A planar diagram approach to the correlation problem

We transpose an idea of 't Hooft from its context of Yang and Mills' theory of strongly interacting quarks to that of strongly correlated electrons in transition metal oxides and show that a Hubbard model of N interacting electron species reduces, to leading orders in N, to a sum of almost planar diagrams. The resulting generating functional and integral equations are very similar to those of the FLEX approximation of Bickers and Scalapino. This adds the Hubbard model at large N to the list of solvable models of strongly correlated electrons. PACS Numbers: 71.27.+a 71.10.-w 71.10.FdComment: revtex, 5 pages, with 3 eps figure

The Superconducting Instabilities of the non half-filled Hubbard Model in Two Dimensions

The problem of weakly correlated electrons on a square lattice is formulated in terms of one-loop renormalization group. Starting from the action for the entire Brillouin zone (and not with a low-energy effective action) we reduce successively the cutoff $\Lambda$ about the Fermi surface and follow the renormalization of the coupling $U$ as a function of three energy-momenta. We calculate the intrinsic scale $T_{co}$ where the renormalization group flow crosses over from the regime ($\Lambda > T_{co}$) where the electron-electron (e-e) and electron-hole (e-h) terms are equally important to the regime ($\Lambda < T_{co}$) where only the e-e term plays a role. In the low energy regime only the pairing interaction $V$ is marginally relevant, containing contributions from all renormalization group steps of the regime $\Lambda > T_{co}$. After diagonalization of $V_{\Lambda =T_{co}}$, we identify its most attractive eigenvalue $\lambda _{\min}$. At low filling, $\lambda _{\min}$ corresponds to the $B_2$ representation ($d_{xy}$ symmetry), while near half filling the strongest attraction occurs in the $B_1$ representation ($d_{x^2-y^2}$ symmetry). In the direction of the van Hove singularities, the order parameter shows peaks with increasing strength as one approaches half filling. Using the form of pairing and the structure of the renormalization group equations in the low energy regime, we give our interpretation of ARPES experiments trying to determine the symmetry of the order parameter in the Bi2212 high-$T_{c}$ compound.Comment: 24 pages (RevTeX) + 11 figures (the tex file appeared incomplete

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

High-pressure transport properties of CeRu_2Ge_2

The pressure-induced changes in the temperature-dependent thermopower S(T) and electrical resistivity \rho(T) of CeRu_2Ge_2 are described within the single-site Anderson model. The Ce-ions are treated as impurities and the coherent scattering on different Ce-sites is neglected. Changing the hybridisation \Gamma between the 4f-states and the conduction band accounts for the pressure effect. The transport coefficients are calculated in the non-crossing approximation above the phase boundary line. The theoretical S(T) and \rho(T) curves show many features of the experimental data. The seemingly complicated temperature dependence of S(T) and \rho(T), and their evolution as a function of pressure, is related to the crossovers between various fixed points of the model.Comment: 9 pages, 10 figure

Andreev Scattering and the Kondo Effect

We examine the properties of an infinite-$U$ Anderson impurity coupled to both normal and superconducting metals. Both the cases of a quantum dot and a quantum point contact containing an impurity are considered; for the latter, we study both one and two-channel impurities. Using a generalization of the noncrossing approximation which incorporates multiple Andreev reflection, we compute the impurity spectral function and the linear-response conductance of these devices. We find generically that the Kondo resonance develops structure at energies corresponding to the superconducting gap, and that the magnitude of the resonance at the Fermi energy is altered. This leads to observable changes in the zero-bias conductance as compared to the case with no superconductivity.Comment: 8 pages, 7 figures; expanded version to appear in PR

