Anomalous quasiparticle thermal transport in the superconducting state of ultra pure URu$_2$Si$_2$ single crystals

In heavy fermion superconductor URu$_2$Si$_2$, although it is believed that superconductivity in this material ($T_c\sim1.5$ K) is unconventional, details of the superconducting gap structure are still unknown. To investigate the quasiparticle transport in the superconducting state of URu$_2$Si$_2$, the thermal conductivity $\kappa$ is measured in ultra pure single crystals with residual resistivity ratio $\sim600$. In zero field, $\kappa/T$ shows a steep increase below $T_c$, indicating that the quasiparticle mean free path is strongly enhanced in the superconducting state. A finite residual term of $\kappa/T$ as $T\rightarrow0$ is clearly resolved, together with a $T^2$ dependence at very low temperatures. With applying magnetic field, thermal conductivity grows rapidly at low magnetic fields, and exhibits a $\sqrt{H}$-dependence. These results strongly indicate a presence of line nodes in the superconducting gap function. We found that $\kappa/T$ exhibits a sudden drop at upper critical field, which has never been observed in any superconductors. We discuss this unusual behavior of thermal conductivity in the context of anomalously large $\omega_c\tau(>1)$ and giant magnetoresistance observed in this material.