The Kondo Lattice Model

In this lecture, we review the experimental situation of heavy Fermions with emphasis on the existence of a quantum phase transition (QPT) and related non-Fermi liquid (NFL) effects. We overview the Kondo lattice model (KLM) which is believed to describe the physics of those systems. After recalling the existing theories based on large-N expansion and various N=2 schemes, we present two alternative approaches: (i) a spin fluctuation-Kondo functional integral approach treating the spin-fluctuation and Kondo effects on an equal footing, and (ii) a supersymmetric theory enlarging the usual fermionic representation of the spin into a mixed fermionic-bosonic representation in order to describe the spin degrees of freedom as well as the Fermi-liquid type excitations. This kind of approaches may open up new prospects for the description of the critical phenomena associated to the quantum phase transition in Heavy-Fermion systems.Comment: 27 pages, 6 figures, 51 references, appeared in the Proceedings of the XXXVIII Cracow School of Theoretical Physics, Zakopane, Poland, June 1-10, 199

Finite-frequency noise in a non-interacting quantum dot

We calculate the non-symmetrized finite-frequency NS-FF noise for a single-level quantum dot connected to reservoirs in the spinless non-interacting case. The calculations are performed within the framework of the Keldysh Green's function formalism in the wide band approximation limit. We establish the general formula for NS-FF noise for any values of temperature, frequency and bias voltage. The electron transfer processes from one to the other reservoir act via the transmission amplitude and transmission coefficient depending on the energy. By taking the symmetrized version of this expression, we show that our result coincides with the expression of the finite frequency noise obtained by B\"uttiker using the scattering theory. We also give the explicit analytical expression for the NS-FF noise in the zero temperature limit. By performing numerical calculations, we finally discuss the evolution of the NS-FF noise spectrum when varying temperature, dot energy level, and coupling strength to the reservoirs, revealing a large variety of behaviors with different symmetry properties.Comment: Proceeding of the UPON 2015 conferenc

Out-of-equilibrium Kondo Effect in a Quantum Dot: Interplay of Magnetic Field and Spin Accumulation

We present a theoretical study of low temperature nonequilibrium transport through an interacting quantum dot in the presence of Zeeman magnetic field and current injection into one of its leads. By using a self-consistent renormalized equation of motion approach, we show that the injection of a spin-polarized current leads to a modulation of the Zeeman splitting of the Kondo peak in the differential conductance. We find that an appropriate amount of spin accumulation in the lead can restore the Kondo peak by compensating the splitting due to magnetic field. By contrast when the injected current is spin-unpolarized, we establish that both Zeeman-split Kondo peaks are equally shifted and the splitting remains unchanged. Our results quantitatively explain the experimental findings reported in KOBAYASHI T. et al., Phys. Rev. Lett. 104, 036804 (2010). These features could be nicely exploited for the control and manipulation of spin in nanoelectronic and spintronic devices.Comment: 6+ pages; 3 figures; final versio

Anderson Model out of equilibrium: decoherence effects in transport through a quantum dot

The paper deals with the nonequilibrium two-lead Anderson model, considered as an adequate description for transport through a d-c biased quantum dot. Using a self-consistent equation-of-motion method generalized out of equilibrium, we calculate a fourth-order decoherence rate $\gamma^{(4)}$ induced by a bias voltage $V$. This decoherence rate provides a cut-off to the infrared divergences of the self-energy showing up in the Kondo regime. At low temperature, the Kondo peak in the density of states is split into two peaks pinned at the chemical potential of the two leads. The height of these peaks is controlled by $\gamma^{(4)}$. The voltage dependence of the differential conductance exhibits a zero-bias peak followed by a broad Coulomb peak at large $V$, reflecting charge fluctuations inside the dot. The low-bias differential conductance is found to be a universal function of the normalized bias voltage $V/T_K$, where $T_K$ is the Kondo temperature. The universal scaling with a single energy scale $T_K$ at low bias voltages is also observed for the renormalized decoherence rate $\gamma^{(4)}/T_K$. We discuss the effect of $\gamma^{(4)}$ on the crossover from strong to weak coupling regime when either the temperature or the bias voltage is increased.Comment: 23 pages, 10 figure

Intermediate coupling fixed point study in the overscreened regime of generalized multichannel SU(N) Kondo models

