Towards full counting statistics for the Anderson impurity model

Gogolin, Alexander O.; Komnik, A.

doi:10.1103/physrevb.73.195301

Cited by 136 publications

(201 citation statements)

References 48 publications

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“…Noise can probe out of equilibrium properties of the model. This has not been much investigated so far since only a few theoretical methods [9,10,11] apply to the out of equilibrium situation in comparison with the equilibrium case. In particular, the shot-noise at low temperature could provide information on the statistics of charge transfer.…”

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confidence: 99%

Current Noise through a Kondo Quantum Dot in aSU(N)Fermi Liquid State

Mora¹,

Leyronas²,

Regnault³

2008

Phys. Rev. Lett.

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The current noise through a mesoscopic quantum dot is calculated and analyzed in the Fermi liquid regime of the SU(N) Kondo model. Results connect the Johnson-Nyquist noise to the shot noise for an arbitrary ratio of voltage and temperature, and show that temperature corrections are sizeable in usual experiments. For the experimentally relevant SU(4) case, quasiparticle interactions are shown to increase the shot noise. PACS numbers: 72.70.+m, 72.15.Qm, 71.10.Ay, 73.63.Fg, 73.63.Kv The Kondo effect [1], i.e. the screening of a local spin by coupling to conduction electrons, is a paradigm for strongly correlated systems as it exhibits sophisticated many-body correlations with a quite simple model. Its tunable realization in mesoscopic quantum dots, semiconductors, or carbon nanotubes, has triggered a renewed interest [2] in Kondo physics probed by transport measurements. In the ground state, the dot spin is screened by a cloud of conduction electrons and forms a singlet. Low energy properties of remaining electrons are described by a local Fermi liquid theory [3]. In this theory, electrons are scattered elastically by the singlet in a similar way as by a resonant level. Electrons also interact through polarization of the spin singlet. The ratio of elastic to inelastic scattering is fixed by universality, i.e. the Kondo temperature T K is the only scale that governs low energy properties of the model. This description applies to SU(2) symmetry but also more generally to SU(N). In that case, both the spin and orbital degrees of freedom are screened by delocalized electrons in the reservoirs. In particular, the SU(4) case has become recently the subject of extensive investigation. Various experimental settings have been proposed [4,5] and its realization has been reported already in vertical quantum dots [6] and carbon nanotubes [7].A promising experimental tool to study Kondo physics is current noise measurement. These experiments are technically challenging in the Kondo regime notwithstanding recent progresses [8]. Noise can probe out of equilibrium properties of the model. This has not been much investigated so far since only a few theoretical methods [9,10,11] apply to the out of equilibrium situation in comparison with the equilibrium case. In particular, the shot-noise at low temperature could provide information on the statistics of charge transfer. Interestingly, a picture has emerged recently [12,13] for the SU(2) Kondo effect at low energy where scattering events of two electrons lead to an effective charge of 5/3 e in the backscattering current. This emphasizes the strong role of interactions for charge transfer even in the vicinity of a Fermi liquid fixed point.The heating due to voltage polarization and the decoupling of phonons to electrons at low energy implies that the temperature of electrons is never really small in practical situations. It is therefore highly desirable to have a theory that holds at finite temperature. The purpose of this letter is to provide a general analysis for the zero-fre...

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confidence: 99%

Current Noise through a Kondo Quantum Dot in aSU(N)Fermi Liquid State

Mora¹,

Leyronas²,

Regnault³

2008

Phys. Rev. Lett.

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“…(28), the contour C is from 0 to t M and back, while that in Eq. (29) is on the Keldysh contour K, that is, from −∞ to t M and back to take into account of adiabatic switch on, replacing ρ(0) by ρ(−∞).…”

Section: B the Expression For Hxmentioning

confidence: 99%

“…In the electronic literature the distribution P (Q L ) of the charge Q L , flowing from the left lead to the junction part, was answered by calculating the corresponding CGF, Z(ξ) = e iξQL , and is given by the celebrated Levitov-Lesovik formula [18][19][20]. This methodology is also known as the full counting statistics [21][22][23][24][25][26][27][28][29][30] in the field of electronic transport. Experimentally the electron counting statistics has been measured in quantum-dot systems [31,32].…”

Section: Introductionmentioning

confidence: 99%

Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems

Agarwalla

Wang

2012

Phys. Rev. E

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We study the statistics of heat transferred in a given time interval tM , through a finite harmonic chain, called the center (C), which is connected with two heat baths, the left (L) and the right (R), that are maintained at two different temperatures. The center atoms are driven by an external time-dependent force. We calculate the cumulant generating function (CGF) for the heat transferred out of the left lead, QL, based on two-time measurement concept and using nonequilibrium Green's function (NEGF) method. The CGF can be concisely expressed in terms of Green's functions of the center and an argument-shifted self-energy of the lead. The expression of CGF is valid in both transient and steady state regimes. We consider three different initial conditions for the density operator and show numerically, for one-dimensional (1D) linear chains, how transient behavior differs from each other but finally approaches the same steady state, independent of the initial distributions. We also derive the CGF for the joint probability distribution P (QL, QR), and discuss the correlations between QL and QR. We calculate the total entropy flow to the reservoirs. In the steady state we explicitly show that the CGF obeys steady state fluctuation theorem (SSFT). Classical results are obtained by taking → 0. The method is also applied to the counting of the electron number and electron energy, for which the associated self-energy is obtained from the usual lead self-energy by multiplying a phase or shifting the contour time, respectively.

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“…While the quantum FCS of particle currents (e.g. electrons) in junctions is well developed [67][68][69][70][71][72][73][74][75][76][77][78] , that of energy was mostly limited to the quantum master equation (QME) approach 71,[79][80][81][82][83][84] with its known limitations 76,85,86 . By numerically calculating efficiency fluctuations for a set of simple models and comparing our NEGF results with those obtained using a QME approach, we identify the regimes where efficiency fluctuations display truly quantum features.…”

Section: Introductionmentioning

confidence: 99%

Efficiency fluctuations in quantum thermoelectric devices

2015

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We present a method, based on charaterizing efficiency fluctuations, to asses the performance of nanoscale thermoelectric junctions. This method accounts for effects typically arising in small junctions, namely, stochasticity in the junction's performance, quantum effects, and nonequilibrium features preventing a linear response analysis. It is based on a nonequilibrium Green's function (NEGF) approach, which we use to derive the full counting statistics (FCS) for heat and work, and which in turn allows us to calculate the statistical properties of efficiency fluctuations. We simulate the latter for a variety of simple models where our method is exact. By analyzing the discrepancies with the semi-classical prediction of a quantum master equation (QME) approach, we emphasize the quantum nature of efficiency fluctuations for realistic junction parameters. We finally propose an approximate Gaussian method to express efficiency fluctuations in terms of nonequilibrium currents and noises which are experimentally measurable in molecular junctions.

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Towards full counting statistics for the Anderson impurity model

Cited by 136 publications

References 48 publications

Current Noise through a Kondo Quantum Dot in aSU(N)Fermi Liquid State

Current Noise through a Kondo Quantum Dot in aSU(N)Fermi Liquid State

Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems

Efficiency fluctuations in quantum thermoelectric devices

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