arXiv subjects

D. L. Cox

Publications and source records attributed to D. L. Cox.

34 records · Page 2Linked to original sources

arXiv1996

Self-consistent Treatment of Crystal-Electric-Field-Levels in the Anderson Lattice

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.

cond-mat↗

arXiv1996

Non Fermi Liquid Dynamics of the Two-Channel Kondo Lattice

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.

cond-mat↗

arXiv1996

A new non-Fermi liquid fixed point

We study a new exchange interaction in which the conduction electrons with pseudo spin $S_c=3/2$ interact with the impurity spin $S_I=1/2$. Due to the overscreening of the impurity spin by higher conduction electron spin, a new non-trivial intermediate coupling strength fixed point is realized. Using the numerical renormalization group (NRG), we show that the low-energy spectra are described by a non-Fermi liquid excitation spectrum. A conformal field theory analysis is compared with NRG results and excellent agreement is obtained. Using the double fusion rule to generate the operator spectrum with the conformal theory, we find that the specific heat coefficient and magnetic susceptibility will diverge as $T^{-2/3}$, that the scaling dimension of an applied magnetic field is $5/6$, and that exchange anisotropy is always relevant. We discuss the possible relevance of our work to two-level system Kondo materials and dilute cerium alloys, and we point out a paradox in understanding the Bethe-Ansatz solutions to the multichannel Kondo model.

cond-mat↗

arXiv1996

Ab Initio Calculation of Crystalline Electric Fields and Kondo Temperatures in Ce-Compounds

We have calculated the band-$f$ hybridizations for Ce$_x$La$_{1-x}$M$_3$ compounds ($x=1$ and $x\rightarrow 0$; M=Pb, In, Sn, Pd) within the local density approximation and fed this into a non-crossing approximation for the Anderson impurity model applied to both dilute and concentrated limits. Our calculations produce crystalline electric field splittings and Kondo temperatures with trends in good agreement with experiment and demonstrate the need for detailed electronic structure information on hybridization to describe the diverse behaviors of these Ce compounds.

cond-mat↗

arXiv1996

Two-Channel Kondo Lattice: An Incoherent Metal

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, the lack of a fermi edge and Drude weight. However, the low-energy density of electronic states is finite. Thus, we identify this system as an incoherent metal. We discuss the relevance of our results for concentrated heavy fermion metals with non-Fermi-Liquid behavior.

cond-mat↗

arXiv1996

Scaling analysis of a model Hamiltonian for Ce$^{3+}$ impurity in a cubic metal

We introduce various exchange interactions in a model Hamiltonian for Ce$^{3+}$ ions in cubic symmetry with three configurations ($f^0$,$f^1$,$f^2$). With the impurity pseudo spin $S_I=1/2$, our Hamiltonian includes: (i) One-channel $S_c=1/2$ Anderson model; (ii) Two-channel $S_c=1/2$ Anderson model; (iii) An unforseen one-channel $S_c=3/2$ Anderson model with a non-trivial fixed point; (iv) Mixing exchange interaction between the $Γ_{6,7}$ and the $Γ_8$ conduction electron partial wave states; (v) Multiple conduction electron partial wave states. Using the third-order scaling (perturbative renormalization group) analysis, we study stability of various fixed points relevant to various exchange interactions for Ce$^{3+}$ ions in cubic symmetry.

cond-mat↗

arXiv1995

One-, Two-, and Three-channel Kondo effects for a model Ce$^{3+}$ Impurity in a Metal

We present studies of a simple Anderson model Hamiltonian for Ce$^{3+}$ ions in cubic symmetry with three configurations ($f^0$,$f^1$,$f^2$). Our Hamiltonian includes: (i) One-channel Anderson model; (ii) Two-channel Anderson model. Using the third order scaling analysis, we study stability of the non-Fermi liquid fixed point of the two-channel Kondo model for Ce$^{3+}$ ions in cubic symmetry against the one-channel Kondo interaction. Using the non-crossing approximation (NCA), we also report detailed studies of our simplified model of one-channel \& two-channel Anderson model which exhibits competition between the Fermi-liquid fixed point of the one-channel Kondo model and the non-Fermi fixed point of the two-channel Kondo model. We provide the phase diagram in the model parameter space and study the thermodynamics and the transport properties of our simplified model Hamiltonian. Thermodynamics and transport coefficients show the distinct behaviors for different numbers of channels. We confirm in detail that the NCA is a valid numerical method for the overcompensated multichannel $S_I=1/2$ Anderson models. Our model study might be relevant to the non-Fermi liquid alloy Ce$_{1-x}$La$_x$Cu$_{2.2}$Si$_2$.

