Unconventional superconductivity in the strong-coupling limit for the heavy fermion system CeCoIn$_5$

We present scanning tunneling spectroscopy measurements of the local quasiparticles' excitation spectra of CeCoIn$_5$ between 440mK and 3K in samples with a bulk $T_{\rm c}=2.25$K. The spectral shape of our low-temperature tunneling data, quite textbook nodal-gap conductance, allow us to confidently fit the spectra with a d-wave density of states considering also a shortening of quasiparticles' lifetime term $\Gamma$. The $\Delta(0)$ value obtained from the fits yields a BCS ratio $2\Delta/kT_{\rm c} =7.73$ suggesting that CeCoIn$_5$ is an unconventional superconductor in the strong coupling limit. The fits also suggest that the height of coherence peaks in CeCoIn$_5$ is reduced with respect to a pure BCS spectra and therefore the coupling of quasiparticles with spin excitations should play a relevant role. In addition, the tunneling conductance shows a depletion at energies smaller than $\Delta$ for temperatures larger than the bulk $T_{\rm c}$, giving further support to the existence of a pseudogap phase that in our samples span up to $T^{*}\sim 1.2 T_{\rm c}$. The phenomenological scaling of the pseudogap temperature observed in various families of cuprates, $2\Delta/kT^{*} \sim 4.3$, is not fulfilled in our measurements. This suggests that in CeCoIn$_5$ the strong magnetic fluctuations might conspire to close the local superconducting gap at a smaller pesudogap temperature-scale than in cuprates.