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Behavior of quantum liquids is a fascinating topic in physics. Even in a strongly correlated case, the linear response of a given system to an external field is described by the fluctuation-dissipation relations based on the two-body correlations in the equilibrium. However, to explore nonlinear non-equilibrium behaviors of the system beyond this well-established regime, the role of higher order correlations starting from the three-body correlations must be revealed. In this work, we experimentally investigate a controllable quantum liquid realized in a Kondo-correlated quantum dot and prove the relevance of the three-body correlations in the nonlinear conductance at finite magnetic field, which validates the recent Fermi liquid theory extended to the non-equilibrium regime., Recent theory has shown that the non-equilibrium response of a Kondo model can be described by the Fermi liquid theory with three-body correlations. Here, the authors experimentally measure such correlations in the nonlinear conductance of a Kondo-correlated quantum dot.

We present a microscopic Fermi-liquid view on the low-energy transport through an Anderson impurity with $N$ discrete levels, at arbitrary electron filling $N_d$. It is applied to nonequilibrium current fluctuations, for which the two-quasiparticle collision integral and the three-body correlations that determine the quasiparticle energy shift play important roles. Using the numerical renormalization group up to $N=6$, we find that for strong interactions the three-body fluctuations are determined by a single parameter other than the Kondo energy scale in a wide filling range $1 \lesssim N_d \lesssim N-1$. It significantly affects the current noise for $N>2$ and the behavior of noise in magnetic fields., 5 pages, 8 figures, supplemental material containing 8 figures

We study Bell-state correlations for quasiparticle pairs excited in nonlinear current through a double quantum dot in the Kondo regime. Exploiting the renormalized perturbation expansion in the residual interactions of the local Fermi liquid and Bell's inequality for cross correlation of spin currents through distinct conduction channels, we derive an asymptotically exact form of Bell's correlation for the double dot at low bias voltages. We find that pairs of quasiparticles and holes excited by the residual exchange interaction violate Bell's inequality for the spin currents.

We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behavior of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behavior at low temperatures $T$ can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a $T^{2}$ coefficient of conductance becomes zero at quarter-filling whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields $B$. We find that the conductance shows the SU($4$) scaling behavior at $\mu_{B}B, Comment: 27 pages, 14 figures

We study spin-entanglement of the quasiparticles of the local Fermi liquid excited in nonlinear current through a quantum dot described by the Anderson impurity model with two degenerate orbitals coupled to each other via an exchange interaction. Applying the renormalized perturbation theory, we obtain the precise form of the cumulant generating function and cross-correlations for the currents with spin angled to arbitrary directions, up to third order in the applied bias voltage. It is found that the exchange interaction gives rise to spin-angle dependency in the cross-correlation between the currents through the two different orbitals, and also brings an intrinsic cross-correlation of currents with three different angular momenta.

Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from $SU(4)$ to $SU(2)$ symmetry of the ground state. High-sensitive current noise measurements combined with the non-equilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover. Our achievement demonstrates that non-linear noise constitutes a measure of quantum fluctuations that can be used to tackle quantum phase transitions., Comment: 5 pages, 4 figures

We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada-Yosida. It includes partly a microscopic clarification of the related achievements based on Nozi\`{e}res' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys.\ Rev.\ B {\bf 95}, 165404 (2017)]. In our formulation, the Fermi-liquid parameters such as the quasi-particle energy, damping, and transport coefficients are related to each other through the total vertex $\Gamma_{\sigma\sigma';\sigma'\sigma} (\omega, \omega'; \omega', \omega)$, which may be regarded as a generalized Landau quasi-particle interaction. We obtain exactly this function up to linear order with respect to the frequencies $\omega$ and $\omega'$ using the anti-symmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half-filling through the non-linear susceptibilities. We also apply the formulation to non-equilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field., Comment: 5 pages, 2 figures, Introduction has been revised

