Search

Break junctions of the heavy-fermion superconductors CeCu 2 Si 2 , UBe 13 , UPt 3 , URu 2 Si 2 , UPd 2 Al 3 , and UNi 2 Al 3 have been investigated. Josephson-like superconducting anomalies could be found only for low-ohmic contacts, but without the oscillatory Fraunhofer pattern of the critical current in a magnetic field. A systematic study on the contact radius demonstrates that these anomalies are mainly due to Maxwell's resistance being suppressed in the superconducting heavy-fermion phase rather than due to Josephson effect and Andreev reflection. We could not find any superconducting features by vacuum-tunneling spectroscopy.

CeNi 9 Ge 4 exhibits unusual non-Fermi liquid behavior with the largest ever recorded value of the electronic specific heat Δ C / T ≅ 5.5 J K - 2 mol - 1 without showing any evidence of magnetic order. Specific heat measurements show that the logarithmic increase of the Sommerfeld coefficient flattens off below 200 mK. In marked contrast, the local susceptibility Δ χ levels off well above 200 mK and already becomes constant below 1 K. Furthermore, the entropy reaches 2 R ln 2 below 20 K corresponding to a four-level system. An analysis of C and χ was performed in terms of an SU ( N = 4 ) single impurity Anderson model with additional crystal electric field (CEF) splitting. Numerical renormalization group calculations point to a possible consistent description of the different low-temperature scales in Δ c and Δ χ stemming from the interplay of Kondo effect and crystal field splitting.

We consider an Anderson lattice model with a spin 1/2 degenerated conduction electron band and localized ionic CEF-levels, classified according to the irreducible representation of the point group of the lattice. We present the self-consistency equations for local approximations ("$d\rightarrow\infty"$ approximation) for the periodic Anderson model. It leads to a matrix formulation of the effective local density of states and the lattice $f$-Green's function. We derive the quasi-particle life-time which enters the Boltzmann transport equations. The impact of a $k$-dependent hybridization is discussed. We prove that vertex corrections will vanish, as long as all states of an irreducible representation couple to the conduction electron band with a hybridization matrix element of the same parity., 3 pages, REVTeX type, proceedings of SCES96 Z\"urich

Spin-noise measurements can serve as direct probe for the microscopic decoherence mechanism of an electronic spin in semiconductor quantum dots (QD).We have calculated the spin-noise spectrum in the anisotropic central spin model using a Chebyshev expansion technique which exactly accounts for the dynamics up to an arbitrary long but fixed time in a finite size system. In the isotropic case, describing QD charged with a single electron, the short-time dynamics is in good agreement with a quasi-static approximation for the thermodynamic limit. The spin-noise spectrum, however, shows strong deviations at low frequencies with a power-law behavior. In the Ising limit, applicable to QDs with heavy-hole spins, the spin-noise spectrum exhibits a threshold behavior above the Larmor frequency. In the generic anisotropic central spin model we have found a crossover from a Gaussian type of spin-noise spectrum to a more Ising-type spectrum with increasing anisotropy in a finite magnetic field. In order to make contact with experiments, we present ensemble averaged spin-noise spectra for QD ensembles charged with single electrons or holes. The Gaussian-type noise spectrum evolves to a more Lorentzian shape spectrum with increasing spread of characteristic time-scales and g-factors of the individual QDs., 24 pages, 16 figures, submitted to PRB

We use the recently proposed scattering states numerical renormalization group (SNRG) approach to calculate $I(V)$ and the differential conductance through a single molecular level coupled to a local molecular phonon. We also discuss the equilibrium physics of the model and demonstrate that the low-energy Hamiltonian is given by an effective interacting resonant level model. From the NRG level flow, we directly extract the effective charge transfer scale $\Gamma_{\rm eff}$ and the dynamically induced capacitive coupling $U_{\rm eff}$ between the molecular level and the lead electrons which turns out to be proportional to the polaronic energy shift $E_p$ for the regimes investigated here. The equilibrium spectral functions for the different parameter regimes are discussed. The additional phonon peaks at multiples of the phonon frequency $\w_0$ correspond to additional maxima in the differential conductance. Non-equilibrium effects, however, lead to significant deviations between a symmetric junction and a junction in the tunnel regime. The suppression of the current for asymmetric junctions with increasing electron-phonon coupling, the hallmark of the Franck-Condon blockade, is discussed with a simple framework of a combination of (i) polaronic level shifts and (ii) the effective charge transfer scale $\Gamma_{\rm eff}$., Comment: 18 papers, 13 figures

