Superconductivity in Li8Hn electrides: The effect of interstitial anionic electrons on electron-phonon coupling

The discovery of superconductivity in electrides, where partial electrons are localized in lattice interstices, labeled as interstitial anionic electrons (IAEs), introduces a different category known as electride superconductors. Understanding the role of IAEs in electron-phonon coupling (EPC) is crucial for the development of electride superconductors. In this study, we demonstrate that an increased net charge of IAEs enhances EPC in 12 $\mathrm{L}{\mathrm{i}}_{8}{\mathrm{H}}_{n}$ ($n=4--7$) electrides, exhibiting cubic/tetragonal symmetry and diverse IAEs topologies. First-principles calculations reveal a nearly linear rise in the EPC constant with the net charge of IAEs. This increase stems from the excitation effect of IAEs on Li $2p$ electrons and their collaborative involvement in the formation of Cooper pairs, facilitated by Li-derived low/medium-frequency phonons. This mechanism is prominently illustrated in $Pm\text{\ensuremath{-}}3m \mathrm{L}{\mathrm{i}}_{8}{\mathrm{H}}_{4}$, featuring a ${T}_{\mathrm{c}}$ of 40.3 K, where Li atoms exhibit compressing and stretching vibrations, inducing IAEs dimerization and the strongest local EPC interaction. Conversely, hydrogen atoms in $\mathrm{L}{\mathrm{i}}_{8}{\mathrm{H}}_{n}$ electrides primarily regulate the net charge and topology of IAEs. Our findings bear significant implications for the advancement of electride superconductors.