D. L. Cox

Hubbard model at infinite dimensions: Thermodynamic and transport properties

We present results on the thermodynamic quantities, resistivity, and optical conductivity for the Hubbard model on a simple hypercubic lattice in infinite dimensions. Our results for the paramagnetic phase display the features expected from an intuitive analysis of the one-particle spectra and substantiate the similarity of the physics of the Hubbard model to those heavy-fermion systems. The calculations were performed using an approximate solution to the single-impurity Anderson model, wich is the key quantity entering the solution of the Hubbard model in this limit

Electronic Pairing in Exotic Superconductors

Investigations of rare earth, Aactinide, organic and oxide compounds have yielded several new classes of exotic superconductors. These include magnetically ordered superconductors, A15 superconductors, buckyball superconductors, heavy‐electron superconductors, organic superconductors and high‐Tc oxide superconductors. These materials have properties significantly different from those of conventional superconductors such as Al and Zn, which are described well by the Bardeen‐Cooper‐Schrieffer model of superconductivity. We carefully distinguish between the BCS model and the more general BCS theory. In the BCS theory superconductivity arises, loosely speaking, from electron pairs that behave essentially as bosons and undergo macroscopic condensation to the lowest energy state at the critical temperature Tc The BCS model, presented in 1957, further specifies that the pairing is mediated by exchange of quantized lattice vibrations (phonons) between the electrons, yielding pairs with zero spin S (spin singlet) ...

The two-channel Kondo route to non-Fermi-liquid metals

We present a pedagogical and critical overview of the two-channel Kondo model and its possible relevance to a number of non-Fermi-liquid alloys and compounds. We survey the properties of the model, how a magnetic two-channel Kondo effect might obtain for ions in metals, and a quadrupolar Kondo effect for ions in metals. We suggest that the incoherent metal behaviour of the two-channel Kondo-lattice model may be useful in understanding the unusual normal-state resistivity of and speculate that the residual resistivity and entropy of the two-channel lattice paramagnetic phase might be removed by either antiferromagnetic (or antiferroquadrupolar) ordering or by a superconducting transition to an odd-frequency pairing state.

Observation of the two-channel quadrupolar Kondo effect in Y1-xUxPd3

Abstract We present measurements of electrical resistivity p ( T ), magnetic susceptibility x ( T ), and specific heat C ( T ) for the system Y 1-x U x Pd 3 . The data are consistent with nearly localized tetravalent uranium ions leading to “Fermi-level tuning” and competition between single ion Kondo (0 x ≤0.2) and cooperative spin glass-like (0.3≤ x ≤0.5) behavior. The Kondo behavior is unusual and well described by the two-channel quadrupolar Kondo effect. At low temperatures T ⪡ T K , where T K is the Kondo temperature, the electrical resistivity varies nearly linearly with temperature p ( T )/ p (0)≈ 1 - T /( aT K ), and the electronic specific heat diverges logarithmically ΔC / T ≈ -(1/ T K)1 nT with a finite residual T 0 entropy S (0)≈( R /2) ln 2. This appears to be the first example of the quadrupolar Kondo effect and two-channel behavior in a dilute alloy and the first example of “marginal Fermi liquid” phenomenology in a fully three-dimensional system.

Selection rules for two-channel Kondo models of U4+ and Ce3+ ions in metals

Abstract Symmetry-based selection rules are developed providing minimal criteria for the existence of two-channel Kondo interactions between conduction electrons and the low energy degrees of freedom on U 4+ and Ce 3+ in a metal host, assuming that the underlying microscopics are regulated by the Anderson Hamiltonian. An additional dynamic selection rule is imposed on Ce 3+ ions. The selection rules restrict the two-channel quadrupolar Kondo effect to U 4+ ions in cubic, tetragonal and hexagonal symmetry. For hexagonal and tetragonal symmetry, the Kondo effect for a U 4+ ion will always be quadrupolar. The selection rules for Ce 3+ ions restrict the two-channel magnetic Kondo effect to one of three possible doublet ionic ground states in hexagonal symmetry and the lone doublet ionic ground state in cubic symmetry. The dynamical selection rule apparently excludes two-channel Kondo behavior for Yb 3+ ions.

Two-Channel Kondo Lattice: An Incoherent Metal.

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. However, the low-energy density of electronic states is finite. We label our model system in this phase an {open_quote}{open_quote}incoherent metal.{close_quote}{close_quote}We discuss the relevance of our results for concentrated heavy fermion metals with non-Fermi-liquid behavior. {copyright} {ital 1996 The American Physical Society.}

Phase Diagram of the Two-Channel Kondo Lattice

Employing the density matrix renormalization group method and strong-coupling perturbation theory, we study the phase diagram of the SU(2)xSU(2) Kondo lattice model in one dimension. We show that, at quarter filling, the system can exist in two phases depending on the coupling strength. The weak-coupling phase is dominated by RKKY exchange correlations, while the strong-coupling phase is characterized by strong antiferromagnetic correlations of the channel degree of freedom. These two phases are separated by a quantum critical point. For conduction-band fillings of less than one-quarter, we find a paramagnetic metallic phase at weak coupling and a ferromagnetic phase at moderate to strong coupling.

Phenomenology of two channel Kondo alloys and compounds

Abstract We report realistic calculations of magnetic response and transport coefficients for a model U 4+ ion in a metal which undergoes the quadrupolar Kondo effect. We find a small critical regime for the √ T term in the resistivity ρ ( T ). The magnitude and sign of the √ T term are argued to be nonuniversal for finite crystal field splitting. Related √ T terms are found in the van Vleck susceptibility which may be observed in UBe 13 . The thermopower S ( T ) and ρ ( T ) show characteristic crystal field related peaks. S ( T ) undergoes a low-temperature sign change when the dominant fluctuation weight is to the excited f n +1 configuration from a stable f n configuration; this may help explain data for UBe 13 and CeCu 2 Si 2 . Considering the two-channel lattice in a particular infinite dimension limit, we argue that ρ ( T = 0) ≠ 0 in the absence of symmetry breaking. This may explain the reproducibly large residual resistivity of UBe 13 .

MAGNETORESISTANCE IN THE TWO-CHANNEL ANDERSON LATTICE

The paramagnetic phase of the two-channel Anderson lattice model in the Kondo limit is investigated in infinite spatial dimensions using the noncrossing approximation. The resistivity exhibits a Kondo upturn with decreasing T, followed by a slow decrease to a finite value at T=0. The decrease reflects lattice coherence effects in concert with particle-hole symmetry breaking. The magnetoresistance obeys an approximate scaling relation, decreasing towards coherent Fermi liquid behavior with increasing field. The magnetic field induces a Drude peak in the optical conductivity. {copyright} {ital 1997} {ital The American Physical Society}

Transport Properties of the Infinite-Dimensional Hubbard Model

Results for the optical conductivity and resistivity of the Hubbard model in infinite spatial dimensions are presented. At half-filling we observe a gradual crossover from a metal with a Drude peak at ? = 0 in the optical conductivity to an insulator as a function of U for temperatures above the antiferromagnetic phase transition. When doped, the insulator becomes a Fermi liquid with a corresponding temperature dependence of the optical conductivity and resistivity. We find a T2-coefficient in the low-temperature resistivity which suggests that the carriers in the system acquire a considerable mass-enhancement due to the strong local correlations. At high temperatures, a crossover into a semi-metallic regime takes place.