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arXiv:1111.6231 · Physical Review B

Full counting statistics of Kondo-type tunneling in a quantum dot: Fluctuation effects of the slave-boson field

Bing Dong, Guo-Hui Ding, X. L. Lei

Published Dec 1, 2011• 3 citations
arXivHTMLPDF

Abstract

We study the full counting statistics (FCS) of electron tunneling through a multiterminal quantum dot in the Kondo regime within the slave-boson mean-field theory. By employing the method of Gogolin and Komnik for calculating the FCS generating function based on the nonequilibrium Green's function [Phys. Rev. B 73, 195301 (2006)], we obtain the counting field $\ensuremath{\lambda}$-dependent self-consistent equations for the mean values of the slave-boson fields and the explicit expression for the derivative of the adiabatic potential of the system with respect to the counting fields. Performing a perturbative expansion to the first order of $\ensuremath{\lambda}$, we find an extra contribution to the shot noise due to the bias-induced Bose field fluctuation, and then confirm that the nonequilibrium particle number fluctuation plays an important role in the current noise of the Kondo dot: enhancement of the current autocorrelation and a positive current cross-correlation.

DOI
10.1103/physrevb.84.235408

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We study the full counting statistics (FCS) of electron tunneling through a multiterminal quantum dot in the Kondo regime within the slave-boson mean-field theory. By employing the method of Gogolin and Komnik for calculating the FCS generating function based on the nonequilibrium Green's function [Phys. Rev. B 73, 195301 (2006)], we obtain the counting field \ensuremathλ\ensuremath{\lambda}\ensuremathλ-dependent self-consistent equations for the mean values of the slave-boson fields and the explicit expression for the derivative of the adiabatic potential of the system with respect to the counting fields. Performing a perturbative expansion to the first order of \ensuremathλ\ensuremath{\lambda}\ensuremathλ, we find an extra contribution to the shot noise due to the bias-induced Bose field fluctuation, and then confirm that the nonequilibrium particle number fluctuation plays an important role in the current noise of the Kondo dot: enhancement of the current autocorrelation and a positive current cross-correlation.
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.
The noise of quantum dots in the ac Kondo regime is investigated by means of slave-boson mean-field method and Floquet theorem. A nonadiabatical formula for the noise power is obtained in the Floquet-Green formalism to take into account interaction effects. We show that, as a manifestation of many-particle correlations, the singularities of photon-assisted noise for noninteracting dots cannot survive in the ac Kondo regime. These peculiar features of the photon-assisted noise thus provide us an alternative probe to distinguish the noninteracting resonant tunneling and the many-particle Kondo resonance.
We apply a recently developed 1/( N − 1) expansion to the full-counting statistics for the N -fold degenerate Anderson impurity model in the Kondo regime. This approach is based on the perturbation theory in the Coulomb interaction U and is different from the conventional large- N theories, such as the usual 1/ N expansion and non-crossing approximation. We have confirmed that the calculations carried out up to order 1/( N − 1) 2 agree closely with those of the numerical renormalization group at N = 4, where the degeneracy is still not so large. This ensures the applicability of our approach for N ≥ 4. We present the results of the cumulants of the probability distribution function for a nonequilibrium current through a quantum dot in the particle-hole symmetric case.
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.
We demonstrate that the probability distribution of the net number of electrons passing through a quantum system in a junction obeys a steady-state fluctuation theorem (FT) which can be tested experimentally by the full counting statistics (FCS) of electrons crossing the lead-system interface. The FCS is calculated using a many-body quantum master equation combined with a Liouville space generating function formalism. For a model of two coupled quantum dots, we show that the FT becomes valid for long binning times, and provide an estimate for the finite-time deviations. The Mandel (or Fano) parameter associated with the incoming or outgoing electron transfers shows sub-Poissonian (antibunching) statistics.
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.