Emerging superconductivity rules in rare-earth and alkaline-earth metal hydrides

Hydrides of alkaline-earth and rare-earth metals have garnered significant interest in high-temperature superconductor research due to their excellent electron-phonon coupling and high T_c upon pressurization. This study explores the electronic structures and electron-phonon coupling of metal hydrides XH_n (n = 4,6), where X includes Ca, Mg, Sc, and Y. The involvement of d-orbital electrons alters the Fermi surface, leading to saddle-point nesting and a charge density wave (CDW) phase transition, which opens the superconducting gap. For instance, in YH₆, the exchange coupling between Y-4d and H-1s holes in the phonon softening region results in T_c values up to 230 K. The study suggests that factors, such as the origin of the CDW order, hydrogen concentration, and d-orbital contributions are crucial to superconductivity. This work proposes a new rule for high T_c superconductors, emphasizing the importance of double gaps and electron-phonon interactions at exchange coupling sites, and predicts potential high-quality superconductors among rare-earth hydrides.