Roles of multipoles and excitons in superconductor PrOs4Sb12 with Th symmetry

A possibility of exciton-mediated mechanism is studied to describe the superconductivity in a Pr skutterudite PrOs4Sb12. In this compound the low-lying crystal-field states of Pr form a pseudo-quartet consisting of Γ1 singlet ground and Γ4(2) triplet excited states. The dispersive crystal-field excitations (excitons) have been detected experimentally. The conduction electrons couple both magnetically and nonmagnetically with the pseudo-quartet. Believing that this coupling should be crucial for various properties of PrOs4Sb12, we determine the effective interaction between conduction electrons and the Pr pseudo-quartet states. It turns out that the nature of exchange processes is related closely to au and tu components of the conduction electrons that correspond to the molecular orbitals of an Sb12 cage surrounding a Pr ion. By the second-order perturbation in the exchange coupling, Cooper pairing interactions are derived both for singlet and triplet superconductivities. First, they are classified with cubic point-group (Oh) bases. Then, the Th symmetry, which is a unique feature of the filled skutterudite compounds, is taken into account; it is shown that the gap functions in different Oh representations are mixed due to the Th symmetry. The Th symmetry in which no fourfold symmetry is present shows up in the gap functions within a weak coupling theory. As a candidate for the superconductivity in PrOs4Sb12, we propose a nonunitary triplet state with twofold symmetry which agrees most naturally with the gap structure observed in the low field phase. We also find that the triplet superconducting state becomes possible owing to the Th crystal-field symmetry. (author)