of correlated charge tunnelling through an impurity in a 1D wire

Alexander Herzog, Ulrich Weiß

We review recent advances in the full counting statistics of a generic transport model of a quantum Brownian particle. The model applies to charge transfer through an impurity embedded in a Luttinger liquid environment, to a coherent one-channel conductor in a resistive environment, and to a resistively shunted Josephson junction device. We derive analytic expressions for the cumulant generating function (CGF) at two particular values of the Luttinger parameter which are related by self-duality. We determine the self-duality relations between the CGFs and between the cumulants.

New Journal of Physics•Apr 30, 2008•4 citations

Numerically exact full counting statistics of the nonequilibrium Anderson impurity model

Michael L. Ridley, Viveka Nand Singh, Emanuel Gull +1 more

The time-dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron-electron interactions on the time-dependent charge cumulants, first-passage time distributions, and $n$-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single-electron transfer events.

arXiv:1801.05010•Physical review. B./Physical review. B•Mar 6, 2018•65 citations

Full counting statistics for SU( N ) impurity Anderson model

Rui Sakano, Akira Oguri, Takeo Kato +1 more

We analyze the full counting statistics of the multiorbital Kondo effect in a quantum dot with SU($N$) symmetry in the framework of renormalized perturbation theory. The current probability distribution function is calculated for an arbitrary dot-site Coulomb repulsion $U$ in the particle-hole-symmetric case. The resulting cumulant up to the leading nonlinear term of applied bias voltages indicates two types of electron transfer, respectively carrying charge $e$ and $2e$, with different $N$ dependences. The cross correlation between different orbital currents shows exponential enhancement with respect to $U$, which directly addresses the formation of the orbital-singlet state.

arXiv:1105.1478•Physical Review B•Jun 8, 2011•26 citations

Resonant Tunneling between Luttinger Liquids: A Solvable Case

A. Komnik, Alexander O. Gogolin

We discuss the conductance of a Luttinger liquid interrupted by a quantum dot containing a single resonant level. Using bosonization and refermionization methods, we find a mapping to a Kondo-type problem which possesses a nontrivial Toulouse-type solvable point. At this point, we obtain an analytic expression for the nonlinear current-voltage characteristics and analyze the differential conductance and the width of the resonance peak as functions of bias and gate voltages, temperature, and barrier asymmetry. We also determine the exact scaling function for the linear conductance.

arXiv:cond-mat/0211474•Physical Review Letters•Jun 19, 2003•56 citations
The generating function for the cumulants of charge current distribution is calculated for two generalized Majorana resonant level models: the Kondo dot at the Toulouse point and the resonant level embedded in a Luttinger liquid with the interaction parameter g=1/2. We find that the low-temperature nonequilibrium transport in the Kondo case occurs via tunneling of physical electrons as well as by coherent transmission of electron pairs. We calculate the third cumulant ("skewness") explicitly and analyze it for different couplings, temperatures, and magnetic fields. For the g=1/2 setup the statistics simplifies and is given by a modified version of the Levitov-Lesovik formula.
We analyze the full counting statistics (FCS) of the charge transport through the Anderson impurity model (AIM) and similar systems with a single conducting channel. The object of principal interest is the generating function for the cumulants of charge current distribution. We derive an exact analytic formula relating the FCS generating function to the self energy of the system in the presence of the measuring field. We first check that our approach reproduces correctly known results in simple limits, such as the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM both perturbatively in the Coulomb interaction and in the Kondo regime at the Toulouse point (we also study a related model of a spinless single-site quantum dot coupled to two half-infinite metallic leads in the Luttinger liquid phase at a special interaction strength). At zero temperature the FCS turns out to be binomial for small voltages. For the generic case of arbitrary energy scales the FCS is shown to be captured very well by generalizations of the Levitov-Lesovik type formula. Surprisingly, the FCS for the AIM indicates a presence of coherent electron pair tunnelling in addition to conventional single-particle processes. By means of perturbative expansions around the Toulouse point we succeeded in showing the universality of the binomial FCS at zero temperature in linear response. Based on our general formula for the FCS we then argue for a more general binomial theorem stating that the linear response zero-temperature FCS for any interacting single-channel setup is always binomial.
The Majorana resonant level model describes the universality class of the two-channel/terminal Kondo model at the Toulouse point as well as of a resonant level between two half-infinite Tomonaga-Luttinger liquids. We analyze the time evolution of the electric current and of the population function after an instantaneous switching on of the tunneling coupling. We find that the only time scale, which governs the relaxation of the initial dot preparation is the inverse contact transparency $\ensuremath{\Gamma}$, whatever the dot offset energy $\ensuremath{\Delta}$, applied bias voltage, or temperature. The voltage alone determines the superimposed oscillatory behavior of the observables for weak detuning $|\ensuremath{\Delta}|<\ensuremath{\Gamma}/2$. In the opposite case of strong detuning $|\ensuremath{\Delta}|>\ensuremath{\Gamma}/2$ a beating pattern emerges. For the current the finite temperature plays the similar role as the hybridization. The dot population function dynamics approaches that of a resonant $(\ensuremath{\Delta}=0)$ setup upon increasing the voltage or/and temperature.
We review recent advances in the full counting statistics of a generic transport model of a quantum Brownian particle. The model applies to charge transfer through an impurity embedded in a Luttinger liquid environment, to a coherent one-channel conductor in a resistive environment, and to a resistively shunted Josephson junction device. We derive analytic expressions for the cumulant generating function (CGF) at two particular values of the Luttinger parameter which are related by self-duality. We determine the self-duality relations between the CGFs and between the cumulants.
The time-dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron-electron interactions on the time-dependent charge cumulants, first-passage time distributions, and nnn-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single-electron transfer events.
We analyze the full counting statistics of the multiorbital Kondo effect in a quantum dot with SU(NNN) symmetry in the framework of renormalized perturbation theory. The current probability distribution function is calculated for an arbitrary dot-site Coulomb repulsion UUU in the particle-hole-symmetric case. The resulting cumulant up to the leading nonlinear term of applied bias voltages indicates two types of electron transfer, respectively carrying charge eee and 2e2e2e, with different NNN dependences. The cross correlation between different orbital currents shows exponential enhancement with respect to UUU, which directly addresses the formation of the orbital-singlet state.
We discuss the conductance of a Luttinger liquid interrupted by a quantum dot containing a single resonant level. Using bosonization and refermionization methods, we find a mapping to a Kondo-type problem which possesses a nontrivial Toulouse-type solvable point. At this point, we obtain an analytic expression for the nonlinear current-voltage characteristics and analyze the differential conductance and the width of the resonance peak as functions of bias and gate voltages, temperature, and barrier asymmetry. We also determine the exact scaling function for the linear conductance.