cond-mat↗

arXiv1995

Theory of One-Channel vs. Multi-Channel Kondo Effects for Ce$^{3+}$ 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$_2$.

cond-mat↗

arXiv1994

Knight Shift Anomalies in Heavy Electron Materials

We calculate non-linear Knight Shift $K$ vs. susceptibility $χ$ 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 $K-vs.- χ$ 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.

cond-mat↗

arXiv1994

Staggered Superconductivity in UPt$_3$: A New Phenomenological Approach

We present a new Ginzburg-Landau theory for superconductivity in UPt$_3$, based upon a multicomponent order parameter transforming under an irreducible space group representation; the phase is staggered in real space. Our model can explain the $H-T-P$ phase diagram including the tetracritical point for all field directions. We motivate this unconventional superconducting state in terms of odd-in-time-reversal pairing that may arise in one- or two-channel Kondo models, and suggest experimental tests.

cond-mat↗

arXiv1994

Resistivity of the Two-Channel Kondo Model in Infinite Dimensions

Analytic results for the resistivity of the two-channel Kondo lattice in a particular infinite dimensional limit (Lorentzian density of states) are presented. It is argued that in the absence of symmetry breaking phase transitions or applied fields there is a residual resistivity at zero temperature due to the spin disorder scattering off of the two-channel screening clouds. This may explain the unusual resistivity of UBe$_{13}$. For the same limit the single channel Kondo lattice is an insulator states at particle hole symmetry and half filling, but metallic away from particle-hole symmetry or in applied magnetic field.

cond-mat↗

arXiv1993

Superconductivity in the Anderson Lattice

Using an anisotropic hybridization matrix element, V($\vec k$), reflecting cubic symmetry at the ``rare-earth'' sites of the infinite U Anderson lattice, we calculate the bare quasiparticle scattering amplitude to order 1/N using slave Bosons and find significant differences with previous results under spherical symmetry. Due to exchange of density fluctuations, we find an instability. toward E$_g$ and T$_{1g}$ (even-parity) pairing.

cond-mat↗

arXiv1992

A Simple Model for Coupled Magnetic and Quadrupolar Instabilities in Uranium Heavy-Fermion Materials

We present a mean-field calculation of the phase diagram of a simple model of localized moments, in the hexagonal uranium heavy-fermion compounds. The model considers a non-Kramers quadrupolar doublet ground state magnetically coupled with a singlet excited-state, favoring in-plane van-Vleck magnetism, as has been conjectured for UPt$_3$. The Hamiltonian which defines the model is Heisenberg like in both, magnetic and quadrupolar moments. Among our main results are: (i) for zero intersite quadrupolar coupling, the magnetic order is achieved by a first order transition above a critical intersite magnetic coupling value which becomes second order at higher coupling strengths. (ii) for finite intersite quadrupolar coupling, at temperatures below a second order quadrupolar ordering transition, the minimal magnetic coupling value is increased but (a) the magnetic ordering temperature is enhanced above this value, and (b) the ordering of first and second order transitions in the phase diagram is reversed.

cond-mat↗

arXiv1992

Selection Rules for Two Channel Kondo Models of U and Ce ions in Metals

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.

cond-mat↗

arXiv1992

The Hubbard Model at Infinite Dimensions: Thermodynamic and Transport Properties

We present results on 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 of heavy fermion systems. The calculations were performed using an approximate solution to the single-impurity Anderson model, which is the key quantity entering the solution of the Hubbard model in this limit. To establish the quality of this approximation we compare its results, together with those obtained from two other widely used methods, to essentially exact quantum Monte Carlo results.

cond-mat↗

arXiv1992

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 normal Fermi-liquid with a Drude peak at $ω=0$ 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 $T^2$-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.

cond-mat↗