Low energy electrodynamics and a hidden Fermi liquid in the heavy-fermion CeCoIn$_5$
We present time-domain THz spectroscopy of thin films of the heavy-fermion superconductor CeCoIn$_5$. Below the $\approx$ 40 K Kondo coherence temperature, a narrow Drude-like peak forms, as the result of the $f$ orbital - conduction electron hybridization and the formation of the heavy-fermion state. The complex optical conductivity is analyzed through a Drude model and extended Drude model analysis. Via the extended Drude model analysis, we measure the frequency-dependent scattering rate ($1/ τ$) and effective mass ($m^*/m_b$). This scattering rate shows a linear dependence on temperature, which matches the dependence of the resistivity as expected. Nevertheless, the width of the low-frequency Drude peak itself that is set by the {\it renormalized} quasiparticle scattering rate ($1 / τ^* = m_b/ m^* τ$) shows a $T^2$ dependence. This is the scattering rate that characterizes the relaxation time of the renormalized quasiparticles. This gives evidence for Fermi liquid state, which in conventional transport experiments is hidden by the strong temperature dependent mass.