Electronic structure of cerium: A comprehensive first-principles study

Cerium, in which the $4f$ valence electrons live on the brink between localized and itinerant characters, exhibits varying crystal structures and therefore anomalous physical properties with respect to temperature and pressure. Understanding its electronic structure and related lattice properties is one of the central topics in condensed matter theory. In the present paper, we employed the state-of-the-art first-principles many-body approach (i.e., the density functional theory in combination with the single-site dynamical mean-field theory) to thoroughly study its electronic structure. The momentum-resolved spectral functions, total and $4f$ partial density of states, optical conductivities, self-energy functions, and atomic eigenstate histograms for cerium's four allotropes under ambient pressure were calculated and analyzed carefully. The calculated results demonstrate that the $4f$ electrons in the $\ensuremath{\alpha},\ensuremath{\beta},\ensuremath{\gamma}$, and $\ensuremath{\delta}$ phases are all correlated with heavily renormalized electron masses. In the $\ensuremath{\alpha}$ phase, the $4f$ electrons tend to be itinerant, which causes strong hybridization between the $4f$ and $spd$ bands and a remarkable $4f$ valence state fluctuation, while for the other phases, the $4f$ electrons are close to being localized. Our calculated results support the Kondo volume collapse scenario for the cerium $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\gamma}$ transition. Finally, we examined the site dependence of the $4f$ electronic structure in the $\ensuremath{\beta}$ phase. The calculated results suggest that it does not exhibit a site-selective $4f$ localized state.