Thermal Conductivity of the Pyrochlore Superconductor ${\mathrm{KOs}}_2{\mathrm{O}}_6$: Strong Electron Correlations and Fully Gapped Superconductivity

To elucidate the nature of the superconducting ground state of the geometrically frustrated pyrochlore ${\mathrm{KOs}}_2{\mathrm{O}}_6$ ($T_c=9.6\mathrm{K}$), the thermal conductivity was measured down to low temperatures ($\sim T_c/100$). We found that the quasiparticle mean free path is strikingly enhanced below a transition at $T_p=7.8\mathrm{K}$, indicating enormous electron inelastic scattering in the normal state. In magnetic fields, the conduction at $T\to 0\mathrm{K}$ is nearly constant up to $\sim 0.4H_{c2}$, in contrast with the rapid growth expected for superconductors with an anisotropic gap. This unambiguously indicates a fully gapped superconductivity, in contrast with previous studies. These results highlight that ${\mathrm{KOs}}_2{\mathrm{O}}_6$ is unique among superconductors with strong electron correlations.

Figure 1

Zero-field thermal conductivity and specific heat in a ${\mathrm{KOs}}_2{\mathrm{O}}_6$ crystal ($0.3\times 0.37\times 0.88{\mathrm{cm}}^3$). Inset: Temperature dependence of the resistivity.

Figure 2

(a) $T$ dependence of $\kappa /T$ in various magnetic fields. The superconducting transition temperatures $T_c(H)$ are shown by arrows. $T_p$ (dashed arrow) is independent of $H$. Upper inset: Schematic figure of $T$ dependence of ${\tau }_{\mathrm{el}\mathrm{\text{−}}\mathrm{ph}}^{-1}$ and ${\tau }_{\mathrm{el}\mathrm{\text{−}}\mathrm{el}}^{-1}$. Lower inset: $\rho$ vs $T^2$ at 0 and 13 T (solid circles). Data for a different crystal at 14 T are also plotted (open circles). The dashed lines represent $\rho (T)={\rho }_0+A{T}^2$. (b) $\kappa /T$ vs $T^2$ at low temperatures. The solid lines are linear fits.

Figure 3

Coefficient $A$ vs Sommerfeld constant $\gamma$ (Kadowaki-Woods plot [23]) for various superconductors. Solid circles are for superconductors believed to have an isotropic gap (or anisotropic $s$-wave symmetry). Open squares are for anisotropic gap with nodes. The lines represent $A=a_{\mathrm{KW}}{\gamma }^2$, with $a_{\mathrm{KW}}={10}^{-5}$ (solid line) and $4\times {10}^{-7}\mu \Omega \mathrm{cm}(\mathrm{K}\mathrm{mol}/\mathrm{mJ}{)}^2$ (dashed line).

Figure 4

$H$ dependence of $\kappa /{\kappa }_n$, as a function of $H/H_{c2}$. For comparison, data for the $s$-wave Nb, ${\mathrm{MgB}}_2$ with two gaps, anisotropic ${\mathrm{CePt}}_3\mathrm{Si}$ (line node), ${\mathrm{LuNi}}_2{\mathrm{B}}_2\mathrm{C}$ (anisotropic $s$), and ${\mathrm{UPt}}_3$ are shown. Crosses indicate values for ${\rho }_0=5\mu \Omega \mathrm{cm}$. Inset: $H$ dependence of $\kappa$ at low fields. The solid and dashed lines represent the data for line and point nodes, respectively.