We study the low-energy behavior of the vertex function of a single Anderson impurity away from half-filling for finite magnetic fields, using the Ward identities with careful consideration of the anti-symmetry and analytic properties. The asymptotic form of the vertex function $\Gamma_{\sigma\sigma';\sigma'\sigma}^{}(i\omega,i\omega';i\omega',i\omega)$ is determined up to terms of linear order with respect to the two frequencies $\omega$ and $\omega'$, as well as the $\omega^2$ contribution for anti-parallel spins $\sigma'\neq \sigma$ at $\omega'=0$. From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida. The $\omega^2$ real part of the self-energy $\Sigma_{\sigma}^{}(i\omega)$ is shown to be expressed in terms of the double derivative $\partial^2\Sigma_{\sigma}^{}(0)/\partial \epsilon_{d\sigma}^{2}$ with respect to the impurity energy level $\epsilon_{d\sigma}^{}$, and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora in the Nozi\`{e}res phenomenological Fermi-liquid theory [Phys.\ Rev.\ B {\bf 95}, 165404 (2017)]. We also calculate the $T^2$ correction of the self-energy, and find that the real part can be expressed in terms of the three-body correlation function $\chi_{\uparrow\downarrow,-\sigma}^{[3]} = \partial \chi_{\uparrow\downarrow}/\partial \epsilon_{d,-\sigma}^{}$. We also provide an alternative derivation of the asymptotic form of the vertex function. Specifically, we calculate the skeleton diagrams for the vertex function $\Gamma_{\sigma\sigma;\sigma\sigma}^{}(i\omega,0;0,i\omega)$ for parallel spins up to order $U^4$ in the Coulomb repulsion $U$. It directly clarifies the fact that the analytic components of order $\omega$ vanish as a result of the cancellation of four related Feynman diagrams which are related to each other through the anti-symmetry operation., Comment: 15 figures, 19pages, and supplemental material (15 pages), typo found in (6.15) has been corrected

We theoretically study an emergent SU(2) symmetry which is suggested by recent magneto-transport measurements, carried out near two electrons filling of a carbon nanotube quantum dot. It emerges in the case where the spin and orbital Zeeman splittings cancel each other out for two of the one-particle dot levels among four. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs at two impurity-electrons filling as magnetic field increases. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. In order to clarify how the ground state evolves during such a crossover, we also reexamine the SU(N) Kondo singlet state for M impurity-electrons filling in the limit of strong exchange interactions. We show that the nondegenerate Fermi-liquid fixed point of Nozi\`{e}es and Blandin can be described as a bosonic Perron-Frobenius vector for M hard-core bosons, each of which consists of one impurity-electron and one conduction hole. This interpretation can also be applied to the Fermi-liquid fixed-point without the SU(N) symmetry., Comment: 20 pages, 10 figures, Sec.III B. has been revised. J.Phys.Soc.Jpn.in press

We describe a formulation to deduce the phase shifts, which determine the ground-state properties of interacting quantum-dot systems with the inversion symmetry, from the fixed-point eigenvalues of the numerical renormalization group (NRG). Our approach does not assume the specific form of the Hamiltonian nor the electron-hole symmetry, and it is applicable to a wide class of quantum impurities connected to noninteracting leads. We apply the method to a triple dot which is described by a three-site Hubbard chain connected to two noninteracting leads, and calculate the dc conductance away from half-filling. The conductance shows the typical Kondo plateaus of Unitary limit in some regions of the gate voltages, at which the total number of electrons N_el in the three dots is odd, i.e., N_el =1, 3 and 5. In contrast, the conductance shows a wide minimum in the gate voltages corresponding to even number of electrons, N_el = 2 and 4. We also discuss the parallel conductance of the triple dot connected transversely to four leads, and show that it can be deduced from the two phase shifts defined in the two-lead case., Comment: 9 pages, 12 figures: Fig. 12 has been added to discuss T_K

We derive an exact expression for the differential conductance for a quantum dot in an arbitrary magnetic field for small bias voltage. The derivation is based on the symmetric Anderson model using renormalized perturbation theory and is valid for all values of the on-site interaction $U$ including the Kondo regime. We calculate the critical magnetic field for the splitting of the Kondo resonance to be seen in the differential conductivity as function of bias voltage. Our calculations for small field show that the peak position of the component resonances in the differential conductance are reduced substantially from estimates using the equilibrium Green's function. We conclude that it is important to take the voltage dependence of the local retarded Green's function into account in interpreting experimental results, Comment: 8 pages, 4 figures; Replaced by a fully revised version with minor corrections in the text