The authors investigated metallic point contacts between a tungsten tip and the superconducting heavy-fermion compounds. On lowering the temperature to below T{sub c} the contact resistance drops by {delta}R. Usually this change in resistance is interpreted by the Andreev-reflection process at the normal-superconducting interface. However, the authors found that {delta}R does not scale with the inverse area of the orifice - as expected for Andreev reflection - but with the inverse radius and the specific resistivity in the normal state. Such a behaviour is characteristic for Maxwell`s resistance being suppressed in the superconducting heavy-fermion phase. Additionally, the residual contact resistance at zero-bias is strongly enhanced compared to the ballistic Sharvin contribution. They discuss the possible microscopic origin for the reduced or even absent Andreev-hole current and the enhanced residual resistance.

A hybrid approach to nonequilibrium dynamics of quantum impurity systems is presented. The numerical renormalization group serves as a means to generate a suitable low-energy Hamiltonian, allowing for an accurate evaluation of the real-time dynamics of the problem up to exponentially long times using primarily the time-adaptive density-matrix renormalization group. We extract the decay time of the interaction-enhanced oscillations in the interacting resonant-level model and show their quadratic divergence with the interaction strength U. Our numerical analysis is in excellent agreement with analytic predictions based on an expansion in 1/U., 5 pages, 3 figures

The time-dependent numerical renormalization-group approach (TD-NRG), originally devised for tracking the real-time dynamics of quantum-impurity systems following a single quantum quench, is extended to multiple switching events. This generalization of the TD-NRG encompasses the possibility of periodic switching, allowing for coherent control of strongly correlated systems by an external time-dependent field. To this end, we have embedded the TD-NRG in a hybrid framework that combines the outstanding capabilities of the numerical renormalization group to systematically construct the effective low-energy Hamiltonian of the system with the prowess of complementary approaches for calculating the real-time dynamics derived from this Hamiltonian. We demonstrate the power of our approach by hybridizing the TD-NRG with the Chebyshev expansion technique in order to investigate periodic switching in the interacting resonant-level model. Although the interacting model shares the same low-energy fixed point as its noninteracting counterpart, we surprisingly find the gradual emergence of damped oscillations as the interaction strength is increased. Focusing on a single quantum quench and using a strong-coupling analysis, we reveal the origin of these interaction-induced oscillations and provide an analytical estimate for their frequency. The latter agrees well with the numerical results., 20 pager, Revtex, 10 figures, submitted to Physical Review B

We discuss the two-channel Kondo problem with a pseudogap density of states, $\rho(\w)\propto|\w|^r$, of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi liquid behavior of the metallic $r=0$ case, is replaced by a stable particle-hole symmetric intermediate-coupling fixed point for $0\rmax$, this non-Fermi liquid phase disappears, and instead a critical fixed point with an emergent spin--channel symmetry appears, controlling the quantum phase transition between two phases with stable spin and channel moments, respectively. We propose low-energy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ epsilon expansion techniques to calculate critical properties near the critical dimensions $r=0$ and $r=1$, the latter being potentially relevant for two-channel Kondo impurities in neutral graphene. We find the analytical results to be in excellent agreement with those obtained from applying Wilson's numerical renormalization group technique., Comment: Added references

Conductance measurements of a molecular wire, contacted between an epitaxial molecule-metal bond and the tip of a scanning tunneling microscope, are reported. Controlled retraction of the tip gradually de-hybridizes the molecule from the metal substrate. This tunes the wire into the Kondo regime in which the renormalized molecular transport orbital serves as spin impurity at half filling and the Kondo resonance opens up an additional transport channel. Numerical renormalization group simulations suggest this type of behavior to be generic for a common class of metal molecule bonds. The results demonstrate a new approach to single-molecule experiments with atomic-scale contact control and prepare the way for the ab initio simulation of many-body transport through single-molecule junctions., Comment: Main text: 41 pages including references and captions, 9 figures. Supplementary information: 5 pages including 2 figures New experimental and theoretical data supporting initial claims are added. The paper has been reworked from the letter format into a longer version

