Kondo Effect In Quantum Dots Research Articles

Kondo effect in quantum dots coupled to ferromagnetic leads with noncollinear magnetizations

Non-equilibrium Green's function technique has been used to calculate spin-dependent electronic transport through a quantum dot in the Kondo regime. The dot is described by the Anderson Hamiltonian and is coupled symmetrically to two ferromagnetic leads, whose magnetic moments are noncollinear. It is shown that the splitting of the zero bias Kondo anomaly in differential conductance decreases monotonously with increasing angle between magnetizations, and vanishes in the limit of antiparallel configuration.

Fano effect and Kondo effect in quantum dots formed in strongly coupled quantum wells

We present lateral transport measurements on strongly, vertically coupled quantum dots formed in separate quantum wells in a GaAs/AlGaAs heterostructure. Coulomb oscillations are observed forming a honeycomb lattice consistent with two strongly coupled dots. When the tunnel barriers in the upper well are reduced we observe the Fano effect due to the interfering paths through a resonant state in the lower well and a continuum state in the upper well. In both regimes an in plane magnetic field reduces the coupling between the wells when the magnetic length is comparable to the center to center separation of the wells. We also observe the Kondo effect which allows the spin states of the double dot system to be probed.

Kondo effect in quantum dots and molecular devices

Kondo effect is a very important many-body phenomenon in condensed matter physics, which explains why the resistance increases as the temperature is lowered (usually <10 K) in dilute magnetic alloy, and why the conductance increases as temperature is decreased in quantum dots. This paper simply introduces equilibrium and non-equilibrium Kondo effects in quantum dots together with the Kondo effect in quantum dots with even number of electrons (when the singlet and triplet states are degenerate). Furthermore, Kondo effect in single atom/molecular transistors is introduced, which indicates a new way to study Kondo effect.

Scaling and Decoherence in the Nonequilibrium Kondo Model

We study the Kondo effect in quantum dots in an out-of-equilibrium state due to an applied dc-voltage bias. Using the method of infinitesimal unitary transformations ("flow equations"), we develop a perturbative scaling picture that naturally contains both equilibrium coherence and nonequilibrium decoherence effects. This framework allows one to study the competition between Kondo effect and current-induced decoherence, and it establishes a large regime dominated by single-channel Kondo physics for asymmetrically coupled quantum dots.

Numerical renormalization group studies of SU(4) Kondo effect in quantum dots

We theoretically study an enhancement of the Kondo effect in quantum dots with two orbitals and spin 1 2 . The Kondo temperature and conductance are evaluated as functions of energy difference Δ between the orbitals, using the numerical renormalization group method. The Kondo temperature is maximal around the degeneracy point ( Δ = 0 ) and decreases with increasing | Δ | following a power law, T K ( Δ ) = T K ( 0 ) ( T K ( 0 ) / | Δ | ) γ , which is consistent with the scaling analysis. The conductance at T = 0 is almost constant 2 e 2 / h . Both the orbitals contribute to the conductance around Δ = 0 , whereas the current through the upper orbital is negligibly small when | Δ | ≳ T K ( 0 ) . These are characteristics of SU(4) Kondo effect.

Spintronic Transport and Kondo Effect in Quantum Dots

We investigate the spin-dependent transport properties of quantum-dot based structures where Kondo correlations dominate the electronic dynamics. The coupling to ferromagnetic leads with parallel magnetizations is known to give rise to nontrivial effects in the local density of states of a single quantum dot. We show that this influence strongly depends on whether charge fluctuations are present or absent in the dot. This result is confirmed with numerical renormalization group calculations and perturbation theory in the on-site interaction. In the Fermi-liquid fixed point, we determine the correlations of the electric current at zero temperature (shot noise) and demonstrate that the Fano factor is suppressed below the Poissonian limit for the symmetric point of the Anderson Hamiltonian even for nonzero lead magnetizations. We discuss possible avenues of future research in this field: coupling to the low energy excitations of the ferromagnets (magnons), extension to double quantum dot systems with interdot antiferromagnetic interaction and effect of spin-polarized currents on higher symmetry Kondo states such as SU(4).

