Orbitally degenerate spin-fluctuation model for heavy-fermion superconductivity.

Manuscript is plain TeX with macros. Figures start at FIGURES BEGIN HERE, with instructions on what to do to get them. In this paper, a generalization of standard spin fluctuation theory is considered by replacing the simple Hubbard interaction by the screened Hartree-Fock interaction for f electrons. This model is then used in both an LS and a JJ coupling scheme to construct the particle-particle scattering vertex in an on-site approximation. This vertex is shown to lead to an instability for a superconducting pair state which obeys Hunds rules, with L=5, S=1, and J=4. The degeneracy of this state is broken by anisotropy of the quasiparticle wavefunctions. Detailed calculations are presented for the case of U P t 3. After over a decade's worth of theoretical work, there is no overall agreement on a microscopic theory for heavy fermion superconductivity. The overall prejudice, though, is that the underlying pairing mechanism is similar to that operative in superfluid 3 He. Most attempts at a theory based on this approach have been to make the simplest possible modifications to the standard single orbital Hubbard interaction used in the 3 He problem. These attempts have had mixed success. The philosophy of this paper will be to actually do for heavy fermions what was done for 3 He, that is to use the Hartree-Fock interaction between f electrons including full orbital and spin-orbital effects and construct the effective particle-particle vertex by the appropriate diagrammatic summation. In principle, this theory contains all relevant physics within a spin fluctuation based approach. Even at the simplest level, new physics emerges which is not present when using a simple Hubbard interaction. In particular, the maximum instability in the particle-particle vertex occurs for a pair state which obeys Hunds rules. For f electrons, this corresponds to a state which has L=5, S=1, and J=4. The degeneracy of this multiplet is broken in real metals by crystalline anisotropy effects in the normal state. This is reflected by (1) the orbital and momentum dependence of the bare susceptibility bubble which forms the internal lines of the vertex and (2) the orbital and momentum dependence of the quasiparticle wavefunctions which form the external lines. In this paper, (1) is treated in a simple manner and (2) is treated within a band theoretic approximation. The frequency dependence of (1) and (2), which acts to set the overall scale for T c , is …