In a recent work Zhang and coworkers (PRB 82, 075111 (2010)) studied the Zeeman splitting of the Kondo resonance for the single impurity Anderson model in a finite magnetic field $B$ with the numerical renormalization group (NRG) method. There, it was found that with increasing magnetic field $B$ the position of the Kondo resonance in the total spectral function \textit{does not} approach its position in the spin resolved spectral function. Additionally, the position of the Kondo maximum exceeded the Zeeman energy for $B/ T_K\gtrsim 5-10$, where $T_K$ is the low energy Kondo scale of the model ($g=2$, $\mu_B=k_B=\hbar=1$). In this comment we argue that both these findings are produced by an improper choice of NRG parameter values. However, we reproduce the crossover in the splitting from Kondo-like behavior to a non-universal splitting larger than the Zeeman energy, but this crossover occurs at much larger fields of the order of the charge scale., Comment: Minor revisions; same version as published

We calculate the nonequilibrium differential conductance $G(V)$ through a quantum dot as function of bias voltage $V$ and applied magnetic field $H$. We use a Keldysh conserving approximation for weakly correlated and the scattering states numerical renormalization group for the intermediate and strongly correlated regime out of equilibrium. In the weakly correlated regime, the Zeeman splitting observable in $G(V)$ strongly depends on the asymmetry of the coupling to the two leads, as well as on particle-hole asymmetry of the quantum dot. In contrast, in the strongly correlated regime, where Kondo-correlations dominate, the position $\Delta_K$ of the Zeeman-split zero-bias anomaly is independent of such asymmetries and always found to be of the order of the Zeeman energy $\Delta_0$. We find a crossover from the purely spin-fluctuation driven Kondo regime at small magnetic fields with $\Delta_K\Delta_0$ as it was observed in recent experiments., Comment: 3 figures

We study kinks in the electronic dispersion of a generic strongly correlated system by dynamic mean-field theory (DMFT). The focus is on doped systems away from particle-hole symmetry where valence fluctuations matter potentially. Three different algorithms are compared to asses their strengths and weaknesses, as well as to clearly distinguish physical features from algorithmic artifacts. Our findings extend a view previously established for half-filled systems where kinks reflect the coupling of the fermionic quasiparticles to emergent collective modes, which are identified here as spin fluctuations. Kinks are observed when strong spin fluctuations are present and, additionally, a separation of energy scales for spin and charge excitations exists. Both criteria are met by strongly correlated systems close to a Mott-insulator transition. The energies of the kinks and their doping dependence fit well to the kinks in the cuprates, which is surprising in view of the spatial correlations neglected by DMFT., Comment: 13 pages, 15 figures

We investigate the charge transfer characteristics of one and two excess charges in a DNA base-pair dimer using a model Hamiltonian approach. The electron part comprises diagonal and off-diagonal Coulomb matrix elements such a correlated hopping and the bond-bond interaction, which were recently calculated by Starikov [E. B. Starikov, Philos. Mag. Lett. 83, 699 (2003)] for different DNA dimers. The electronic degrees of freedom are coupled to an ohmic or a superohmic bath serving as dissipative environment. We employ the numerical renormalization group method in the nuclear tunneling regime and compare the results to Marcus theory for the thermal activation regime. For realistic parameters, the rate that at least one charge is transferred from the donor to the acceptor in the subspace of two excess electrons significantly exceeds the rate in the single charge sector. Moreover, the dynamics is strongly influenced by the Coulomb matrix elements. We find sequential and pair transfer as well as a regime where both charges remain self-trapped. The transfer rate reaches its maximum when the difference of the on-site and intersite Coulomb matrix element is equal to the reorganization energy which is the case in a guanine/cytosine (GC)-dimer. Charge transfer is completely suppressed for two excess electrons in adenine/thymine (AT)-dimer in an ohmic bath and replaced by damped coherent electron-pair oscillations in a superohmic bath. A finite bond-bond interaction $W$ alters the transfer rate: it increases as function of $W$ when the effective Coulomb repulsion exceeds the reorganization energy (inverted regime) and decreases for smaller Coulomb repulsion.

The electronic spectrum of a chemically contacted molecule in the junction of a scanning tunneling microscope can be modified by tip retraction. We analyze this effect by a combination of density functional, many-body perturbation and numerical renormalization group theory, taking into account both the non-locality and the dynamics of electronic correlation. Our findings, in particular the evolution from a broad quasiparticle resonance below to a narrow Kondo resonance at the Fermi energy, correspond to the experimental observations., Comment: 4 pages, 3 figures

The interplay of a direct ferromagnetic exchange interaction I>0 between local and band states and an indirect antiferromagnetic exchange -J >I in terms of a universal picture as well as the crossover near J approximately=I to the trivial regime J<

