Superconducting ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$: A Thermal Conductivity Study

The superconducting state of the heavy fermion ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$ is studied by heat transport measurements on a highly homogeneous single crystal exhibiting only one transition peak in the specific heat. The field and temperature dependence of the thermal conductivity confirm multiband superconductivity and point to fully open gaps on the whole Fermi surface.

Figure 1

Specific heat $C_p/T$, electric resistivity $\rho$, and thermal conductivity $\kappa (T)/T$ in zero field around $T_c$, documenting the collapse of the double transition (observed only in sample B1) and the high homogeneity of sample B2. Nevertheless, a kink at 1.9 K on $\rho (T)$ reveals some “traces” of the upper transition in sample B2, but the bulk sc transition clearly corresponds to the lower $T_c$ from $C_p/T$ of sample B1.

Figure 2

$\kappa /T(T)$ in zero field: comparison of former (A, open squares) and present (B2, open circles) samples. For sample B2, we separate the phonon ${\kappa }^{\mathrm{ph}}$ (dashed-dotted line) and electronic ${\kappa }^{\mathrm{el}}$ (crosses) contributions. The dashed line is a fit of ${\kappa }^{\mathrm{el}}$ within the MBSC scenario, with exponential behavior (fully open gaps); see text. The inset shows the estimated temperature dependence of the phonon mean free path.

Figure 3

$\kappa /T(H)$, normalized to ${\kappa }_n$ (its value in the normal state) at 50 mK for samples A and B. The arrows indicate the lower ($H_{c1}$) and upper ($H_{c2}$) critical fields. The data in the “field cooled” mode reveal residual flux pinning below 50 mT and a sensitivity of $\kappa$ to fields as low as 5 mT.

Figure 4

Electric $R_c^e(T)$ (solid symbols) and thermal $R_c^{\mathrm{th}}(T).L_{0}T$ (open symbols) resistance of the $\mathrm{Au}\mathrm{\text{−}}{\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$ or $\mathrm{Au}\mathrm{\text{−}}{\mathrm{CeCoIn}}_5$ contacts. Solid lines: Fits of $R_c^{\mathrm{th}}(T)$ according to Eq. (2). $R_c^e(T)$ are temperature and field independent, but $R_c^{\mathrm{th}}(T)$ shows a highly singular behavior in zero field below 200 mK on ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$. This further supports a fully open gap in this system (see text).