Observation of an Emergent Coherent State in the Iron-Based Superconductor KFe$_\mathbf{2}$As$_\mathbf{2}$

The optical properties of KFe$_2$As$_2$ have been measured for light polarized in the a-b planes over a wide temperature and frequency range. Below $T^\ast\simeq 155$ K, where this material undergoes an incoherent-coherent crossover, we observe a new coherent response emerging in the optical conductivity. A spectral weight analysis suggests that this new feature arises out of high-energy bound states. Below about $T_{\rm FL} \simeq 75$ K the scattering rate for this new feature is quadratic in temperature, indicating a Fermi-liquid response. Theory calculations suggest this crossover is dominated by the $d_{xy}$ orbital. Our results advocate for Kondo-type screening as the mechanism for the orbital-selective incoherent-coherent crossover in hole-overdoped KFe$_2$As$_2$.