Superconductivity of cerium hydride at high pressure from DFT+DFPT+DMFT

Lanthanide hydrides are attracting considerable attention in condensed matter physics due to their high-temperature superconductivity under extreme pressure. The majority of the Lanthanides have valence f-orbital electrons, which suggests that strongly correlated interactions will play an important role in determining their physical properties. In this work, we propose a novel method to calculate the density of states, band structure, and phonon dispersion combining density functional theory with dynamical mean-field theory (DFT+DMFT). These results are then used in the context of density functional perturbation theory combined with maximally localized Wannier functions to evaluate the superconducting transition temperature of Lanthanide hydrides, taking CeH9 as an example. We find significant differences in the superconducting transition temperature when electronic correlations are included in the calculations. Our approach should be valuable for the study of phonon and electron-phonon related properties in strongly correlated materials.