Exciton mediated triplet superconductivity in Th system PrOs4Sb12

We investigate a possibility of triplet superconductivity mediated by crystal-field excitations in a skutterudite PrOs$_4$Sb$_{12}$. The dispersive excitation modes (excitons) are caused by an effective exchange interaction due to the conduction electrons coupled with the Pr $f^2$ states. The Cooper pairing interaction reflects the point group symmetry of the Pr site rather than the global symmetry of the Fermi surface. The $T_h$ symmetry (without fourfold symmetric axes) of the skutterudite crystals is a key to stability of the triplet Cooper pairing. We attempt to explain a possible superconducting state with broken time-reversal symmetry and a multiple superconducting phase in a magnetic field, recently reported by experiments.