High-T_c nearly-free-electron superconductivity in quaternary hydrides under ambient pressure

We report a theoretical investigation into superconductivity within the MAXH₆ quaternary hydride system using first-principles calculations, where M and A denote alkali and alkaline earth elements, respectively, and X represents transition metal elements. Systematic analysis of electronic band structures, phonon dispersions, and electron-phonon coupling reveals that substitution of MA binary metal combinations and X metal atoms can create favorable conditions for superconductivity. Mapping of superconducting critical temperatures, combined with dynamical stability analysis through phonon calculations, identifies ten superconducting candidates at ambient pressure. Among these, LiNaAgH₆ exhibits nearly-free-electron behavior reminiscent of monovalent electron superconductors. It demonstrates exceptional superconducting properties with electron-phonon coupling λ = 2.707, which yields a superconducting transition temperature T_c of 206.4 K using the Allen-Dynes formula. Its structural analogs MgNaPdH₆, LiMgPdH₆, LiMgAgH₆, LiMgAuH₆ all exhibit superconducting transition temperatures above 110 K. These findings advance our fundamental understanding of superconductivity in quaternary hydrides and provide guidance for rational design of new high-temperature superconducting materials.