Giant Nernst effect in the Pr-filled skutterudite PrFe$_4$P$_{12}$

The phase transition of PrFe$_{4}$P$_{12}$ at T$_{O}=6.5$ K, probably associated with antiferroquadrupolar ordering, is explored by measuring thermal and thermoelectric transport coefficients. The transition leads to a drastic increase in lattice thermal conductivity pointing to a large drop in carrier concentration induced by the transition 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 latter attains a magnitude larger than what is reported for any metal. The results are reminiscent of the hidden-order state of URu$_{2}$Si$_{2}$. According to our analysis of the data, most carriers disappear at the transition, paving the way for an enhanced mean-free-path of both phonons and the residual quasi-particles. Thus, the ordered state of PrFe$_{4}$P$_{12}$ emerges as a heavy-fermion semi-metal.