High-pressure electrides have opened a promising path to high-temperature superconductors and attracted considerable attention. However, the origins of superconductivity from discrepant sources remain puzzling. In this study, we propose a different type of $p$-orbital-like electride state to shed light on the causality that induces high $T_c$. Taking our predicted $R-3\mathrm{m}$ phase in ${\mathrm{Li}}_6\mathrm{P}$ as a representative, with a high $T_c$ of 41.36 K, our first-principles studies unveil that the $p$-orbital-like electride states play a dominant role in $T_c$ by softening the acoustic phonon and forming itinerantly hybridized $p$-orbital-like (IHP) electride-states-dependent phonon-coupled bands, which are corroborated by hole doping. Compared to the nonitinerant $s$-orbital-like electride states with low $T_c$, the IHP electride states exhibit greater freedom of orbital multiplicity and hence a higher propensity to form Cooper pairs, promoting electron-phonon coupling (EPC), and demonstrating the derivation of differential $T_c\mathrm{s}$. Of particular note, the IHP electride states originate from the atypical nature of concurrent oxidization states, characterized by electrons donated from electronegative phosphorus and electropositive lithium. Our finding provides crucial insights into the role of electride states in EPC, elucidates the origin of superconductivity, and identifies the characteristics of high-$T_c$ electrides, with profound implications for exploring this class of multifunctional superconductors.

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• Electronic structure
• Impurities in superconductors
• Pressure effects
• Superconducting phase transition
• High-temperature superconductors
• Density functional calculations