We study a generalized multichannel single-impurity Kondo model, in which the impurity spin is described by a representation of the SU(N) group which combines bosonic and fermionic degrees of freedom. The impurity spin states are described by Abrikosov pseudofermions, and we make use of a method initiated by Popov and Fedotov which allows a proper handling of the fermionic constraint. The partition function is derived within a path integral approach. We use renormalization group techniques to calculate the $\beta$ scaling function perturbatively in powers of the Kondo coupling constant, which is justified in the weak coupling limit. The truncated expansion is valid in the overscreened (Nozieres-Blandin) regime, for an arbitrary SU(N) group and any value of the parameters characterizing the impurity spin representation. The intermediate coupling fixed point is identified. We derive the temperature dependence of various physical quantities at low T, controlled by a unique critical exponent, and show that the physics of the system in the overscreened regime governed by the intermediate coupling fixed point is characterized by a non-Fermi liquid behavior. Our results are in accordance with those obtained by other methods, as Bethe ansatz and boundary conformal field theory, in the case of various impurity spin symmetries. We establish in a unified way that the Kondo models in which the impurity spin is described successively by a fundamental, symmetric, antisymmetric and mixed symmetry representation yield all the same low-energy physics in the overscreened regime. Possible generalizations of the analysis we present to the case of arbitrary impurity spin representations of SU(N) are also discussed.Comment: 21 pages, 7 figures, REVTeX; final version accepted for publicatio

Transition from a strong-coupling fixed point to an intermediate-coupling fixed point in a single-channel SU(N) Kondo model: role of the filling and two-stage screening

We study an extended SU(N) single-impurity Kondo model in which the impurity spin is described by a combination of Abrikosov fermions and Schwinger bosons. Our aim is to describe both the quasiparticle-like excitations and the locally critical modes observed in various physical situations, including non-Fermi liquid behavior in heavy fermion systems in the vicinity of a quantum critical point. We identify the strong coupling fixed point of the model and study its stability within second order perturbation theory. Already in the single channel case and in contrast with either the pure bosonic or the pure fermionic case, the strong coupling fixed point is unstable against the conduction electron kinetic term as soon as the amount of Abrikosov fermions reaches a critical value. In the stability region, the partially screened, dressed impurity at site 0 repels the conduction electrons on adjacent sites. In the instability region, the impurity tends to attract $(N-1)$ conduction electrons to the neighboring sites, giving rise to a two-stage Kondo effect with additional screening.This result opens the route to the existence of an intermediate coupling fixed point, characterized by non-Fermi liquid behavior

Comportement non liquide de Fermi dans un modèle Kondo généralisé, Antiferromagnétisme et singulet de Spin dans l'apparition de la supraconductivité à haute température critique

Dans une première partie, nous étudions les points fixes associés à un modèle Kondo généralisé. Ce travail est motivé par la récente découverte d'un comportement non liquide de Fermi dans certains composés de fermions lourds. Nous considérons un modèle Kondo à une impureté dont le spin est décrit par une représentation mixte du groupe SU(N), combinant des degrés de liberté bosoniques et fermioniques. La stabilité du point fixe de couplage fort est discutée dans le cadre d'une théorie de perturbation au deuxième ordre autour de ce point fixe. Ce dernier est instable pour certaines classes de représentations du spin de l'impureté. Nous développons une approche basée sur le groupe de renormalisation perturbatif afin d'identifier le point fixe de couplage intermédiaire et en déduisons les propriétés de basses énergies du système. Dans une seconde partie, nous étudions la supraconductivité à haute température critique des cuprates sur la base d'une interprétation de type magnétique. Le premier mécanisme considéré correspond à la formation d'une onde de densité de spin, résultant de l'échange de fluctuations de spin antiferromagnétiques. Le second repose sur un état résonant de liaison de valence (RVB), avec formation d'un singulet de spin dans les plans de Cuivre-Oxygène. Nous avons développé une théorie de champ moyen, permettant de décrire la coexistence entre ces deux mécanismes. Dans un formalisme d'intégration fonctionnelle, nous dérivons le potentiel effectif d'appariement entre quasiparticules de type BCS, médié par les fluctuations gaussiennes des champs considérés. Nous discutons également la symétrie du gap supraconducteur.GRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

Finite‐Frequency Noise and Dynamical Charge Susceptibility in Single and Double Quantum Dot Systems

International audienceAbstract This study reports on finite‐frequency noise and dynamical charge susceptibility in out‐of‐equilibrium quantum dot systems. Both single and double quantum dots connected to one or two reservoirs of electrons are considered, and these quantities are calculated by using the non‐equilibrium Green function technique. The results are discussed in the light of experimental results, particularly in the low‐frequency limit for which an interpretation in terms of an equivalent RC‐circuit is made. Anti‐symmetrized noise is also studied, defined as the difference between absorption and emission noises, and its relationship with the dynamical charge susceptibility in single quantum dots is established. In double quantum dots, the similarities between the dynamical charge susceptibility, the absorption noise, and the dot occupancy, are highlighted by comparing their respective variations with the bias voltage applied between the two reservoirs, and the detuning energy defined as the difference between the lowest level energies in the two dots