Design principles for high-Tc electrides: Dominant factor of electron-phonon coupling in I4/mmm A4B electrides (A=Li, Na; B=Co, Rh, Ir, Pd, Ru)

Electrides, distinguished by non-nuclear attractors at interstitial sites, exhibit superconducting properties driven by enhanced electron--phonon coupling (EPC). Through crystal structure predictions and first-principles calculations, we identify $I4/mmm\ensuremath{-}{\mathrm{Li}}_{4}\mathrm{Co}$ as a high-pressure electride stabilized at pressures above 413 GPa, with a record-high superconducting critical temperature $({T}_{\mathrm{c}}=123.5 \mathrm{K})$ among known electrides. This exceptional ${T}_{\mathrm{c}}$ arises from the combined effects of high-density satellite interstitial electrons (SIEs) and large, closed Fermi surfaces, which together strengthen EPC. A comparative analysis of the $I4/mmm\ensuremath{-}{A}_{4}B$ structure family $(A=\mathrm{Li}, \mathrm{Na}; B=\mathrm{Co}, \mathrm{Rh}, \mathrm{Ir}, \mathrm{Pd}, \mathrm{Ru})$ reveals two key design principles for high-${T}_{\mathrm{c}}$ electrides: (1) a high density of states of SIEs and SIE-related atoms (SSADOS) near the Fermi level, and (2) a minimal interstitial space volume for SIEs (IAS). We introduce a compliance parameter, $Q=\frac{\mathrm{SSADOS}}{{e}^{0.2\ensuremath{\sum}\mathrm{IAS}}}$, that quantitatively integrates these key factors and shows a linear correlation with the EPC strength. These findings provide critical insights into the design of high-${T}_{\mathrm{c}}$ electrides and offer a roadmap for optimizing their electronic structures and superconducting properties.