We discuss a particular source of error in the Numerical Renormalization Group (NRG) method for quantum impurity problems, which is related to a renormalization of impurity parameters due to the bath propagator. At any step of the NRG calculation, this renormalization is only partially taken into account, leading to systematic variation of the impurity parameters along the flow. This effect can cause qualitatively incorrect results when studying quantum critical phenomena, as it leads to an implicit variation of the phase transition's control parameter as function of the temperature and thus to an unphysical temperature dependence of the order-parameter mass. We demonstrate the mass-flow effect for bosonic impurity models with a power law bath spectrum, J(w) ~ w^s, namely the dissipative harmonic oscillator and the spin-boson model. We propose an extension of the NRG to correct the mass-flow error. Using this, we find unambiguous signatures of a Gaussian critical fixed point in the spin-boson model for s, 13 pages, 11 figs

The quantum transport through nanoscale junctions is governed by the charging energy $U$ of the device. We employ the recently developed scattering-states numerical renormalization group approach to open quantum systems to study nonequilibrium Green functions and current-voltage characteristics of such junctions for small and intermediate values of $U$. The reliability of the approach is established by the excellent agreement with diagrammatic Kadanoff-Baym-Keldysh results at small values of the $U$. We demonstrate the limits of the diagrammatic approaches at intermediate Coulomb repulsion. These approaches predict two different low-energy scale for magnetic and charge fluctuations in zero bias while the numerical renormalization group approach correctly yields only one single, universal scale. At large voltages and intermediate values of the Coulomb repulsion the self-consistent second Born as well as the GW approximation reproduce the SNRG spectral functions quite well for a symmetric junctions, while for the asymmetric model the voltage-dependent redistribution of spectral weight differs significantly. The second-order perturbation theory does not capture the correct single-particle dynamics at large bias and violates current conservation for asymmetric junctions., Comment: To be published in Phys. Rev. B 81, Issue 16

We investigate the influence of spin-orbit coupling on the Kondo effects in carbon nanotube quantum dots, using the numerical renormalization group technique. A sufficiently large spin-orbit coupling is shown to destroy the SU(4) Kondo effects at zero magnetic field, leaving only two SU(2) Kondo effects in the one- and three-electron Coulomb blockade valleys. On applying a finite magnetic field, two additional, spin-orbit induced SU(2) Kondo effects arise in the three- and two-electron valleys. Using physically realistic model parameters, we calculate the differential conductance over a range of gate voltages, temperatures and fields. The results agree well with measurements from two different experimental devices in the literature, and explain a number of observations that are not described within the standard framework of the SU(4) Anderson impurity model., Comment: 15 pages, 11 figures

An account is given of transport coefficients of heavy fermion systems in magnetic field as calculated by perturbation theory with respect to hybridization, i.e, the LNCA-technique, applied to a Kondo-lattice model. After a short discussion of the underlying approximations, including the use of a proper relaxation time and its calculation via local self-energy, and of the reliability of the LNCA in magnetic field, numerical results for the Hall constant, magnetoresistivity and thermopower as functions of temperature and field are presented. The discussion concentrates on the coherent Fermi-liquid regime at low temperature and field and concludes with a short comparison to a semiphenomenological treatment within Fermi-liquid theory.

A thorough account is given on the accuracy of assumptions and the validity of mathematical manipulations underlying the derivation of the Friedel sum rule and the so called density of states sum rule for electrons with strong local correlations. While possible exceptions are pointed out and discussed, the sum rules should hold rather well for realistically chosen parameters in models describing e.g. heavy fermion systems. They are used to assert the correctness of NCA calculations for large degeneracyN and to estimate their shortcomings forN=2. A discussion of the corresponding violation of Fermiliquid properties is extended to the case of an applied magnetic field and put into context with the calculation of (magneto-) transport properties of Kondo impurities and Kondo lattices.

The influence of substitutional disorder on the transport properties of heavy-fermion systems is investigated. We extend the dynamical mean-field theory treatment of the periodic Anderson model (PAM) to a coherent-potential approximation for disordered strongly correlated electron systems. Considering two distinct local environments of a binary alloy $A_c B_{1-c}$ with arbitrary concentration $c$, we explore two types of disorder: on the f site and on the ligand sites. We calculate the spectral functions and self-energies for the disordered PAM as well as the temperature dependence of the resistivity and the thermoelectric power. The characteristic concentration dependence as well as the order of magnitude of transport properties are reproduced for metallic heavy-fermion systems and Kondo insulators. In particular, sign changes of the Seebeck coefficient as function of temperature and concentration are observed., 17 pages, 22 figures, published version

