Kondo effect in a quantum dot coupled to ferromagnetic leads: a numerical renormalization group analysis.

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.

We study the temperature dependence of the linear conductance and tunnel magnetoresistance of quantum dots coupled to ferromagnetic leads. Using the numerical renormalization group method, we determine transport properties for a wide range of temperatures $T$, ranging from zero through the Kondo temperature ${T}_{K}$ up to the high-temperature regime. We show that tunnel magnetoresistance in the local moment regime displays a nonmonotonic dependence on $T$ and vanishes when $T~{T}_{K}$. In addition, we also analyze the spin polarization $\mathcal{P}$ of the linear conductance in the parallel configuration and show that $\mathcal{P}$ is suppressed in the odd electron Coulomb blockade valley and can be enhanced above the spin polarization of the leads in the even Coulomb valley.

We investigate the Josephson effect through a two-level quantum dot with an exchange coupling between two dot electrons. We compute the superconducting phase relationship and construct the phase diagram in the superconducting gap--exchange coupling plane in the regime of the singlet-triplet transition driven by the exchange coupling. In our study two configurations for the dot-lead coupling are considered: one where effectively only one channel couples to the dot, and the other where the two dot orbitals have opposite parities. Perturbative analysis in the weak-coupling limit reveals that the system experiences transitions from 0 to $\pi$ (negative critical current) behavior, depending on the parity of the orbitals and the spin correlation between dot electrons. The strong coupling regime is tackled with the numerical renormalization group method, which first characterizes the Kondo correlations due to the dot-lead coupling and the exchange coupling in the absence of superconductivity. In the presence of superconductivity, many-body correlations such as two-stage Kondo effect compete with the superconductivity and the comparison between the gap and the relevant Kondo temperature scales allows to predict a rich variety of phase diagrams for the ground state of the system and for the Josephson current. Numerical calculations predicts that our system can exhibit Kondo-driven 0-$\pi$-0 or $\pi$-0-$\pi$ double transitions and, more interestingly, that if proper conditions are met a Kondo-assisted $\pi$-junction can arise, which is contrary to a common belief that the Kondo effect opens a resonant level and makes the 0-junction. Our predictions could be probed experimentally for a buckminster fullerene sandwiched between two superconductors.

Strong correlation behaviors play a pivotal role in realizing novel, high-performance, low-power nanoscale electronic devices. In this study, we theoretically design a molecular switch based on a metal-free polycyclic aromatic hydrocarbon diradical molecule dominated by strong electron-electron repulsions. By establishing a customized simulation framework that combines density functional theory with the numerical renormalization group method, and with the aid of a side-coupled two-orbital Anderson model, we systematically simulate the quantum transport governed by various kinds of Kondo effects. When the central energy level sweeps upward, the linear conductance tends to reach its unitary limit in the low-temperature regime, driven by the broadening two-stage Kondo effect window. As the side energy increases, a quantum phase transition from the two-stage Kondo effect to the spin-1/2 Kondo effect emerges, resulting in a stable, full conductance plateau. Furthermore, by tuning the exchange coupling between the central and the side orbitals, we simulate the impact of precisely adjusting the intramolecular dihedral angle of the molecule on the transport properties. The linear conductance exhibits a transition from zero to the unitary limit as the molecule smoothly evolves from the antiferromagnetic to the ferromagnetic regime. These findings provide valuable insights into the dynamical and thermodynamical properties of complex polycyclic aromatic hydrocarbon systems. Our suggested "abinitio + model calculation" theoretical framework may offer a promising methodology for exploring the complex Kondo physics in real magnetic nanosystems.

We discuss the Kondo effect in an electron system dynamically coupled with local Jahn-Teller phonons. For the purpose, we consider the two-orbital Anderson model including both Coulomb interactions and the coupling between electrons and Jahn-Teller phonons on an impurity site. Note that in this paper, we consider a quarter-filling case. First we analyze a local problem and confirm a spin-vibronic quartet ground state, characterized by the direct product of spin and vibronic degrees of freedom. Next we include the hybridization term and analyze the model by using a numerical renormalization group method. From the evaluation of entropy, specific heat, and several kinds of susceptibilities, it is found that spin and total angular momenta are simultaneously screened by conduction electrons, leading to the Kondo phenomenon due to the entropy release of ln 4 of the local spin-vibronic state. A possibility of heavy-electron formation in the spin-vibronic Kondo effect is briefly discussed.