We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems., Comment: One typo found in Eq.(3) in previous version has been corrected

We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level $\tilde\epsilon_d$, an effective hybridization $\tilde V$, and a quasiparticle interaction $\tilde U$. The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a Falikov-Kimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level., Comment: 14 pages, 12 figures; Revised Sec. 2 and 4

Interacting quantum many-body systems constitute a fascinating playground for researchers since they form quantum liquids with correlated ground states and low-lying excitations, which exhibit universal behaviour. In fermionic systems, such quantum liquids are realized in helium-3 liquid, heavy fermion systems, neutron stars and cold gases. Their properties in the linear-response regime have been successfully described by the theory of Fermi liquids. However, non-equilibrium properties beyond this regime have still to be established and remain a key issue of many-body physics. Here, we show a precise experimental demonstration of Landau Fermi-liquid theory extended to the non-equilibrium regime in a 0-D system. Combining transport and ultra-sensitive current noise measurements, we have unambiguously identified the SU(2) and SU(4) symmetries of quantum liquid in a carbon nanotube tuned in the universal Kondo regime. We find that, while the electronic transport is well described by the free quasi-particle picture around equilibrium, a two-particle scattering process due to residual interaction shows up in the non-equilibrium regime. By using the extended Fermi-liquid theory, we obtain the interaction parameter "Wilson ratio" $R=1.9 \pm 0.1$ for SU(2) and $R=1.35 \pm 0.1$ for SU(4) as well as the corresponding effective charges, characterizing the quantum liquid behaviour. This result, in perfect agreement with theory, provides a strong quantitative experimental background for further developments of the many-body physics. Moreover, we discovered a new scaling law for the effective charge, signalling as-yet-unknown universality in the non-equilibrium regime. Our method to address quantum liquids through their non-equilibrium noise paves a new road to tackle the exotic nature of quantum liquids out-of-equilibrium in various physical systems., Comment: accepted for publication in Nature Physics

We study the nonequilibrium Keldysh Green's function for an N-orbital Anderson model at high bias voltages, extending a previous work, which for the case only with the spin degrees of freedom N=2, to arbitrary N. Our approach uses an effective non-Hermitian Hamiltonian that is defined with respect to a Liouville-Fock space in the context of a thermal field theory. The result correctly captures the relaxation processes at high energies, and is asymptotically exact not only in the high-bias limit but also in the high-temperature limit at thermal equilibrium. We also present an explicit continued-fraction representation of the Green's function. It clearly shows that the imaginary part is recursively determined by the decay rate of intermediate states with at most N-1 particle-hole-pair excitations. These high-bias properties follow from the conservations of a generalized charge and current in the Liouville-Fock space. We also examine temperature dependence of the spectral function in equilibrium, comparing the exact results with both the finite-T and infinite-T results of the non-crossing approximation (NCA)., 16 pages, 6 figures, typos have been corrected and DOI has been provided

Transport through small interacting systems connected to noninteracting leads is studied based on the Kubo formalism using a Eliashberg theory of the analytic properties of the vertex part. The transmission probability, by which the conductance is expressed as $g = (2e^2/h) \int d\epsilon (- \partial f / \partial \epsilon) {\cal T}(\epsilon)$, is introduced for interacting electrons. Here $f(\epsilon)$ is the Fermi function, and the transmission probability ${\cal T}(\epsilon)$ is defined in terms of a current vertex or a three-point correlation function. We apply this formulation to a series of Anderson impurities of size N (=1,2,3,4), and calculate ${\cal T}(\epsilon)$ using the order $U^2$ self-energy and current vertex which satisfy a generalized Ward identity. The results show that ${\cal T}(\epsilon)$ has much information about the excitation spectrum: ${\cal T}(\epsilon)$ has two broad peaks of the upper and lower Hubbard bands in addition to N resonant peaks which have direct correspondence with the noninteracting spectrum. The peak structures disappear at high temperatures., Comment: 18 pages, 16 figures

The spatial distribution of the nonequilibrium current and charge distributions in a series of two point contacts are studied in the presence of a magnetic field making use of a recursive Green function method based on the Keldysh formalism. Numerical results show that the structure of vortices appearing in between two barriers depends strongly on the applied bias voltage. The chemical potential dependence of the total current is also investigated.