We propose a numerical renormalization group (NRG) approach to steady-state currents through nano-devices. A discretization of the scattering-states continuum ensures the correct boundary condition for an open quantum system. We introduce two degenerate Wilson chains for current carrying left and right-moving electrons reflecting time-reversal symmetry in the absence of a finite bias $V$. We employ the time-dependent NRG to evolve the known steady-state density operator for a non-interacting junction into the density operator of the fully interacting nano-device at finite bias. We calculate the temperature dependent current as function of $V$ and applied external magnetic field using a recently developed algorithm for non-equilibrium spectral functions., 4 pages, 6 figures

Electron transfer processes play a central role in many chemical and biological systems. Already the transfer of a single electron from the donor to the acceptor can be viewed as a complicated many-body problem, due to the coupling of the electron to the infinitely many environmental degrees of freedom, realized by density fluctuations of the solvent or molecular vibrations of the protein matrix. We focus on the quantum mechanical modelling of two-electron transfer processes whose dynamics is governed by the Coulomb interaction between the electrons as well as the environmental degrees of freedoms represented by a bosonic bath. We identify the regime of parameters in which concerted transfer of the two electrons occurs and discuss the influence of the Coulomb repulsion and the coupling strength to the environment on the electron transfer rate. Calculations are performed using the non-perturbative numerical renormalization group approach for both equilibrium and non-equilibrium properties.

We investigate nonequilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures, Marcus transfer rates are evaluated, and at low temperatures, we calculate equilibrium and nonequilibrium population probabilities of the donor and acceptor with the nonperturbative numerical renormalization group approach. We obtain the nonequilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend nonmonotonically on the difference between the intersite and on-site Coulomb interaction, which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.

We present a method for the calculation of dynamical correlation functions of quantum impurity systems out of equilibrium using Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain and embeds the recently derived algorithm for equilibrium spectral functions. Our method fulfills the spectral weight conserving sum-rule exactly by construction. A local Coulomb repulsion $U>0$ is switched on at $t=0$, and the asymptotic steady-state spectral functions are obtained for various values of $U$ as well as magnetic field strength $H$ and temperature $T$. These benchmark tests show excellent agreement between the time-evolved and the directly calculated equilibrium NRG spectra for finite $U$. This method could be used for calculating steady-state non-equilibrium spectral functions at finite bias through interacting nano-devices., 21 pages, 6 figures

We present numerical renormalization group calculations for the zero-bias conductance of quantum dots made from semiconducting carbon nanotubes. These explain and reproduce the thermal evolution of the conductance for different groups of orbitals, as the dot-lead tunnel coupling is varied and the system evolves from correlated Kondo behavior to more weakly correlated regimes. For integer fillings $N=1,2,3$ of an SU(4) model, we find universal scaling behavior of the conductance that is distinct from the standard SU(2) universal conductance, and concurs quantitatively with experiment. Our results also agree qualitatively with experimental differential conductance maps., Comment: 4 pages, 5 figures

We study the spin-1/2 single-channel Anderson impurity model with correlated (occupancy dependent) hybridization for molecular transistors using the numerical renormalization-group method. Correlated hybridization can induce nonuniversal deviations in the normalized zero-bias conductance and, for some parameters, modestly enhance the spin polarization of currents in applied magnetic field. Correlated hybridization can also explain a gate-voltage dependence to the Kondo scale similar to what has been observed in recent experiments., 4 pages, 5 figures

Employing the non-perturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with spectral density J(omega) propto omega^s. We show that, in contrast to the case of ohmic damping, the delocalized phase of the sub-ohmic model cannot be characterized by a single energy scale only, due to the presence of a non-trivial quantum phase transition. In the strongly sub-ohmic regime, s<, 4 pages, 6 figures; final version, as published

Nonlinear susceptibility $({\ensuremath{\chi}}_{3})$ measurements were performed on single crystals of the heavy fermion superconductor ${\mathrm{PrOs}}_{4}{\mathrm{Sb}}_{12}$ in order to probe the nature of the ${\mathrm{Pr}}^{3+}$ ground state in the crystalline electric field. Calculations of ${\ensuremath{\chi}}_{3}(T)$ have been carried out (i) within a mean field model of intersite magnetic and quadrupolar interactions for an ionic (zero hybridization) crystal field ${\ensuremath{\Gamma}}_{1}$ singlet ground state and a first excited state magnetic triplet, and (ii) within a two-channel Anderson impurity model assuming a ${\ensuremath{\Gamma}}_{23}$ doublet ground state. The experimental ${\ensuremath{\chi}}_{3}$ results are in best agreement with the nonmagnetic ${\ensuremath{\Gamma}}_{1}$ ground state in the tetrahedral crystalline electric field of the ${\mathrm{Pr}}^{3+}$ ions with antiferroquadrupolar intersite coupling and weak antiferromagnetic intersite coupling.

