Anomalous 4f fine structure in TmSe_1-xTe_x across the metal-insulator transition

Hybridization between localized 4f and itinerant 5d6s states in heavy fermion compounds is a well-studied phenomenon and commonly captured by the paradigmatic Anderson model. However, the investigation of additional electronic interactions, beyond the standard Anderson model, has been limited, despite their predicted important role in the exotic quasiparticle formation in mixed-valence systems. We investigate the 4f states in TmSe_1-xTe_x throughout a semimetal-insulator phase transition, which drastically varies the interactions related to the 4f states. Using synchrotron-based hard x-ray and extreme ultraviolet photoemission spectroscopy, we resolve subtle peak splitting in the 4f peaks near the Fermi level in the mixed-valent semimetal phase. The separation is enhanced by several tens of meV by increasing the lattice parameter by a few percent. Our results elucidate the evolving nature of the 4f state across the phase transition, and provide direct experimental evidence for electronic interactions beyond the standard Anderson model in mixed-valence systems.