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Thermal conductivity measurements were performed on single crystal samples ofthe superconducting filled skutterudite compounds PrOs$_4$Sb$_{12}$ andPrRu$_4$Sb$_{12}$ both as a function of temperature and magnetic field appliedperpendicular to the heat current. In zero magnetic field, the low temperatureelectronic thermal conductivity of PrRu$_4$Sb$_{12}$ is vanishingly small,consistent with a fully-gapped Fermi surface. For PrOs$_4$Sb$_{12}$, however,we find clear evidence for residual electronic conduction as the temperaturetends to zero Kelvin which is consistent with the presence of nodes in thesuperconducting energy gap. The field dependence of the electronic conductivityfor both compounds shows a rapid rise immediately above H$_{c1}$ andsignificant structure over the entire vortex state. In the fully gappedsuperconductor PrRu$_4$Sb$_{12}$, this is interpreted in terms of multi-bandeffects. In PrOs$_4$Sb$_{12}$, we consider the Doppler shift of nodalquasiparticles at low fields and multiband effects at higher fields.

Multi-symmetry and Multi-band Superconductivity in Filled-skutterudites PrOs$_4$Sb$_{12}$ and PrRu$_4$Sb$_{12}$