Electronic structure of semiconducting CeFe$_4$P$_{12}$: Strong hybridization and relevance of single-impurity Anderson model

Semiconducting skutterudite CeFe$_4$P$_{12}$ is investigated by synchrotron x-ray photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). Ce 3$d$ core-level PES and 3$d-4f$ XAS, in combination with single impurity Anderson model (SIAM) calculations, confirm features due to $f^0$, $f^1$ and $f^2$ configurations. The Ce 4$f$ density of states (DOS) indicates absence of a Kondo resonance at Fermi level, but can still be explained by SIAM with a small gap in non-$f$ DOS. While Ce 4$f$ partial DOS from band structure calculations are also consistent with the main Ce 4$f$ DOS, the importance of SIAM for core and valence spectra indicates Kondo semiconducting mixed valence for CeFe$_4$P$_{12}$, derived from strong hybridization between non-$f$ conduction and Ce 4$f$ DOS.