Drastic change in transport of entropy with quadrupolar ordering in PrFe$_{4}$P$_{12}$

The antiferroquadrupolar ordering of PrFe$_{4}$P$_{12}$ is explored by probing thermal and thermoelectric transport. The lattice thermal conductivity drastically increases with the ordering, as a consequence of a large drop in carrier concentration and a strong electron-phonon coupling. The low level of carrier density in the ordered state is confirmed by the anomalously large values of the Seebeck and Nernst coefficients. The results are reminiscent of URu$_{2}$Si$_{2}$ and suggest that both belong to the same class of aborted metal-insulator transitions. The magnitude of the Nernst coefficient, larger than in any other metal, indicates a new route for Ettingshaussen cooling at Kelvin temperatures.