Quasiparticle interactions in the Anderson lattice: Effects of crystalline anisotropy

Trees, B.R.; Cox, D. L.

doi:10.1103/physrevb.49.16066

Cited by 2 publications

(1 citation statement)

References 17 publications

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“…It is difficult to conceive of simple explanations for these resistivity discrepancies, but we do note a number of important considerations which could modify the behavior: (i) The resistivity is significantly dependent on the details of the hybridization matrix elements between conduction states and the U 5f states. For example, in the simplest M = 1, S I = 1/2 model for Ce 3+ ions, a low temperature downturn in the resistivity is possible due to the "hot-spots" along principle axis directions at which the Γ 7 conduction partial wave states must have vanishing hybridization matrix elements (see Cox [1987c], and Trees [1993 (Trees and Cox [1994]) for a discussion of the hybridization hot-spots and Kim and Cox [1995b] for a discussion of their influence on resistivity). (ii) The T 1/2 coefficient expected at sufficiently low temperatures can experience a sign reversal for sufficiently large potential scattering on the U site which breaks particle-hole symmetry (Affleck and Ludwig [1993]-see eqn.…”

Section: Experimental Data On Two-channel Quadrupolar and Magnetic Ca...mentioning

confidence: 99%

Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres

Cox

Zawadowski

1998

Advances in Physics

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The ordinary single channel Kondo model consists of one or more spin 1/2 local moments interacting antiferromagnetically with conduction electrons in a metal. This model has provided a paradigm for understanding many phenomena of strongly correlated electronic materials, ranging from the formation of heavy fermion fermi liquids to the mapping to a one-band model in the cuprate superconductors. The simplest extension of this ordinary Kondo model in metals which yields exotic non-Fermi liquid physics is the multichannel Kondo impurity model in which the conduction electrons are given an extra quantum label known as the channel or flavor index. In the overcompensated regime of this model non-Fermi liquid physics is possible, in contrast to the single channel model. We overview here the multichannel Kondo impurity model candidates most extensively studied for explaining real materials, specifically the two level system Kondo model relevant for metallic glasses, nanoscale devices, and some doped semiconductors, and the quadrupolar and magnetic two-channel Kondo models developed for rare earth and actinide ions with crystal field splittings in metals. We provide an extensive justification for the derivation of the theoretical models, noting that whenever the local impurity degree of freedom is non-magnetic a two-channel Kondo model must follow by virtue of the magnetic spin degeneracy of the conduction electrons. We carefully delineate all energetic and symmetry restrictions on the applicability of these models. We describe the various 1 methods used to study these models along with their results and limitations (multiplicative renormalization group, numerical renormalization group, non-crossing approximation, conformal field theory, and abelian bosonization), all of which provide differing and useful views of the physics. We pay particular attention to the role that scale invariance plays in all of these theoretical approaches. We point out in each case how various perturbing fields (magnetic, crystalline electric, electric field gradients, uniaxial stress) may destabilize the non-Fermi liquid fixed point. We then provide an extensive discussion of the experimental evidence for the relevance of the two-level system Kondo model to metallic glasses, nanoscale devices, and of the quadrupolar/magnetic two-channel models to a number of heavy fermion based alloys and compounds. We close with a discussion of the extension of the single impurity models which comprise the main focus of this review to other sytems (Coulomb blockade), multiple impurities, and lattice models. In the latter case, we provide an overview of the relevance of the two-channel Kondo lattice model to non-fermi liquid behavior and exotic superconductivity in heavy fermion compounds and to the theoretical possibility of odd-frequency superconductivity, which is realized (for the first time) in the limit of infinite spatial dimensions for this model.

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Section: Experimental Data On Two-channel Quadrupolar and Magnetic Ca...mentioning

confidence: 99%

Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres

Cox

Zawadowski

1998

Advances in Physics

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629

706

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Superconducting instability in the infinite-UAnderson lattice in the presence of crystal electric fields

Trees

1995

Phys. Rev. B

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We report evidence of a superconducting instability (of T 1g symmetry) in the infinite-U Anderson lattice in the presence of crystal fields of cubic symmetry. We assume a lattice of 4f sites, each with a total angular momentum of J = 5/2 that is split by crystal fields into a low-lying doublet of Γ 7 symmetry and an excited quartet of Γ 8 symmetry. Slave Bosons on the 4f sites create and destroy 4f 0 configurations and Lagrange multipliers at each 4f site enforce the occupancy constraint due to the infinite Coulomb repulsion. Quasiparticle interactions are due to exchange of 4f density fluctuations, which are represented by fluctuations in the slave Bosons and Lagrange multipliers. We use the so-called analytic tetrahedron method to calculate the dressed (to order 1/N) Boson Green functions. In weak couping, the exchange 1 of the dressed Bosons gives rise to a superconducting instability of T 1g , xy(x 2 − y 2 ), symmetry. The A 1g , "s-wave", channel has strongly repulsive interactions and hence no pairing instability. The T 2g channel exhibits weakly repulsive interactions. Average quasiparticle interactions in the E g , x 2 − y 2 , 3z 2 − r 2 , channel fluctuate strongly as a function of the number of tetrahedra used to calculate the Bosonic Green functions, lending only weak evidence for an instability of E g symmetry.PACS No. 74.70.Tx site. Our work is novel in that we also include, at the Ce sites, crystal electric fields of cubic symmetry, which has the effect of splitting the spin-orbit coupled (J = 5/2) multiplet into a doublet (of Γ 7 symmetry) and a quartet (of Γ 8 symmetry). We take the Γ 7 doublet to be the ground multiplet, with a crystal field splitting, ∆ CEF , to the Γ 8 quartet that is much larger than the Kondo temperature of the low-lying doublet, T o7 . (∆ CEF ≫ T o7 ) Previous theoretical work has focused on understanding the heavy Fermion compounds mainly through the SU(N) version of the periodic Anderson model[11],[12],[13], [14],[15]. In the SU(N) model, the 4f multiplet is N-fold degenerate, and the (planewave) conduction bands are assumed N-fold degenerate as well. The matrix element, V ( k), for hybridization between a conduction electron and a 4f electron, is taken to be isotropic in momentum space. Within the SU(N) model, Lavagna, Millis, and Lee[15], Auerbach and Levin[12], and Houghton, Read, and Won[16] have studied quasiparticle interactions due to the exchange of 4f density fluctuations. The lowest order diagrams contributing to the interactions are of order 1/N, where N is the 4f multiplet degeneracy. In Ce, in the absence of crystal field splitting, the low-lying J = 5/2 multiplet is six-fold degenerate (N = 6). So it seems reasonable to truncate the diagrams at order 1/N. Lavagna, Millis, and Lee found such a spinless density exchange yielded a d-wave superconducting instability in the spin-singlet pairing channel. F. C. Zhang and T. K. Lee[17] have performed a more realistic calculation (as far as heavy Fermion compounds are concerned) by including spin-orbit coupling at the...

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Quasiparticle interactions in the Anderson lattice: Effects of crystalline anisotropy

Cited by 2 publications

References 17 publications

Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres

Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres

Superconducting instability in the infinite-UAnderson lattice in the presence of crystal electric fields

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