Anomalous quasiparticle transport in the superconducting state of ${\mathrm{CeCoIn}}_5$

We report on a study of thermal Hall conductivity ${\kappa }_{xy}$ in the superconducting state of ${\mathrm{CeCoIn}}_5$. The scaling relation and the density of states of the delocalized quasiparticles, both obtained from ${\kappa }_{xy}$, are consistent with $d$-wave superconducting symmetry. The onset of superconductivity is accompanied by a steep increase in the thermal Hall angle, pointing to a striking enhancement in the quasiparticle mean free path. This enhancement is drastically suppressed in a very weak magnetic field. These results highlight that ${\mathrm{CeCoIn}}_5$ is unique among superconductors. A small Fermi energy, a large superconducting gap, a short coherence length, and a long mean free path all indicate that ${\mathrm{CeCoIn}}_5$ is clearly in the superclean regime $({\epsilon }_F∕\Delta ⪡\ell ∕\xi )$, in which a peculiar vortex state is expected.

Figure 1

Temperature dependence of the thermal Hall conductivity divided by $B,\mid {\kappa }_{xy}\mid ∕B$. The zero-field limit is obtained from the $H$-linear dependence of $\mid {\kappa }_{xy}\mid$ at low field [see Fig. 3(a)]. Inset: Temperature dependence of the thermal conductivity divided by $T,{\kappa }_{xx}∕T$.

Figure 2

(a) Field dependence of thermal conductivity ${\kappa }_{xx}$. Arrows indicate $H_{c2}$ determined by resistivity measurements. (b) The same data for the thermal Hall conductivity $\mid {\kappa }_{xy}\mid$. Inset: Thermal Hall conductivity in the low field regime. Thin solid lines represent the initial Hall slope.

Figure 3

Scaling plot ${\kappa }_{xy}∕T^2$ vs $x=\sqrt{H∕H_{c2}^{\mathrm{orb}}}∕(T∕T_c)$. We used $H_{c2}^{\mathrm{orb}}=12\mathrm{T}$. The data collapse into the same curve at low temperatures. Inset: Field dependence of ${\kappa }_{xx}^{2}B∕\mid {\kappa }_{xy}\mid$, which is proportional to the DOS of the delocalized QPs $N_{\mathrm{del}}\left(E\right)$ at 0.46 K. The dashed line indicates $\sqrt{H}$ dependence.

Figure 4

Temperature dependence of thermal Hall angle (● and ∎), $\tan \Theta \equiv {\kappa }_{xy}∕{\kappa }_{xx}$, and electrical Hall angle (◯ and ◻), $\tan {\Theta }_e\equiv {\sigma }_{xy}∕{\sigma }_{xx}$, divided by $B$ in zero-field limit and in the normal state at 5.2 T. The dashed line represents the relation ${\lim }_{B\to 0}\mid \cot {\Theta }_e\mid ∕B=a+b{T}^2$. $T^{*}$ is the coherence temperature. See text for details. Inset: Temperature dependence of the QP mean free path $\ell$ in zero field estimated from the thermal Hall angle [Eq. (2)].

Figure 5

Field dependence of the QP mean free path estimated from the thermal Hall angle below $H=1\mathrm{T}$ at $T=0.46\mathrm{K}$. Inset: The same data up to $H_{c2}$ plotted on a log-log scale. The dashed line represents the average vortex distance $a_v=\sqrt{{\Phi }_0∕H}$.