The emergence of flat bands in twisted bilayer graphene at the magic angle can be understood in terms of a vanishing Fermi velocity of the Dirac cone. This is associated with van Hove singularities approaching the Fermi energy and becoming higher-order. In the density of states, this is reflected by flanking logarithmic van Hove divergences pinching off the central Dirac cone in energy space. The low-energy pseudogap of the Dirac cone away from the magic angle is replaced by a power-law divergence due to the higher-order van Hove singularity at the magic angle. This plays an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. Here we investigate one such correlation effect---the Kondo effect due to a magnetic impurity embedded in twisted bilayer graphene. We use the Bistritzer-MacDonald model to extract the low-energy density of states of the material as a function of twist angle and study the resulting quantum impurity physics using perturbative and numerical renormalization group methods. Although at zero temperature the impurity is only Kondo screened precisely at the magic angle, we find highly nontrivial behavior at finite temperatures relevant to experiments, due to the complex interplay between Dirac, van Hove, and Kondo physics.

Kondo effects in quantum dots systems

The effect of a magnetic field on the spectral density of a S = 1/2 Kondo impurity is investigated at zero and finite temperatures by using Wilson's numerical renormalization group method. A splitting of the total spectral density is found for fields larger than a critical value H(c)(T = 0) approximately 0.5T(K), where T(K) is the Kondo scale. The splitting correlates with a peak in the magnetoresistivity of dilute magnetic alloys which we calculate and compare with the experiments on CexLa1-xAl2,x = 0.0063. The linear magnetoconductance of quantum dots exhibiting the Kondo effect is also calculated.

We investigate the resistivity and dephasing rate in the Kondo regime due to magnetic impurities in graphene with different chemial potentials ($\mu$). The Kondo effect due to either carbon vacancies or magnetic adatoms in graphene is described by the single-orbital pseudo-gap asymmetric Anderson impurity model. We find that although the Anderson impurity model considered here is a mixed valence system, it can be drived into either the Kondo [$\mu > \mu_c$ (critical value) $>0$] or mixed valency ($\mu \approx \mu_c$) or empty orbital ($\mu < \mu_c$) regime by a gate voltage, giving rise to characteristic features in resistivity and dephasing rate in each regime. Specifically, in the case of $\mu < \mu_c$, the shapes of the resistivity (dephasing rate) curves for different $\mu$ are nearly identical. However, as temperature decreases, they start to increase to their maxima at a lower $T/T_K$ but more rapidly [as $(T_K/T)^{3/2}$] than in normal metals [here $T$ ($T_K$) denotes the (Kondo) temperature]. As $T$ further decreases, after reaching the maximum, the dephasing rate drops more quickly than in normal metals, behaving as $(T/T_K)^3$ instead of $(T/T_K)^2$. Furthermore, the resistivity has a distinct peak above the saturation value near $T_K$. In the case of $\mu > \mu_c$, in contrast, the resistivity curve has an additional broad shoulder above 10$T_K$ and the dephasing rate exhibits an interesting shoulder-peak shape. In the narrow boundary region ($\mu \approx \mu_c$), both the resistivity and dephasing rate curves are similar to the corresponding ones in normal metals. This explains the conventional Kondo like resistivity from recent experiments on graphene with defects. The resistivity and dephasing rate are analysized in terms of the calculated $T$-dependent spectral function, correlation self-energy and renormalized impurity level.

Preface V. Chandrasekhar, et al. Introduction N.O. Birge, et al. Finite Size Effects in Kondo Alloys. Effect of Disorder on the Kondo Behavior of Thin Cu(Mn) Films T.M. Jacobs, N. Giordano. The Kondo Effect and Weak Localization P. Phillips, I. Martin. Surface Magnetic Anisotropy of Kondo Impurities Induced by Spin-Orbit Scattering O. Ujsaghy. Finite Size Effects in Spin Glass Alloys. Thermopower of Mesoscopic Spin Glasses C. Strunk, et al. Shape-Induced Magnetic Anisotropy in Dilute Magnetic Alloys V.N. Gladilin, et al. Zero-Bias Transport Anomaly in Metallic Nanobridges H.B. Weber, et al. Conductance Noise and Irreversibility in Diluted Magnetic Semiconductors J. Jaroszynski, et al. Point Contact Spectroscopy and Tunnelling Spectroscopy of Kondo Impurities. Enhancement of Kondo Temperature in Nanometer-Size Point Contacts I.K. Yanson, et al. Scanning Tunnelling Spectroscopy of a Single Kondo Impurity R. Berndt, W.-D. Schneider. Two-Level Systems and Dephasing in Thin Metal Structures. Two-Channel Kondo Effect from Tunneling Impurities G. Zarand. Electron Decoherence at Zero Temperature P. Mohanty. Probing Interactions in Mesoscopic Gold Wires F. Pierre, et al. Kondo Effect in Non-Equilibrium J. Kroha. Kondo Effect in Quantum Dots. Tunneling Through a Quantum Dot A. Schiller. Electron Transport Through Quantum Dots: An Unusual Kondo Effect S. De Franceschi, et al. The Kondo Effect in a Single-Electron Transistor D. Goldhaber-Gordon, et al. Contributions Related to Poster Presentations. Flux Dependent Dielectric Response of Stacked Nanoscopic Rings K.-H. Ahn, P. Fulde.High-Frequency Response of Two-Level Systems in NixNb1-x Metallic Point Contacts O.P. Balkashin, et al. Giant Magnetoresistance of a Single Interface J. Balogh, et al. Fermi Edge Singularities in Transport Through Quantum Dots E. Bascones, et al. Theory of Magnetoresistance in Films of Dilute Magnetic Alloys L. Borda. Current and Shot Noise in a Ferromagnetic Double Tunnel Junction with an Atomic Size Spacer B.R. Bulka, et al. Positive Domain-Wall Magnetoresistance of Ferromagnetic Point Contacts J. Caro, et al. Enhancement of Kondo Effect Due to Spin-Singlet-Triplet Competition in Quantum Dots M. Eto, Y.V. Nazarov. Diagrammatic Theory of the Anderson Impurity Mod with Finite Coulomb Interaction K. Haule, et al. Generalized Conductance Sum Rule in Atomic Break Junctions S. Kirchner, et al. Is CeNiSn a Kondo Semiconductor? Y.G. Naidyuk, et al. The Influence of Single Magnetic Impurities on the Conductance of Quantum Microconstrictions A. Namiranian, et al. 7 Additional Chapters.