Theory of One-Channel vs. Multi-Channel Kondo Effects for Ce3+^{3+} Impurities

We introduce a model for Ce$^{3+}$ impurities in cubic metals which exhibits competition between the Fermi-liquid fixed point of the single channel Kondo model and the non-Fermi-liquid fixed point of the two- and three-channel Kondo models. Using the non-crossing approximation and scaling theory, we find: (i) A possible three-channel Kondo effect between the one- and two-channel regimes in parameter space. (ii) The sign of the thermopower is a fixed point diagnostic. (iii) Our results will likely survive the introduction of additional $f^2$ and conduction states. We apply this model to interpret the non-Fermi liquid alloy La$_{1-x}$Ce$_x$Cu$_{2.2}$Si$_2$.Comment: 13 pages, Revtex, To appear in Phys. Rev. Let

Non-interacting Cooper pairs inside a pseudogap

I present a simple analytical model describing the normal state of a superconductor with a pseudogap in the density of states, such as in underdoped cuprates. In nearly two-dimensional systems, where the superconducting transition temperature is reduced from the mean-field BCS value, Cooper pairs may be present as slow fluctuations of the BCS pairing field. Using the self-consistent T-matrix (fluctuation exchange) approach I find that the fermion spectral weight exhibits two BCS-like peaks, broadened by fluctuations of the pairing field amplitude. The density of states becomes suppressed near the Fermi energy, which allows for long-lived low-energy Cooper pairs that propagate as a sound-like mode with a mass. A self-consistency requirement, linking the width of the pseudogap to the intensity of the pairing field, determines the pair condensation temperature. In nearly two-dimensional systems, it is proportional to the degeneracy temperature of the fermions, with a small prefactor that vanishes in two dimensions.Comment: LaTeX (prbbib.sty included), 24 pages, 4 PostScript figures To appear in Phys.Rev.

Operator projection method applied to the single-particle Green's function in the Hubbard model

A new non-perturbative framework for many-body correlated systems is formulated by extending the operator projection method (OPM). This method offers a systematic expansion which enables us to project into the low-energy structure after extracting the higher-energy hierarchy. This method also opens a way to systematically take into account the effects of collective excitations. The Mott-Hubbard metal-insulator transition in the Hubbard model is studied by means of this projection beyond the second order by taking into account magnetic and charge fluctuations in the presence of the high-energy Mott-Hubbard structure. At half filling, the Mott-Hubbard gap is correctly eproduced between the separated two bands. Near half filling, a strongly renormalized low-energy single-particle excitations coexisting with the Mott-Hubbard bands are shown to appear. Signifcance of momentum-dependent self-energy in the results is stressed.Comment: 6 pages, final version to appear in J. Phys. Soc. Jp

Spin-Dependent Mass Enhancement under Magnetic Field in the Periodic Anderson Model

In order to study the mechanism of the mass enhancement in heavy fermion compounds in the presence of magnetic field, we study the periodic Anderson model using the fluctuation exchange approximation. The resulting value of the mass enhancement factor z^{-1} can become up to 10, which is significantly larger than that in the single-band Hubbard model. We show that the difference between the magnitude of the mass enhancement factor of up spin (minority spin) electrons z^{-1}_up and that of down spin (majority spin) electrons z^{-1}_down increases by the applied magnetic field B//z, which is consistent with de Haas-van Alphen measurements for CeCoIn_5, CeRu_2Si_2 and CePd_2Si_2. We predict that z^{-1}_up >z^{-1}_down in many Ce compounds, whereas z^{-1}_up < z^{-1}_down in Yb compounds.Comment: 5 pages, 4 figure

Thermopower of Aharonov-Bohm Interferometer with a Quantum Dot

We report on the thermopower of an Aharonov-Bohm interferometer (AB) with a quantum dot in the Kondo limit. The thermopower is anomalously enhanced due to the Kondo effect as in heavy fermion systems. In contrast to the bulk systems, the sign of the thermopower can be changed by adjusting the energy level scheme or the particle-hole asymmetry of a dot with the gate voltage. Further the magnitude and even the sign of the thermopower in the AB ring can be changed at will with varying either magnetic fields or the gate voltages.Comment: 4 pages, 3 figures, accepted for publication in Physical Review Letter