Anomalous quasiparticle transport in the superconducting state of CeCoIn$_{5}$

To investigate the quasiparticle dynamics in the superconducting state of quasi-two dimensional heavy fermion superconductor CeCoIn$_ {5}$, the thermal Hall conductivity $\kappa_{xy}$ is measured. In zero magnetic field, thermal Hall angle shows up a steep increase below $T_{c}$, indicating that the quasiparticle mean free path is strongly enhanced. In spite of the presence of a periodic vortex lattice, this enhancement is easily suppressed by a very weak magnetic field. We found that the density states of the delocalized quasiparticles $N_{\mathrm{del}} $, which is obtained from $\kappa_ {xx}$ and $\kappa_{xy}$, exhibits a $\sqrt{H}$- dependence, indicating a Volovik effect. Moreover, $\kappa_{xy}$ reveals the scaling relation with respect to $T/\sqrt{H}$, which is expected for $d $-wave symmetry. These results provide a further support for $d$-wave superconducting symmetry in CeCoIn$_{5}$. We also argue that a small Fermi energy, a short coherence length, and a long quasiparticle mean free path all indicate CeCoIn$_{5}$ is in the superclean regime. These results highlight that CeCoIn$_{5}$ is unique among superconductors.