Composite Spin-Triplet Superconductivity in an $SU(2)\otimes SU(2)$ Symmetric Lattice Model

The two-channel Anderson lattice model which has $SU(2)\otimes SU(2)$ symmetry is of relevance to understanding of the magnetic, quadrupolar and superconducting phases in U${}_{1-x}$Th${}_x$Be${}_{13}$ or Pr base skutterudite compounds such as PrFe${}_4$P${}_{12}$ or PrOs${}_4$Sb${}_{12}$. Possible unconventional superconducting phases of the model are explored. They are characterized by a composite order parameter comprising of a local magnetic or quadrupolar moment and a triplet conduction electron Cooper-pair. This binding of local degrees of freedom removes the entropy of the non Fermi-liquid normal state. We find superconducting transitions in the intermediate valence regime which are suppressed in the stable moment regime. The gap function is non analytic and odd in frequency: a pseudo-gap develops in the conduction electron density of states which vanishes as $\mathrm{\mid }\omega \mathrm{\mid }$ close to $\omega =0$. In the strong intermediate valent regime, the gap function acquires an additional $\text{k}$-dependence.