Based on the Quantum Monte Carlo (QMC) technique, we developed a method to calculate the tunneling conductance of the quantum dot systems for which the Kondo effect becomes important. The method computes the conductance directly from the current correlation function, and is applicable to the cases in which the calculation is not reduced to the computation of single particle Green's function. We compare the calculated conductance with experiments, and found good qualitative agreement. The temperature in experiments seems to be not low enough compared with the Kondo temperature in the mid region of the two paired Coulomb oscillation peaks. We studied the Zeeman field effect, and showed that the conductance is strongly suppressed when it has been enhanced by the Kondo effect. The conductance of an Aharonov-Bhom circuit including dots was also studied.

We present renormalised perturbation theory calculations for the description of the dynamics of quasiparticles in the Anderson impurity model in magnetic field. Our calculations are compared with NRG spectra and good agreement is found for magnetic fields of the order of the Kondo temperature, when an appropriate perturbation series is chosen. We point out how this approach can be generalised to the non-equilibrium situation, where it is relevant for the description of quantum dots.

The electronic structure of CuGeO 3 in the spin-Peierls (SP) phase with the space group of Bbcm is calculated for the first time within the local-density approximation (LDA) and the LDA + U scheme where the local 3d–3d Coulomb interaction U is introduced on the Cu sites. Although the insulating antiferromagnetic solution is obtained in the LDA, the obtained bandgap of 0.19 eV and a magnetic moment of 0.39 μ B / Cu are much smaller than the experimental bandgap of 3.7 eV and the magnetic moment of 0.7 μ B / Cu , respectively. With the value of U = 6.7 eV determined using an electron spectroscopy, the LDA + U calculation yields a charge-transfer bandgap of 1.63 eV and gives a magnetic moment of 0.72 μ B / Cu . The essential electronic and magnetic properties of CuGeO 3 in the SP phase can be described by means of the LDA + U scheme.

The spatial distribution of the nonequilibrium current in a series of two point contacts under a finite bias voltage is investigated numerically making use of a recursive Green-function method based on the Keldysh formalism. The results of the current distribution show an interesting behavior such as the existence of vortices in between the two barriers. The temperature dependence of the nonlinear current-voltage characteristic is also studied.

A numerical analysis for evaluating the transport coefficient through a small interacting system is examined using the quantum Monte Carlo (QMC) method. To formulate the analysis, we consider a finite interacting system on a one-dimensional lattice that is connected to noninteracting leads, and investigate the expression of the dc conductance making use of the Kubo formula with the perturbation theory in the Coulomb interaction. At $T=0$ the dc conductance is written in terms of the transmission coefficient, which can be obtained numerically by extrapolating the QMC data for the Matsubara Green's function as $i{\ensuremath{\varepsilon}}_{n}\ensuremath{\rightarrow}{i0}^{+}$. We apply the analysis to the dc conductance through a region with a few resonance states.

We describe some exact high-energy properties of a single Anderson impurity connected to two noninteracting leads in a nonequilibrium steady state. In the limit of high bias voltages, and also in the high-temperature limit at thermal equilibrium, the model can be mapped on to an effective non-Hermitian Hamiltonian consisting of two sites, which correspond to the original impurity and its image that is defined in a doubled Hilbert space referred to as Liouville-Fock space. For this, we provide a heuristic derivation using a path-integral representation of the Keldysh contour and the thermal field theory, in which the time evolution along the backward contour is replicated by extra degrees of freedom corresponding to the image. We find that the effective Hamiltonian can also be expressed in terms of charges and currents. From this, it can be deduced that the dynamic susceptibilities for the charges and the current fluctuations become independent of the Coulomb repulsion U in the high bias limit. Furthermore, the equation of motions for the Green's function and two other higher-order correlation functions constitute a closed system. The exact solution obtained from the three coupled equations extends the atomic-limit solution such that the self-energy correctly captures the imaginary part caused by the relaxation processes at high energies. The spectral weights of the upper and lower Hubbard levels depend sensitively on the asymmetry in the tunneling couplings to the left and right leads., Comment: 12 pages, 5 figures, typos have been corrected

