Landau Renormalizations of Superfluid Density in the Heavy-Fermion Superconductor CeCoIn5

The formation of heavy fermion (HF) 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(FL) renormalizations. Leggett predicted for liquid $^3$He that FL renormalizations change in the superconducting state, leading to a temperature(T) dependence of the London penetration depth~$\Lambda$ quite different from that in the BCS theory. Using Leggett's theory, as modified for HF, it is possible to extract from the measured T dependence of $\Lambda$ in high quality samples both Landau parameters $F_0^s$ and $F_1^s$; this has never been accomplished before. A modification of the T dependence of the specific heat $C_{\mathrm{el}}$, related to that of $\Lambda$, is also expected. We have carefully determined the magnitude and T dependence of $\Lambda$ in 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 find a consistent change in the T dependence of electronic specific heat $C_{\mathrm{el}}$. This, the first determination of $F_1^s$ with a value~$\ll F_0^s$ in a HF compound, tests the basic assumption of the theory of HF,that the frequency dependence of the self-energy is much more important than its momentum dependence.