Unpaired Electrons in the Heavy-Fermion Superconductor ${\mathrm{CeCoIn}}_5$

Thermal conductivity and specific heat were measured in the superconducting state of the heavy-fermion material ${\mathrm{Ce}}_{1-x}{\mathrm{La}}_x{\mathrm{CoIn}}_5$. With increasing impurity concentration $x$, the suppression of $T_c$ is accompanied by the increase in residual electronic specific heat expected of a $d$-wave superconductor, but it occurs in parallel with a decrease in residual electronic thermal conductivity. This contrasting behavior reveals the presence of uncondensed electrons coexisting with nodal quasiparticles. An extreme multiband scenario is proposed, with a $d$-wave superconducting gap on the heavy-electron sheets of the Fermi surface and a negligible gap on the light, three-dimensional pockets.

Figure 1

Temperature dependence of specific heat $C$ of ${\mathrm{Ce}}_{1-x}{\mathrm{La}}_x{\mathrm{CoIn}}_5$ for $x=0$ (open circles), 0.02 (open up-triangles), 0.05 (open down-triangles), 0.1 (open squares), and 0.15 (solid stars) in zero magnetic field plotted as $C/T$ vs $T$. The data of Petrovic et al. [5] for pure ${\mathrm{CeCoIn}}_5$ in zero field (solid circles) and at 5 T (solid up-triangles) are shown for comparison. Inset shows residual ${\gamma }_{0S}$ as a function of $x$.

Figure 2

Thermal conductivity $\kappa$ of ${\mathrm{Ce}}_{1-x}{\mathrm{La}}_x{\mathrm{CoIn}}_5$ with $x=0$, 0.01, 0.02, 0.05, and 0.1 (top to bottom) in zero magnetic field, plotted as $\kappa /T$ vs $T$ (note logarithmic scale). Arrows indicate $T_c$. Inset shows determination of residual linear term ${\kappa }_{0S}/T$ of pure ($x=0$) samples for in-plane (squares) and interplane (triangles) heat flow directions (linear scale).

Figure 3

Residual ($T\to 0$) electronic thermal conductivity in the normal (${\kappa }_{0N}/T$, $H>H_{c2}$, triangles) and superconducting (${\kappa }_{0S}/T$, $H=0$, circles) states of ${\mathrm{Ce}}_{1-x}{\mathrm{La}}_x{\mathrm{CoIn}}_5$ as a function of the normal-state residual resistivity ${\rho }_0$ [26]. The universal behavior expected of a superconductor with line nodes is shown as a dashed line (${\kappa }_{0\mathrm{node}}/T$). The dash-dotted line is a sum of uncondensed (dotted line) and nodal (dashed line) contributions, $\eta {\kappa }_{0N}/T+{\kappa }_{0\mathrm{node}}/T$, with $\eta =0.16$.