Landau Renormalizations of Superfluid Density in the Heavy-Fermion Superconductor ${\mathrm{CeCoIn}}_5$

The formation of heavy-fermion bands can occur by means of the conversion of a periodic array of local moments into itinerant electrons via the Kondo effect and the huge consequent Fermi-liquid renormalizations. Leggett predicted for liquid ${}^3\mathrm{He}$ that Fermi-liquid renormalizations change in the superconducting state, leading to a temperature dependence of the London penetration depth $\mathrm{\Lambda }$ quite different from that in BCS theory. Using Leggett’s theory, as modified for heavy fermions, it is possible to extract from the measured temperature dependence of $\mathrm{\Lambda }$ in high quality samples both Landau parameters $F_0^s$ and $F_1^s$; this has never been accomplished before. A modification of the temperature dependence of the electronic specific heat $C_{\mathrm{el}}$, related to that of $\mathrm{\Lambda }$, is also expected. We have carefully determined the magnitude and temperature dependence of $\mathrm{\Lambda }$ in ${\mathrm{CeCoIn}}_5$ by muon spin relaxation rate measurements to obtain $F_0^s=36\pm 1$ and $F_1^s=1.2\pm 0.3$, and we find a consistent change in the temperature dependence of $C_{\mathrm{el}}$. This, the first determination of $F_1^s$ with a value $\ll F_0^s$ in a heavy-fermion compound, tests the basic assumption of the theory of heavy fermions, that the frequency dependence of the self-energy is much more important than its momentum dependence.

Figure 1

TF $\mu \mathrm{SR}$ asymmetry spectra $A(t)$ of ${\mathrm{CeCoIn}}_5$ in the normal (triangles) and superconducting (circles) states, taken at ${\mu }_{0}H=30\mathrm{mT}$ for $H\parallel c$. Curves represent fits to the data (see text). The data are shown in a frame rotating at a frequency corresponding to a field of 25 mT [9].

Figure 2

Temperature dependence of the muon Gaussian relaxation rate ${\sigma }_s$ in ${\mathrm{CeCoIn}}_5$ under a transverse magnetic field ${\mu }_{0}H=30\mathrm{mT}$ for $H\parallel c$. Solid lines: power-law fits to the data as described in the text. Arrow: $T_c$.

Figure 3

Superfluid density ${\mathrm{\Lambda }}^{-2}(T/T_c)/{\mathrm{\Lambda }}^{-2}(0)$ as a function of normalized temperature $T/T_c$ in ${\mathrm{CeCoIn}}_5$. Curved line: fit of Eq. (9) to the data.

Figure 4

Dependence of specific heat divided by temperature $C_{\mathrm{el}}(T)/T$ on normalized temperature $T/T_c$ in ${\mathrm{CeCoIn}}_5$. Data from Ref. [11]. Curved lines: fits of Eq. (10) (plus small offsets [30]) for $F_1^s=0$ and 1.2 to the data. The fits and data are nearly indistinguishable except near $T_c$.