Beyond the Nca: New Results for the Spectral Properties of the Anderson Model

In the framework of direct perturbation theory a fully self-consistent approximation beyond the well known NCA will be presented for the Anderson Model. The resummation of a class of skeleton diagrams up to infinite order in $V$ includes all contribution up to the order $O(1/N^2)$ ( $N$ = degeneracy of the magnetic state). Qualitative improvements in maintaining local Fermi-Liquid relations and one-particle spectral properties in comparison to the well known NCA will be reported. The location and temperature dependence of the AS-resonance for the case $N=2$ is found to be rather close to the chemical potential in excellent agreement with Friedel's sum rule; the static magnetic susceptibility exhibits the same $N$-dependence as the exact {\em Bethe-Ansatz} solution.Comment: 3 pages including 4 figures, Postscript file, self-extracting shell script;(submitted to the SCES 94 Conference, Amsterdam

Fluctuation Exchange Analysis of Superconductivity in the Standard Three-Band CuO2 Model

The fluctuation exchange, or FLEX, approximation for interacting electrons is applied to study instabilities in the standard three-band model for CuO2 layers in the high-temperature superconductors. Both intra-orbital and near-neigbor Coulomb interactions are retained. The filling dependence of the d(x2-y2) transition temperature is studied in both the "hole-doped" and "electron-doped" regimes using parameters derived from constrained-occupancy density-functional theory for La2CuO4. The agreement with experiment on the overdoped hole side of the phase diagram is remarkably good, i.e., transitions emerge in the 40 K range with no free parameters. In addition the importance of the "orbital antiferromagnetic," or flux phase, charge density channel is emphasized for an understanding of the underdoped regime.Comment: REVTex and PostScript, 31 pages, 26 figures; to appear in Phys. Rev. B (1998); only revised EPS figures 3, 4, 6a, 6b, 6c, 7 and 8 to correct disappearance of some labels due to technical problem

Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling

We present a general framework how to investigate stability of solutions within a single self-consistent renormalization scheme being a parquet-type extension of the Baym-Kadanoff construction of conserving approximations. To obtain a consistent description of one- and two-particle quantities, needed for the stability analysis, we impose equations of motion on the one- as well on the two-particle Green functions simultaneously and introduce approximations in their input, the completely irreducible two-particle vertex. Thereby we do not loose singularities caused by multiple two-particle scatterings. We find a complete set of stability criteria and show that each instability, singularity in a two-particle function, is connected with a symmetry-breaking order parameter, either of density type or anomalous. We explicitly study the Hubbard model at intermediate coupling and demonstrate that approximations with static vertices get unstable before a long-range order or a metal-insulator transition can be reached. We use the parquet approximation and turn it to a workable scheme with dynamical vertex corrections. We derive a qualitatively new theory with two-particle self-consistence, the complexity of which is comparable with FLEX-type approximations. We show that it is the simplest consistent and stable theory being able to describe qualitatively correctly quantum critical points and the transition from weak to strong coupling in correlated electron systems.Comment: REVTeX, 26 pages, 12 PS figure

Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.Comment: 17 pages, 4 figures, REVTe

Superconducting instability in the Holstein-Hubbard model: A numerical renormalization group study

We have studied the d-wave pairing-instability in the two-dimensional Holstein-Hubbard model at the level of a full fluctuation exchange approximation which treats both Coulomb and electron-phonon (EP) interaction diagrammatically on an equal footing. A generalized numerical renormalization group technique has been developed to solve the resulting self-consistent field equations. The $d$-wave superconducting phase diagram shows an optimal T_c at electron concentration ~ 0.9 for the purely electronic Hubbard system. The EP interaction suppresses the d-wave T_c which drops to zero when the phonon-mediated on-site attraction $U_p$ becomes comparable to the on-site Coulomb repulsion $U$. The isotope exponent $\alpha$ is negative in this model and small compared to the classical BCS value $\alpha_{BCS} = 1/2$ or compared to typical observed values in non-optimally doped cuprate superconductors.Comment: 4 pages RevTeX + 3 PS figures include

