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 $T_{\mathrm{F}\mathrm{L}}\simeq 75$ 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${}_2$.