A detailed derivation of the recently proposed time-dependent numerical renormalization-group (TD-NRG) approach to nonequilibrium dynamics in quantum impurity systems is presented. We demonstrate that the method is suitable for fermionic as well as bosonic baths. A comparison with exact analytical results for the charge relaxation in the resonant-level model and for dephasing in the spin-boson model establishes the accuracy of the method. The real-time dynamics of a single spin coupled to both types of baths is investigated. We use the TD-NRG to calculate the spin relaxation and spin precession of a single Kondo impurity. The short- and long-time dynamics is studied as a function of temperature in the ferromagnetic and antiferromagnetic regimes. The short-time dynamics agrees very well with analytical results obtained at second order in the exchange coupling $J$. In the ferromagnetic regime, the long-time spin decay is described by the scaling variable $x = 2\rho_F J(T) T t$. In the antiferromagnetic regime it is governed for $T < T_K$ by the Kondo time scale $1/T_K$. Here $\rho_F$ is the conduction-electron density of states and $T_K$ is the Kondo temperature. Results for spin precession are obtained by rotating the external magnetic field from the x axis to the z axis., Comment: Revtex, 21 pages, 11 figures, 1 table

We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain. In contrast to all previous methods, it does not suffer from overcounting of excitation. By construction, it always fulfills sum rules for spectral functions. Furthermore, it accurately reproduces local thermodynamic expectation values, such as occupancy and magnetization, obtained directly from the numerical renormalization group calculations., Comment: 13 pages, 7 figure

Mechanical-controllable break junctions of the heavy-fermion superconductors can show Josephson-like superconducting anomalies. But a systematic study on the contact size demonstrates that these anomalies are mainly due to Maxwell's resistance being suppressed in the superconducting heavy-fermion phase. Up to day, we could not find any superconducting features by vacuum-tunnelling spectroscopy, providing further evidence for the pair-breaking effect of the heavy-fermion interfaces.

We develop a general approach to the nonequilibrium dynamics of quantum impurity systems for arbitrary coupling strength. The numerical renormalization group is used to generate a complete basis set necessary for the correct description of the time evolution. We benchmark our method with the exact analytical solution for the resonant-level model. As a first application, we investigate the equilibration of a quantum dot subject to a sudden change of the gate voltage and external magnetic field. Two distinct relaxation times are identified for the spin and charge dynamics., 5 pages, 5 figures

The impurity Green function and dynamical susceptibilties for the two-channel Anderson impurity model are calculated. An exact expression for the self-energy of the impurity Green function is derived. The imaginary part of the self-energy scales as $\sqrt{|\w/T_K|}$ for $T\to 0$ serving as a hallmark for non-Fermi behavior. The many-body resonance is pinned to a universal value $1/(2\pi\Delta)$ at $\w=0$. Its shape becomes increasingly more symmetric for the Kondo-regimes of the model. The dynamical susceptibilities are governed by two energy scales $T_K$ and $T_h$ and approach a constant value for $\w\to 0$, whereas relation $\chi''(\w)\propto \w$ holds for the single channel model., Comment: 4 pages, 4 figure, revtex

The recently reported unusual behavior of the static and dynamical magnetic susceptibility as well as the specific heat in Ce$_{1-x}$La$_{x}$Ni$_{9}$Ge$_4$ has raised the question of a possible non-Fermi liquid ground state in this material. We argue that for a consistent physical picture the crystal field splitting of two low lying magnetic doublets of the Ce $4f$-shell must be taken into account. Furthermore, we show that for a splitting of the order of the low temperature scale $T^*$ of the system a crossover behavior between an SU(4) and an SU(2) Kondo effect is found. The screening of the two doublets occurs on different temperature scales leading to a different behavior of the magnetic susceptibility and the specific heat at low temperatures. The experimentally accessible temperature regime down to 50mK still lies in the extended crossover regime into a strong coupling Fermi-liquid fixed point., Comment: 4 pages, 4 figures, revtex4