We study the superconducting (SC) states with d x 2 - y 2 and extended s symmetry in the three-band Hubbard model on a CuO 2 plane using the variational Monte Carlo method in the limit U d →∞, where U d is the Coulomb repulsion between holes on a Cu site. By comparing the energy among the SC, paramagnetic (PM), and antiferromagnetic (AFM) states, we obtain a phase diagram and find that the d x 2 - y 2 -wave SC state becomes the lowest energy state near the phase boundary between the PM and AFM phases. In contrast to the d x 2 - y 2 -wave SC state, the energy of the extended s -wave SC state is always higher than that of the AFM state.

In the Van Vleck metals such as Pr, an indirect interaction arises between the conduction electrons through the virtual excitation of the crystal-field singlet ground state. By solving the Eliashberg equations, it is shown that this effective interaction can bring about superconductivity in a way similar to the spin-fluctuation-mediated pairing due to the repulsive short-range interaction. For the free-electron band the triplet {ital p}-wave pairing is formed. Spin degeneracy of the triplet states is lifted by the crystal-field anisotropy to choose the highest {ital T}{sub {ital c}}. The retardation effect brought by the effective interaction and the depairing effects due to the scattering of the conduction electrons by the crystal-field states are analyzed in detail. Of all these effects, it is the mass renormalization effect that strongly depresses {ital T}{sub {ital c}}.

The effect of on-site Coulomb repulsion on the process of resonant tunneling through a small interacting region is studied in the presence of a magnetic field by using the recursive Green's function method within a mean field approximation. The conductance is calculated as a function of the chemical potential µ making use of the Kubo formula, and calculations are performed for single- and double-mode quasi-one-dimensional quantum wires. In a magnetic field, some resonance levels close each other to form a single Landau level, so that the electron correlation in the small region is enhanced, and the µ-dependence of the conductance is changed by rather small value of the Coulomb repulsion. For the double-mode wire a collinear-type electronic state, in which spins in the small region are aligned antiferromagnetically in the x -direction and ferromagnetically in the y -direction, is found to be stable over a wide range of the chemical potential.

Effects of Coulomb repulsion on the process of resonant tunneling through a single quantum level are studied by applying the quantum Monte Carlo method and the maximum-entropy method to the Wolf model on a one-dimensional chain. In the calculated spectral function there is a sharp Kondo peak near the chemical potential \ensuremath{\mu}, which contributes to the resonance tunneling. Correspondingly, the conductance calculated by using the Friedel sum rule shows the expected transparency, i.e., the transmission probability is almost unity when \ensuremath{\mu} is in the range ${\mathrm{\ensuremath{\epsilon}}}_{0}$${\mathrm{\ensuremath{\epsilon}}}_{0}$+U, where ${\mathrm{\ensuremath{\epsilon}}}_{0}$ is the on-site energy of the single quantum level and U is the Coulomb repulsion.

We study non-equilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling $J$, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case, shows that spin-triplet and spin-singlet pairs of quasiparticles are formed in the current due to the Hund's rule coupling and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value $F_b = (9M+6)/ (5M+4)$ determined by the orbital degeneracy $M$. We also investigate crossover between the small and large $J$ limits in the two-orbital case M=2, using the numerical renormalization group approach., Comment: 5 pages, 3 figures

We study the Kondo effect in side-coupled double quantum dots with particular focus on the crossover between two distinct singlet ground states, using the numerical renormalization group. The crossover occurs as the quantized energy level of the embedded dot, which is connected directly to the leads, is varied. In the parameter region where the embedded dot becomes almost empty or doubly occupied, the local moment emerging in the other dot at the side of the path for the current is screened via a superexchange process by the conduction electrons tunneling through the embedded dot. In contrast, in the other region where the embedded dot is occupied by a single electron, the local moment emerges also in the embedded dot, and forms a singlet bond with the moment in the side dot. Furthermore, we derive two different Kondo Hamiltonians for these limits carrying out the Schrieffer-Wolff transformation, and show that they describe the essential feature of the screening for each case., 9 pages, 9 figures