Interplay between the Mesoscopic Stoner and Kondo Effects in Quantum Dots

We consider electrons confined to a quantum dot interacting antiferromagnetically with a spin-1 / 2 Kondo impurity. The electrons also interact among themselves ferromagnetically with a dimensionless coupling J , where J =1 denotes the bulk Stoner transition. We show that as J approaches 1 there is a regime with enhanced Kondo correlations, followed by one where the Kondo effect is destroyed and impurity is spin polarized opposite to the dot electrons. The most striking signature of the first, Stoner-enhanced Kondo regime is that a Zeeman field increases the Kondo scale, in contrast to the case for noninteracting dot electrons. Implications for experiments are discussed.

Kondo effect in quantum dots and molecular devices

Kondo effect in quantum dots and molecular devices

Fermi Liquid Theory for the Nonequilibrium Kondo Effect at Low Bias Voltages

In this paper, we describe a recent development in a Fermi liquid theory for the Kondo effect in quantum dots under a finite bias voltage V . Applying the microscopic theory of Yamada and Yosida to a nonequilibrium steady state, we derive the Ward identities for the Keldysh Green's function, and determine the low-energy behavior of the differential conductance d I /d V exactly up to terms of order ( e V ) 2 for the symmetric Anderson model. These results are deduced from the fact that the Green's function at the impurity site is a functional of a nonequilibrium distribution f eff (ω), which at e V =0 coincides with the Fermi function. Furthermore, we provide an alternative description of the low-energy properties using a renormalized perturbation theory (RPT). In the nonequilibrium state the unperturbed part of the RPT is determined by the renormalized free quasiparticles, the distribution function of which is given by f eff (ω). The residual interaction between the quasiparticles \(\widetilde{U}\), which is defined by the full vertex part at zero frequencies, is taken into account by an expansion in the power series of \(\widetilde{U}\). We also discuss the application of the RPT to a high-bias region beyond the Fermi-liquid regime.

Coherence and Coulomb blockade in single-electron devices: A unified treatment of interaction effects

We study the interplay between Coulomb blockade and the Kondo effect in quantum dots. We use a self-consistent scheme which describes mesoscopic devices in terms of a collective phase variable (slave rotor) and quasiparticle degrees of freedom. In the strong Coulomb blockade regime, we recover the description of metallic islands in terms of a phase only action. For a dot with well-separated levels, our method leads to the Kondo effect. We identify the regime where a crossover between the Coulomb blockade regime at high temperatures and the formation of a Kondo resonance at lower temperature takes place. In addition, we find that for a dot with many overlapping resonances, an {\it inverse crossover} can take place. A Kondo resonance which involves many levels within the dot is first formed, and this coherent state is suppressed by correlation effects at lower temperatures. A narrower Kondo resonance, due to a single level in the dot can emerge at even lower temperatures.

Kondo Effect in the Presence of Itinerant-Electron Ferromagnetism Studied with the Numerical Renormalization Group Method

The Kondo effect in quantum dots (QDs)-artificial magnetic impurities-attached to ferromagnetic leads is studied with the numerical renormalization group method. It is shown that the QD level is spin split due to the presence of ferromagnetic electrodes, leading to a suppression of the Kondo effect. We find that the Kondo effect can be restored by compensating this splitting with a magnetic field. Although the resulting Kondo resonance then has an unusual spin asymmetry with a reduced Kondo temperature, the ground state is still a locally screened state, describable by Fermi liquid theory and a generalized Friedel sum rule, and transport at zero temperature is spin independent.

Mesoscopic Fluctuations of Co-Tunneling and Kondo Effect in Quantum Dots

Conductance of a quantum dot in the Coulomb blockade regime is discussed. At moderately low temperatures, the thermally-assisted transport of electrons through the dot gives way to elastic co-tunneling [1]. The amplitude of the elastic co-tunneling is sensitive to the specific structure of electron wave functions in a given sample. The conductance exhibits strong mesoscopic fluctuations [2]. Statistical properties of these fluctuations are reviewed in this lecture. At lower temperatures, conductance through a dot is altered by the Kondo effect, if the number of electrons on the dot is odd. We describe the universal features of the Kondo conductance [3, 4], and briefly discuss the manifestations of this effect in the limiting cases of weak and strong [5] dot-lead coupling.

Nonequilibrium Kondo effect in quantum dots

The nonequilibrium Kondo effect in a quantum dot coupled to metallic leads is analyzed theoretically. Electron interaction on the dot is taken into account in terms of the Hubbard model for an arbitrary value of the correlation parameter U. The nonequilibrium Green function technique is used to calculate electric current and density of states. The key point of the approach is the consistency of the approximations used to calculate the lesser and retarded (advanced) Green functions. The Green functions are calculated on equal footing, i.e., within the same approximation in the framework of the equation of motion method.

