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

Abstract

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...

Universality of non-equilibrium fluctuations in strongly correlated quantum liquids

“…This two-particle scattering is characterized by an effective charge e * larger than e (electron charge). This value, closely related to the Wilson ratio, is universal for the Fermi liquid in the Kondo regime as it depends only on the symmetry group of the system [13][14][15] . Although some aspects of Kondo-associated noise have been reported 8,16,17 , a rigorous, selfconsistent treatment in a regime where universal results apply is at the core of the present work.…”

“…, an enhancement of the current fluctuations is detected out of equilibrium and perfectly explained by an e ective charge induced by the residual interaction between quasi-particles 8, [10][11][12][13][14][15][16][17] . Moreover, an as-yet-unknown scaling law for the e ective charge is discovered, suggesting a new non-equilibrium universality.…”

“…A remarkable prediction of the non-equilibrium Fermi liquid theory is that the residual interaction between quasi-particles creates an additional scattering of two quasi-particles which enhances the noise (see the lower panel of Fig. 1a) 10,[12][13][14][15] . This two-particle scattering is characterized by an effective charge e * larger than e (electron charge).…”

Noisy Kondo impurities

“…Presently available FL theories [21][22][23][24] provide the correct description only at very low energies and give unphysical results for the temperature and bias range of our experiment. On the other hand, the SBMF theory turns out be more robust up to the energy range of our experiment 20 .…”

Quantum Criticality and Formation of a Singular Fermi Liquid in the Attractive SU(N>2) Anderson Model

“…The SU(N ) variant of the Anderson model has also attracted a lot of attention recently due to its relevance in various nanostructures [13,43,44] and in ultracold settings [45]. Its behavior has been extensively analyzed in the repulsive regime [46][47][48][49][50][51], where it displays properties analogous to the SU(2) case: it exhibits mixed valence fluctuations at energies ε ≈ U (k − N −1 2 ) with k = 0, . .…”