We apply recently developed 1/(N-1) expansion to a particle-hole asymmetric SU(N) Anderson model with finite Coulomb interaction U. To leading order in 1/(N-1) it describes the Hartree-Fock random phase approximation (HF-RPA), and the higher-order corrections describe systematically the fluctuations beyond the HF-RPA. We show that the next-leading order results of the renormalized parameters for the local Fermi-liquid state agree closely with the numerical renormalization group results at N=4. It ensures the reliability of the next-leading order results for N>4, and we examine the N dependence of the local Fermi-liquid parameters. Our expansion scheme uses the standard Feynman diagrams, and has wide potential applications.

We study low-energy transport through a quantum dot coupled to one normal and two superconducting (SC) leads in a junction of Y-shape. In this geometry a crossover between Kondo dominated and Cooper-pairing dominated states occurs by tuning the parameters such as the quantized energy level of the dot and the Josephson phase, which induces a supercurrent flowing between the two SC leads through the dot. Furthermore, Andreev scattering takes place at the interface between the dot and normal lead. The low-lying energy states of this system can be described by a local Fermi-liquid theory for interacting Bogoliubov particles. In a description based on an Anderson impurity model we calculate transport coefficients, renormalized parameters and spectral function, using Wilson's numerical renormalization group (NRG) approach, in the limit of large SC gap. Our results demonstrate how the Andreev resonance level approaches the Fermi level in the crossover region between Cooper-pairing singlet state and strong coupling situation as the impurity level or Josephson phase are varied. The strong coupling situation shows a Kondo effect with a significantly renormalized resonance width. The crossover is smeared when the coupling between the dot and normal lead is large. Furthermore, asymmetry in the Josephson junction suppresses the cancellations of the SC proximity for finite Josephson phase, and it favors the SC singlet state rather than the Kondo singlet., Comment: 12 pages, 11 figures, some brief explanations are added

We apply a recently developed 1/(N-1) expansion to the full counting statistics for the N-fold degenerate Anderson impurity model in the Kondo regime. This approach is based on the perturbation theory in the Coulomb interaction U and is different from the conventional large N theories, such as the usual 1/N expansion and non-crossing approximation. We have confirmed that the calculations carried out up to order 1/(N-1)^2 agree closely with those of the numerical renormalization group at N=4, where the degeneracy is still not so large. This ensures the applicability of our approach for N>4. We present the results of the cumulants of the probability distribution function for a nonequilibrium current through a quantum dot in the particle-hole symmetric case., 4 pages, 6 figures, typos have been corrected

We study the interplay between the Kondo and Andreev-Josephson effects in a quantum dot coupled to one normal and two superconducting (SC) leads. In the large gap limit, the low-energy states of this system can be described exactly by a local Fermi liquid for the interacting Bogoliubov particles. The phase shift and the renormalized parameters for the Bogoliubov particles vary depending on the Josephson phase between the two SC leads. We explore the precise features of a crossover that occurs between the Kondo singlet and local Cooper-pairing states as the Josephson phase varies, using the numerical renormalization group approach., 4 pages, 4 figures, contribution to SCES 2011

We study low-energy properties of the $N$-fold degenerate Anderson model. Using a scaling that takes $u=(N\ensuremath{-}1)U$ as an independent variable in place of the Coulomb interaction $U$, the perturbation series in $U$ is reorganized as an expansion in powers of $1/(N\ensuremath{-}1)$. We calculate the renormalized parameters, which characterize the Kondo state, to the next leading order in the $1/(N\ensuremath{-}1)$ expansion at half-filling. The results, especially the Wilson ratio, agree very closely with the exact numerical renormalization group results at $N=4$. This ensures the applicability of our approach to $Ng4$, and we present highly reliable results for nonequilibrium Kondo transport through a quantum dot.