Mesoscopic fluctuations in quantum dots in the Kondo regime

Properties of the Kondo effect in quantum dots depend sensitively on the coupling parameters and so on the realization of the quantum dot -- the Kondo temperature itself becomes a mesoscopic quantity. Assuming chaotic dynamics in the dot, we use random matrix theory to calculate the distribution of both the Kondo temperature and the conductance in the Coulomb blockade regime. We study two experimentally relevant cases: leads with single channels and leads with many channels. In the single-channel case, the distribution of the conductance is very wide as $T_K$ fluctuates on a logarithmic scale. As the number of channels increases, there is a slow crossover to a self-averaging regime.

Kondo effect in quantum dots coupled to ferromagnetic electrodes

The Kondo effects in transport through a quantum dot (QD) coupled to ferromagnetic leads are shown to be modified by the spin polarization of the electrodes. For parallel alignment of the magnetization of the leads the zero-bias anomaly in the differential conductance is split even in the absence of an external magnetic field. For antiparallel alignment the peaks are split only in the presence of a magnetic filed, but show a characteristic asymmetry.

Multiparameter scaling of the Kondo effect in quantum dots with an even number of electrons

We address a recent theoretical discrepancy concerning the Kondo effect in quantum dots with an even number of electrons where spin-singlet and -triplet states are nearly degenerate. We show that the discrepancy arises from the fact that the Kondo scaling involves many parameters, which makes the results depend on concrete microscopic models. We illustrate this by the scaling calculations of the Kondo temperature ${T}_{\mathrm{K}}$ as a function of the energy difference between the singlet and triplet states $\ensuremath{\Delta}.$ ${T}_{\mathrm{K}}(\ensuremath{\Delta})$ decreases with increasing $\ensuremath{\Delta},$ showing a crossover from a power law with a universal exponent to that with a nonuniversal exponent. The crossover depends on the initial parameters of the model.

Finite-size effects in conductance measurements on quantum dots.

The observation of the Kondo effect in quantum dots has provided new opportunities to finally observe the controversial Kondo screening cloud. Here we study the conductance of a quantum dot embedded in a finite length quantum wire, predicting a change in behavior when the length of the wire is comparable to the size of the screening cloud.

Kondo effects in quantum dots at large bias

Recently, the issue of whether the Kondo problem in quantum dots at large bias is a weak-coupling problem or not has been raised. In this paper, we revisit this problem by carefully analyzing a corresponding model in the solvable limit -- the Emery-Kivelson line, where various crossover energy scales can be easily identified. We then try to extract the scaling behavior of this problem from various physical correlation functions within the spirit of ``poor man's scaling.'' Our conclusions support some recent suggestions made by Coleman {\em et al.} [Phys. Rev. Lett. {\bf 86}, 4088 (2001)], which are obtained by perturbative analysis: The voltage acts as a cutoff of the renormalization group flow for {\em only} half of the impurity so that the low-temperature physics is controlled by a strong-coupling fixed point. But the low-temperature response functions in general show one-channel Kondo behaviors with two-channel Kondo behaviors occurring only through proximity to a quantum critical point.

Resource Letter: MesP-1: Mesoscopic physics

This Resource Letter provides a guide to the literature on mesoscopic electron physics of solids. Journal articles, conference proceedings, and books are cited for the following topics: conductance fluctuations in disordered and quantum-chaotic systems, conductance quantization, conduction of a Luttinger liquid, electron noise in mesoscopic devices, mesoscopic superconductivity, electron–electron interactions in mesoscopic systems and the Coulomb blockade phenomenon, and Kondo effect in quantum dots.

Two-stage Kondo effect in a quantum dot at a high magnetic field.

We report a strong Kondo effect (Kondo temperature approximately 4 K) at high magnetic field in a selective area growth semiconductor quantum dot. The Kondo effect is ascribed to a singlet-triplet transition in the ground state of the dot. At the transition, the low-temperature conductance approaches the unitary limit. Away from the transition, for low bias voltages and temperatures, the conductance is sharply reduced. The observed behavior is compared to predictions for a two-stage Kondo effect in quantum dots coupled to single-channel leads.