Reduction of Tc due to Impurities in Cuprate Superconductors

In order to explain how impurities affect the unconventional superconductivity, we study non-magnetic impurity effect on the transition temperature using on-site U Hubbard model within a fluctuation exchange (FLEX) approximation. We find that in appearance, the reduction of Tc roughly coincides with the well-known Abrikosov-Gor'kov formula. This coincidence results from the cancellation between two effects; one is the reduction of attractive force due to randomness, and another is the reduction of the damping rate of quasi-particle arising from electron interaction. As another problem, we also study impurity effect on underdoped cuprate as the system showing pseudogap phenomena. To the aim, we adopt the pairing scenario for the pseudogap and discuss how pseudogap phenomena affect the reduction of Tc by impurities. We find that 'pseudogap breaking' by impurities plays the essential role in underdoped cuprate and suppresses the Tc reduction due to the superconducting (SC) fluctuation.Comment: 14 pages, 28 figures To be published in JPS

A model of semimetallic behavior in strongly correlated electron systems

Metals with values of the resistivity and the Hall coefficient much larger than typical ones, e.g., of sodium, are called semimetals. We suggest a model for semimetals which takes into account the strong Coulomb repulsion of the charge carriers, especially important in transition-metal and rare-earth compounds. For that purpose we extend the Hubbard model by coupling one additional orbital per site via hybridization to the Hubbard orbitals. We calculate the spectral function, resistivity and Hall coefficient of the model using dynamical mean-field theory. Starting from the Mott-insulating state, we find a transition to a metal with increasing hybridization strength (``self-doping''). In the metallic regime near the transition line to the insulator the model shows semimetallic behavior. We compare the calculated temperature dependence of the resistivity and the Hall coefficient with the one found experimentally for $\rm Yb_4As_3$. The comparison demonstrates that the anomalies in the transport properties of $\rm Yb_4As_3$ possibly can be assigned to Coulomb interaction effects of the charge carriers not captured by standard band structure calculations.Comment: 9 pages RevTeX with 7 ps figures, accepted by PR

Knight Shift Anomalies in Heavy Electron Materials

We calculate non-linear Knight Shift $K$ vs. susceptibility $\chi$ anomalies for Ce ions possessing local moments in metals. The ions are modeled with the Anderson Hamiltonian and studied within the non-crossing approximation (NCA). The $K-vs.- \chi$ non-linearity diminishes with decreasing Kondo temperature $T_0$ and nuclear spin- local moment separation. Treating the Ce ions as an incoherent array in CeSn$_3$, we find excellent agreement with the observed Sn $K(T)$ data.Comment: 4 pages, Revtex, 3 figures available upon request from [email protected]

Theory of Scanning Tunneling Spectroscopy of a Magnetic Adatom on a Metallic Surface

A comprehensive theory is presented for the voltage, temperature, and spatial dependence of the tunneling current between a scanning tunneling microscope (STM) tip and a metallic surface with an individual magnetic adatom. Modeling the adatom by a nondegenerate Anderson impurity, a general expression is derived for a weak tunneling current in terms of the dressed impurity Green function, the impurity-free surface Green function, and the tunneling matrix elements. This generalizes Fano's analysis to the interacting case. The differential-conductance lineshapes seen in recent STM experiments with the tip directly over the magnetic adatom are reproduced within our model, as is the rapid decay, \sim 10\AA, of the low-bias structure as one moves the tip away from the adatom. With our simple model for the electronic structure of the surface, there is no dip in the differential conductance at approximately one lattice spacing from the magnetic adatom, but rather we see a resonant enhancement. The formalism for tunneling into small clusters of magnetic adatoms is developed.Comment: 12 pages, 9 figures; to appear in Phys. Rev.

STUDIES IN PORPHYRIA

Porphyrin biosynthesis in mammalian skin and in skin obtained from patients with selected types of porphyria has been studied. Cutaneous porphyrinogenesis required the precursor δ-aminolevulinic acid (ALA) which, when added to murine, rat, and human skin in vitro, was rapidly converted to porphyrins. Total porphyrin content was quantitated by fluorescence assay, and spectral studies indicated that more than 80% of the porphyrin produced was protoporphyrin. The majority of skin porphyrinogenesis occurred in epidermis or in epidermal derivatives such as hair roots. Known inducers of hepatic δ-aminolevulinic acid synthetase (ALAS), the rate-limiting enzyme for heme biosynthesis, were not inducers when added to skin in vitro.Skin from patients with acute intermittent porphyria demonstrated a 43% decrease in cutaneous porphyrin production as compared to unaffected normals. This is consistent with the known deficiency of uroporphyrinogen synthetase that has been previously demonstrated in the liver and red blood cells of these patients. Porphyrinogenesis in skin of patients with porphyria cutanea tarda was not different from controls.These studies demonstrate that skin has the enzymatic capacity to synthesize porphyrins from added ALA and that cutaneous porphyrinogenesis from ALA is deficient in patients with acute intermittent porphyria