We investigate out of equilibrium transport through an orbital Kondo system realized in a single quantum dot, described by the multiorbital impurity Anderson model. Shot noise and current are calculated up to the third order in bias voltage in the particle-hole symmetric case, using the renormalized perturbation theory. The derived expressions are asymptotically exact at low energies. The resulting Fano factor of the backscattering current $F_b$ is expressed in terms of the Wilson ratio $R$ and the orbital degeneracy $N$ as $F_b =\frac{1 + 9(N-1)(R-1)^2}{1 + 5(N-1)(R-1)^2}$ at zero temperature. Then, for small Coulomb repulsions $U$, we calculate the Fano factor exactly up to terms of order $U^5$, and also carry out the numerical renormalization group calculation for intermediate $U$ in the case of two- and four-fold degeneracy ($N=2,\,4$). As $U$ increases, the charge fluctuation in the dot is suppressed, and the Fano factor varies rapidly from the noninteracting value $F_b=1$ to the value in the Kondo limit $F_b=\frac{N+8}{N+4}$, near the crossover region $U\sim \pi \Gamma$, with the energy scale of the hybridization $\Gamma$., Comment: 10 pages, 4 figures

The difference between parallel and perpendicular conductance in magnetic superlattices such as Fe/Cr are studied numerically with the Kubo formula and a recursion method. In the calculation, the multilayered structure of superlattices is taken into account through a periodic potential along the direction normal to the interfaces. It is shown that the magnetoresistance for the current parallel to the layers ${\mathit{MR}}_{\mathrm{\ensuremath{\parallel}}}$ is increased by the interface roughness and decreased by the bulk impurity scattering. Since the Brillouin zone is divided into a series of minizones due to the periodic potential, the magnetoresistance for the current perpendicular to the layers ${\mathit{MR}}_{\mathrm{\ensuremath{\perp}}}$ is determined by the miniband structure and becomes larger than ${\mathit{MR}}_{\mathrm{\ensuremath{\parallel}}}$.

We review the basic ideas of a renormalized perturbation theory which works directly in terms of fully dressed quasiparticles, and its application to the calculation of the current through a quantum dot both in equilibrium and non- equilibrium steady state conditions. The method is illustrated for the impurity Anderson model. We show how the relevant renormalized parameters can be de- duced from a numerical renormalization group calculation, and also how they can be generalized to include an arbitrary magnetic field. In applying the method to elec- tron transmission through quantum dot, we show how the zero field conductance can be expressed in terms of the renormalized parameters, and how asymptotically exact results at low bias voltages can be derived from the expansion to second order. The potential for the further application of this approach to this class of problems is assessed.

The triangular triple quantum dot is an interesting system which can demonstrate various types of the Kondo effects, such as the one due to the local spin S=1 moment caused by the Nagaoka ferromagnetic mechanism and the SU(4) Kondo effect. We theoretically study the low-temperature properties and the Kondo energy scale of the triangular triple quantum dot, using the Wilson numerical renormalization group. We have explored a wide parameter region of the electron-filling and distortions which break the symmetry of an equilateral structure. Our results give a comprehensive overview of how the Kondo behavior varies in the different the regions in the wide parameter space of the triangular triple quantum dot., 18 pages; 21 figures (Figs.17 and 20 are added)

We study the low-energy properties of a triangular triple quantum dot connected to two noninteracting leads in a wide parameter range, using the numerical renormalization group (NRG). Various kinds of Kondo effects take place in this system depending on the electron filling ${N}_{\text{tot}}$, or the level position ${ϵ}_{d}$ of the triple dot. The SU(4) Kondo behavior is seen in the half-filled case ${N}_{\text{tot}}\ensuremath{\simeq}3.0$ at the dip of the series conductance, and it causes a charge redistribution between the even and odd orbitals in the triangle. We show generally that the quasiparticle excitations from a local Fermi-liquid ground state acquire a channel symmetry at zero points of the two-terminal conductance, in the case the system has time-reversal and inversion symmetries. It causes the SU(4) behavior at low energies, while the orbital degeneracy in the triangle determines the high-energy behavior. At four-electron filling ${N}_{\text{tot}}\ensuremath{\simeq}4.0$, a local $S=1$ moment emerges at high temperatures due to a Nagaoka ferromagnetic mechanism. It is fully screened by the electrons from the two conducting channels via a two-stage Kondo effect, which is caused by a difference in the charge distribution in the even and odd orbitals.

