Multigap Superconductivity in the Heavy-Fermion System ${\mathrm{CeCoIn}}_5$

New thermal conductivity experiments on the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$ down to 10 mK rule out the suggested existence of unpaired electrons. Moreover, they reveal strong multigap effects with a remarkably low “critical” field $H_{c2}^S$ for the small gap band, showing that the complexity of heavy-fermion band structure has a direct impact on their response under magnetic field.

Figure 1

Specific heat $C_p(T)/T$, electric resistivity $\rho (T)$, and thermal conductivity $\kappa (T)/T$ in zero field around $T_c$. The small width (0.04 K) of the specific heat jump and the coincidence with the upturn in $\kappa (T)/T$ document the good sample quality. As common in the 115 compounds, the resistive transition (midheight) lies about 10% higher.

Figure 2

(a) Thermal conductivity $\kappa (T)/T$ of ${\mathrm{CeCoIn}}_5$ across its superconducting transition at $T_c=2.3\mathrm{K}$, down to 10 mK. A huge increase is observed below $T_c$ in zero field, owing to the suppression of inelastic scattering. The data at 6 T give a normal state behavior, but they include the effect of the strong positive magnetoresistance. (b) Normalized Lorenz number $L(T)/L_0$, which approaches 1 (within 5%) below 0.1 K at 6 T. (c) Comparison of our very low temperature results in zero field with those of Tanatar et al. [4]. The dotted line marked “${\kappa }_{0S}/T$” corresponds to the universal limit [4].

Figure 3

Very low field behavior of $\kappa (T)/T$ of ${\mathrm{CeCoIn}}_5$ (field cooled), with the heat current parallel to the $a$ axis, and the magnetic field either parallel to $c$ (full symbols) or parallel to the heat current (open symbols). At these low fields, a constant $\kappa (T)/T$ behavior is recovered below 0.1 K, representing at 8 mT ($\approx 1.6\times {10}^{-3}{H}_{c2}$) about $1/5{\kappa }_n(0)$. It points to the presence of a field scale much lower than $H_{c2}$.

Figure 4

Field scans of $\kappa /T$ (zero field cooled) for both field directions at 25 mK up to 0.1 T, revealing a jump of $\kappa /T$ as soon as the applied field is above the penetration field $H_{c1}$ in the sample: $H_{c2}^S$, is lower than $H_{c1}$. Inset: field scan up to 7 T at 50 mK, $H\parallel c$, with a jump at $H_{c2}$ [20].