In this paper, we examine the mean field electronic structure of the f 1 − f 2 Anderson lattice model in a slave boson approximation, which should be useful in understanding the physics of correlated metals with more than one f electron per site such as uranium-based heavy fermion superconductors. We find that the multiplet structure of the f 2 ion acts to quench the crystal field splitting in the quasiparticle electronic structure. This is consistent with experimental observations in such metals as U P t 3

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...

No abstract