The random exchange potential at the interfaces between magnetic and nonmagnetic layers is proposed to be an origin of the giant magnetoresistance in metallic superlattices. The material dependence of the potential is calculated for transition metal elements. An analysis using the Boltzmann equation shows that the theoretical results of the potential explain the giant magnetoresistance observed.

We study the transport through side-coupled double quantum dots, connected to normal and superconducting (SC) leads with a T-shape configuration. We find, using the numerical renormalization group, that the Coulomb interaction suppresses SC interference in the side dot, and enhances the conductance substantially in the Kondo regime. This behavior stands in total contrast to a wide Kondo valley seen in the normal transport. The SC proximity penetrating into the interfacial dot pushes the Kondo clouds, which screens the local moment in the side dot, towards the normal lead to make the singlet bond long. The conductance shows a peak of unitary limit as the cloud expands. Furthermore, two separate Fano structures appear in the gate-voltage dependence of the Andreev transport, where a single reduced plateau appears in the normal transport., 6 pages, 5 figures

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., Comment: 4 pages, 4 figs: typos just below (4) are corrected, results are not affected

We investigate the Josephson current J(\phi) through a quantum dot embedded between two superconductors showing a phase difference \phi. The system is modeled as a single Anderson impurity coupled to BCS leads, and the functional and the numerical renormalization group frameworks are employed to treat the local Coulomb interaction U. We reestablish the picture of a quantum phase transition occurring if the ratio between the Kondo temperature T_K and the superconducting energy gap \Delta or, at appropriate T_K/\Delta, the phase difference \phi or the impurity energy is varied. We present accurate zero- as well as finite-temperature T data for the current itself, thereby settling a dispute raised about its magnitude. For small to intermediate U and at T=0 the truncated functional renormalization group is demonstrated to produce reliable results without the need to implement demanding numerics. It thus provides a tool to extract characteristics from experimental current-voltage measurements., Comment: version accepted for publication in PRB

We examine Hall effect in layered cobalt oxides with hexagonal structure. In the $\mathrm{Co}{\mathrm{O}}_{2}$ layer, the cobalt ions form a triangular lattice. However, the electron trajectory makes up the kagome lattice due to the orbital degeneracy of ${t}_{2g}$ states. It is shown that this kagome lattice hidden in the $\mathrm{Co}{\mathrm{O}}_{2}$ layer exhibits the anomalous high-temperature Hall effect recently observed by Wang et al. (cond-mat/0305455), indicating importance of the electronic lattice different from the crystal.

We study transport through a quantum dot coupled to normal and superconducting leads using the numerical renormalization group method. We show that the low-energy properties of the system are described by the local Fermi liquid theory despite of the superconducting correlations penetrated into the dot due to a proximity effect. We calculate the linear conductance due to the Andreev reflection in the presence of the Coulomb interaction. It is demonstrated that the maximum structure appearing in the conductance clearly characterizes a crossover between two distinct spin-singlet ground states, i.e. the superconducting singlet state and the Kondo singlet state. It is further elucidated that the gate-voltage dependence of the conductance shows different behavior in the superconducting singlet region from that in the Kondo singlet region., 10 pages, 6 figures; a typo in eq. (B.5) corrected, which does not affect any other results of the paper

We theoretically study the Andreev tunneling through a quantum dot (QD) coupled to normal and superconducting leads by means of the numerical renormalization group (NRG) method. As the coupling between the QD and the normal lead gets smaller, we find that the peak structure is developed in the conductance, which clearly features crossover behavior between two distinct regions of spin‐singlet ground states, i.e. the superconducting singlet state and the Kondo singlet state. We discuss the characteristic transport properties of the Andreev tunneling in the light of local electron correlations in the QD.