High-pressure superconducting electrides have attracted extensive attention because of the coexistence of accumulated interstitial electride states (IAEs) and the superconducting state, providing a novel platform for exploring high-temperature superconductors. Nevertheless, the driving force behind the formation of the superconducting state without pressure effect in electrides remains unclear, particularly how intrinsic IAEs reconciling within the high-locality nature, as per the traditional view, effectively form Cooper pairs. Here, we have revealed the correlated superconducting state intertwined with IAEs in the electride $Pm\text{−}3m\text{-H}{\mathrm{f}}_4\mathrm{C}$ at ambient pressure, which is identified through high-throughput screening combined with element substitution. Our first-principles calculations uncover IAEs distributed within the energy range from the maximum of the effective potential to the Fermi level, indicating delocalized behaviors dominate the electronic density. Of particular note, these IAEs, characterized by forming hybridized electronic states with Hf-$d$ orbital components above unbound-state bands, are scattered by low-frequency phonon modes associated with hafnium atoms, resulting in electron-phonon coupling interaction with a critical temperature of 3.95 K. Our results elucidate the physical picture of the distribution of IAEs in energy space and their positive correlation with pressure-independent superconducting states, offering a unique perspective for understanding superconducting electrides.

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• Density of states
• Electrical properties
• Electronic structure
• Superconductivity
• Superconductors
• First-principles calculations