The f-electron spectral function of the Falicov-Kimball model is calculated within the dynamical mean-field theory using the numerical renormalization group method as the impurity solver. Both the Bethe lattice and the hypercubic lattice are considered at half filling. For small U we obtain a single-peaked f-electron spectral function, which --for zero temperature-- exhibits an algebraic (X-ray) singularity ($|\omega|^{-\alpha}$) for $\omega \to 0$. The characteristic exponent $\alpha$ depends on the Coulomb (Hubbard) correlation U. This X-ray singularity cannot be observed when using alternative (Keldysh-based) many-body approaches. With increasing U, $\alpha$ decreases and vanishes for sufficiently large U when the f-electron spectral function develops a gap and a two-peak structure (metal-insulator transition)., Comment: 8 pages, 8 figures, revtex

The non-Fermi-liquid properties of an ultrasmall quantum dot coupled to a lead and to a quantum box are investigated. Tuning the ratio of the tunneling amplitudes to the lead and box, we find a line of two-channel Kondo fixed points for arbitrary Coulomb repulsion on the dot, governing the transition between two distinct Fermi-liquid regimes. The Fermi liquids are characterized by different values of the conductance. For an asymmetric dot, spin and charge degrees of freedom are entangled: a continuous transition from a spin to a charge two-channel Kondo effect evolves. The crossover temperature to the two-channel Kondo effect is greatly enhanced away from the local-moment regime, making this exotic effect accessible in realistic quantum-dot devices., 5 figures

An ultrasmall quantum dot coupled to a lead and to a quantum box (a large quantum dot) is investigated. Tuning the tunneling amplitudes to the lead and box, we find a line of unstable non-Fermi-liquid fixed points as function of the gate potentials of the quantum dots, extending to arbitrary charging energies on the small and large quantum dots. These quantum-critical fixed points possess a finite residual entropy. They govern the cross over from one Fermi-liquid regime to another, characterized by distinct (high and low) conductance values., 2 pages, 3 figures, Elsevier Science style

The charging of a quantum box, coupled to a lead by tunneling through a single resonant level, is studied near the degeneracy points of the Coulomb blockade. Combining Wilson's numerical renormalization-group method with perturbative scaling approaches, the corresponding low-energy Hamiltonian is solved for arbitrary temperatures, gate voltages, tunneling rates, and energies of the impurity level. Similar to the case of a weak tunnel barrier, the shape of the charge step is governed at low temperatures by the non-Fermi-liquid fixed point of the two-channel Kondo effect. However, the associated Kondo temperature TK is strongly modified. Most notably, TK is proportional to the width of the level if the transmission through the impurity is close to unity at the Fermi energy, and is no longer exponentially small in one over the tunneling matrix element. Focusing on a particle-hole symmetric level, the two-channel Kondo effect is found to be robust against the inclusion of an on-site repulsion on the level. For a large on-site repulsion and a large asymmetry in the tunneling rates to box and to the lead, there is a sequence of Kondo effects: first the local magnetic moment that forms on the level undergoes single-channel screening, followed by two-channel overscreening of the charge fluctuations inside the box., 21 pages, 19 figures

The charging of a quantum box connected to a lead by a single-mode point contact is solved for arbitrary temperatures, tunneling amplitudes, and gate voltages, using a variant of Wilson's numerical renormalization group. The charge inside the box and the capacitance of the junction are calculated on equal footing for all physical regimes, including weak tunneling, near perfect transmission, and the crossover regime in between. At the charge plateaus, perturbation theory is found to break down at fairly small tunneling amplitudes. Near perfect transmission, we confirm Matveev's scenario for the smearing of the Coulomb-blockade staircase. A surprising reentrance of the Coulomb-blockade staircase is found for large tunneling amplitudes. At the degeneracy points, we obtain two-channel Kondo behavior directly from the Coulomb-blockade Hamiltonian, without the restriction to two charge configurations or the introduction of an effective cutoff.

Heavy fermion systems (HFS) are described by the periodic Anderson model (PAM), which is studied within the dynamical mean-field theory (DMFT), mapping the PAM on an effective single-impurity Anderson model (SIAM) to be determined selfconsistently, which becomes exact in the limit of high spatial dimensions, d → ∞. We use the modified perturbation theory (MPT) as approximation for the effective SIAM. The MPT is exact up to second order in the Coulomb correlation U and simultaneously reproduces the exact results for the atomic limit and the lowest moments. Within this approximation we have calculated the temperature dependence of the resistivity, the thermopower and the frequency and temperature dependence of the dynamical conductivity. For all these quantities the typical HFS-behavior is qualitatively well reproduced within our treatment.

