Kondo Interactions from Band Reconstruction in YbInCu$_{\mathrm{4\thinspace }}$

We combine resonant inelastic x-ray scattering and model calculations in the Kondo lattice compound YbInCu$_{\mathrm{4}}$, a system characterized by a dramatic increase in Kondo temperature and associated valence fluctuations below a first-order valence transition at T $\simeq $ 42 K. The bulk-sensitive, element-specific, and valence-projected charge excitation spectra reveal an unusual quasigap in the Yb-derived state density which drives an instability of the electronic structure and renormalizes the low-energy effective Hamiltonian at the transition. Our results provide long-sought experimental evidence for a link between temperature-driven changes in the low-energy Kondo scale and the higher-energy electronic structure of this system.