Electronic structure and oxidation states in high-pressure synthesized isostructural CeCN$_5$ and TbCN$_5$

Abstract: Understanding the behavior of 4$f$ electrons in materials containing rare earth elements is one of the fundamental questions within condensed matter physics. In this work the electronic properties of isostructural CeCN$_5$ and TbCN$_5$, both recently synthesized at extreme pressure, are investigated using Density Functional Theory (DFT) calculations. We include the on-site Coulomb repulsion between localized 4$f$ states within the static DFT+U framework; the DFT+U results are cross-checked with DFT+dynamical mean-field theory (DMFT) calculations within the quasi-atomic (Hubbard-I) approximation. Despite CeCN$_5$ and TbCN$_5$ being isostructural compounds Ce and Tb show different oxidation states, 4+ and 3+ respectively. This leads to distinctly different electronic properties: the former compound is an insulator, while the latter is a metal. An extra electron which is donated by Ce to the polymeric C-N network is distributed across the network. This leads to a modification of the bond length in CeCN$_5$ compared to TbCN$_5$. Still, the polymeric C-N networks can accommodate the different oxidation states in isostructural lanthanide-carbon-nitrogen (LnCN) compounds. Our results underline that LnCN compounds under high pressure offer a unique platform for probing the interplay between 4$f$-electron behavior and structural complexity.