The quantitative control of the dynamic correlations of single impurity Anderson models is essential in several very active fields. We analyze the one-particle Green function with a constant energy resolution by dynamic density-matrix renormalization. In contrast to other approaches, sharp dominant resonances at high energies are found. Their origin and importance are discussed., Comment: 4 pages, 5 figures included, final version

An unconventional superconducting phase is explored developing out of a non Fermi-liquid phase of the two-channel Anderson lattice model. It is characterized by a composite order parameter comprising of a local spin or orbital degree of freedom bound to triplet Cooper pairs with an isotropic and a nearest neighbour form factor. The superconducting transition temperature peaks in the moderate intermediate valence regime and vanishes at integral valence. The gap function is non analytic and odd in frequency, and a pseudo-gap develops in the conduction electron density of states which vanishes as $|\omega|$ close to $\omega=0$., Comment: 4 pages, 4 figures, RevTex 4

Including explicitly the exchange interaction between conduction electrons and f-electrons in the Anderson Hamiltonian the competition between the hopping-induced antiferromagnetic interaction and the ferromagnetic exchange interaction in dynamical quantities is investigated using scaling ideas. Furthermore, the influence of Coulomb interactions between conduction electrons and empty f-sites is studied.

The magnetic properties of the two-channel periodic Anderson model for uranium ions, comprised of a quadrupolar and a magnetic doublet are investigated through the crossover from the mixed-valent to the stable moment regime using dynamical mean field theory. In the mixed-valent regime ferromagnetism is found for low carrier concentration on a hyper-cubic lattice. The Kondo regime is governed by band magnetism with small effective moments and an ordering vector $\q$ close to the perfect nesting vector. In the stable moment regime nearest neighbour anti-ferromagnetism dominates for less than half band filling and a spin density wave transition for larger than half filling. $T_m$ is governed by the renormalized RKKY energy scale $\mu_{eff}^2 ^2 J^2\rho_0(\mu)$., Comment: 4 pages, RevTeX, 3 eps figures

We investigate the mixed-valent regime of a two-configuration Anderson impurity model for uranium ions, with separate quadrupolar and magnetic doublets. With a new Monte Carlo approach and the non-crossing approximation we find: (i) A non-Fermi-liquid fixed point with two-channel Kondo model critical behavior; (ii) Distinct energy scales for screening the low-lying and excited doublets; (iii) A semi-quantitative explanation of magnetic-susceptibility data for U$_{1-x}$Th$_x$Be$_{13}$ assuming 60-70% quadrupolar doublet ground-state weight, supporting the quadrupolar-Kondo interpretation., 4 Pages, 3 eps figures; submitted to Phys. Rev. Lett

We investigate the (electronic) transport properties and the characteristic low-temperature scales of heavy-fermion systems (HFS), which are described within the periodic Anderson model (PAM). The PAM is mapped onto an effective single impurity Anderson model (SIAM) by dynamical mean-field theory (DMFT). The SIAM is treated with the numerical renormalisation group (NRG), a non-perturbative method which yields the accurate Kondo temperature scale and low-temperature properties. We calculate the temperature dependence of the resistivity and the thermoelectrical power and are able to reproduce qualitatively the experimental results typical for HFS.

We use different numerical approaches to calculate the double occupancy and mag- netic susceptibility as a function of a bias voltage in an Anderson impurity model. Specifically, we compare results from the Matsubara-voltage quantum Monte-Carlo approach (MV-QMC), the scattering-states numerical renormalization group (SNRG), and real-time quantum Monte-Carlo (RT-QMC), covering Coulomb repulsions ranging from the weak-coupling well into the strong- coupling regime. We observe a distinctly different behavior of the double occupancy and the magnetic response. The former measures charge fluctuations and thus only indirectly exhibits the Kondo scale, while the latter exhibits structures on the scale of the equilibrium Kondo tempera- ture. The Matsubara-voltage approach and the scattering-states numerical renormalization group yield consistent values for the magnetic susceptibility in the Kondo limit. On the other hand, all three numerical methods produce different results for the behavior of charge fluctuations in strongly interacting dots out of equilibrium., Comment: 6 pages, 4 figures

The paramagnetic phase of the two-channel Kondo lattice model is examined with a Quantum Monte Carlo simulation in the limit of infinite dimensions. We find non-Fermi-liquid behavior at low temperatures including a finite low-temperature single-particle scattering rate, no Fermi distribution discontinuity, and zero Drude weight. Both the optical and quasiparticle mass enhancement and scattering relaxation rate show consistent evidence of non-fermi liquid behavior. However, the low-energy density of electronic states is finite., 5 pages, LaTeX and 4 PS figures