Screened spin−1 and −1/2 Kondo effect in a triangular quantum dot system with interdot Coulomb repulsion

We study the conductance through a triangular triple quantum dot, which are connected to two noninteracting leads, using the numerical renormalization group (NRG). It is found that the system shows a variety of Kondo effects depending on the filling of the triangle. The SU(4) Kondo effect occurs at half-filling, and a sharp conductance dip due to a phase lapse appears in the gate-voltage dependence. Furthermore, when four electrons occupy the three sites on average, a local S = 1 moment, which is caused by the Nagaoka mechanism, is induced along the triangle. The temperature dependence of the entropy and spin susceptibility of the triangle shows that this moment is screened by the conduction electrons via two separate stages at different temperatures. The two-terminal and four-terminal conductances show a clear difference at the gate voltages, where the SU(4) or the S = 1 Kondo effects occurring.

The thermoelectric properties of strongly correlated quantum dots, described\nby a single level Anderson model coupled to conduction electron leads, is\ninvestigated using Wilson's numerical renormalization group method. We\ncalculate the electronic contribution, $K_{\\rm e}$, to the thermal conductance,\nthe thermopower, $S$, and the electrical conductance, $G$, of a quantum dot as\na function of both temperature, $T$, and gate voltage, ${\\rm v}_g$, for strong,\nintermediate and weak Coulomb correlations, $U$, on the dot. For strong\ncorrelations and in the Kondo regime, we find that the thermopower exhibits two\nsign changes, at temperatures $T_{1}({\\rm v}_g)$ and $T_{2}({\\rm v}_g)$ with\n$T_{1}&lt; T_{2}$. Such sign changes in $S(T)$ are particularly sensitive\nsignatures of strong correlations and Kondo physics. The relevance of this to\nrecent thermopower measurements of Kondo correlated quantum dots is discussed.\nWe discuss the figure of merit, power factor and the degree of violation of the\nWiedemann-Franz law in quantum dots. The extent of temperature scaling in the\nthermopower and thermal conductance of quantum dots in the Kondo regime is also\nassessed.\n

We investigate f-electron charge susceptibility in a two-impurity Anderson model on the basis of Wilson's numerical renormalization group method. The f-electron charge susceptibility diverges logarithmically at the critical point of this model when conduction-electron bands exhibit particle–hole symmetry. Although the critical point disappears without the particle–hole symmetry, the f-electron charge fluctuation is much more enhanced near the crossover regime between the Kondo–Yosida singlet and intersite spin-singlet states than that in the single-impurity case. This result shows that charge fluctuations are enhanced owing to the competition between intersite and Kondo–Yosida spin singlets. A possible scenario for the enhanced residual resistivity near the region where the Kondo temperature becomes comparable with the Néel temperatures under pressure in some heavy-fermion compounds is proposed.

Numerical analysis of the simplest odd-numbered system of coupled quantum dots reveals an interplay between magnetic ordering, charge fluctuations and the tendency of itinerant electrons in the leads to screen magnetic moments. The transition from local-moment to molecular-orbital behavior is visible in the evolution of correlation functions as the inter-dot coupling is increased. Resulting novel Kondo phases are presented in a phase diagram which can be sampled by measuring the zero-bias conductance. We discuss the origin of the even-odd effects by comparing with the double quantum dot.