Nodal to Nodeless Superconducting Energy-Gap Structure Change Concomitant with Fermi-Surface Reconstruction in the Heavy-Fermion Compound ${\mathrm{CeCoIn}}_5$

The London penetration depth $\lambda (T)$ was measured in single crystals of ${\mathrm{Ce}}_{1-x}{R}_x{\mathrm{CoIn}}_5$, $R=\mathrm{La}$, Nd, and Yb down to $T_{\min }\approx 50\mathrm{mK}$ ($T_c/T_{\min }\sim 50$) using a tunnel-diode resonator. In the cleanest samples $\mathrm{\Delta }\lambda (T)$ is best described by the power law $\mathrm{\Delta }\lambda (T)\propto T^n$, with $n\sim 1$, consistent with the existence of line nodes in the superconducting gap. Substitutions of Ce with La, Nd, and Yb lead to similar monotonic suppressions of $T_c$; however, the effects on $\mathrm{\Delta }\lambda (T)$ differ. While La and Nd substitution leads to an increase in the exponent $n$ and saturation at $n\sim 2$, as expected for a dirty nodal superconductor, Yb substitution leads to $n>3$, suggesting a change from nodal to nodeless superconductivity. This superconducting gap structure change happens in the same doping range where changes of the Fermi-surface topology were reported, implying that the nodal structure and Fermi-surface topology are closely linked.

Figure 1

Left column panels (a) to (c) show the temperature dependence of normalized rf magnetic susceptibility of ${\mathrm{Ce}}_{1-x}{R}_x{\mathrm{CoIn}}_5$ for $R=\mathrm{La}$ (top panel (a), $x=0$, 0.02 and 0.05 right to left), $R=\mathrm{Nd}$ (middle panel (b), $x=0$, 0.02 and 0.05 right to left), and $x=\mathrm{Yb}$ (bottom panel (c), $x=0$, 0.002, 0.015, 0.037, and 0.039, right to left). Right column panels (d) to (f) show $T_c(x)$ as determined in our measurements (red solid dots) in comparison with the literature data for ${\mathrm{Ce}}_{1-x}{\mathrm{La}}_x{\mathrm{CoIn}}_5$ (panel (d), data from Petrovic et al. [41]), ${\mathrm{Ce}}_{1-x}{\mathrm{Nd}}_x{\mathrm{CoIn}}_5$ (panel (e), data from Petrovic et al. [36]), and ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{CoIn}}_5$ (panel (f), solid line is from Shimozawa et al. [46]).

Figure 2

London penetration depth $\mathrm{\Delta }\lambda (T)$ in three nominally pure samples of ${\mathrm{CeCoIn}}_5$ (S1, S2, and S3) and in a slightly Yb doped sample $x=0.002$. Note that the nominally pure ${\mathrm{CeCoIn}}_5$ sample S3 has $T_c$ lower than the Yb-doped sample. The exponent $n$ of the power law fit $\mathrm{\Delta }\lambda (T)=A{T}^n$ (inset), strongly depends on $T_c$, tending to $n=1$ in the best samples.

Figure 3

London penetration depth of (a) La-, Nd-, and (b) Yb-substituted ${\mathrm{CeCoIn}}_5$, plotted vs a normalized $(T/T_c{)}^2$ scale. The data for the pure material ($x=0$, S1) shows a clear downturn, consistent with $n=1.25<2$. The data for La- and Nd-doped samples closely follow a $T^2$ dependence, expected in dirty nodal superconductors for all doping levels. In Yb-substituted samples, there is a clear crossover from sublinear to superlinear, suggesting a rapid increase of the exponent $n$, and $n>2$ for samples with $x=0.015$, 0.037, and 0.039. (c) Floating fitting range analysis in pure and Yb-substituted ${\mathrm{CeCoIn}}_5$ samples. The data were fit using a power-law function over the temperature range from base temperature to $T_{\text{up}}<T_c/3$, and the resultant exponent $n$ was plotted as a function of $T_{\text{up}}$.

Figure 4

The average exponent $n$ of the power-law fit of $\mathrm{\Delta }\lambda (T)$ as a function of $T_c$ for La (black circles), Nd (blue up-triangles) and Yb substitution (red down-triangles) (left panel). The values are obtained by the averaging the exponent obtained from the range fitting, see Fig. 3. The right panel shows the same data plotted as a function of $x$.