Endohedral gallide cluster superconductors and superconductivity in ReGa₅

We present transition metal-embedded (T@Ga_n) endohedral Gaclusters as a favorable structural motif for superconductivity and develop empirical, molecule-based, electron counting rules that govern the hierarchical architectures that the clusters assume in binary phases. Among the binary T@Ga_n endohedral cluster systems, Mo₈Ga₄₁, Mo₆Ga₃₁, Rh₂Ga₉, and Ir₂Ga₉ are all previously known superconductors. The well-known exotic superconductor PuCoGa₅ and related phases are also members of this endohedral gallide cluster family. We show that electron-deficient compounds like Mo₈Ga₄₁ prefer architectures with vertex-sharing gallium clusters, whereas electron-rich compounds, like PdGa₅, prefer edge-sharing cluster architectures. The superconducting transition temperatures are highest for the electron-poor, corner-sharing architectures. Based on this analysis, the previously unknown endohedral cluster compound ReGa₅ is postulated to exist at an intermediate electron count and a mix of corner sharing and edge sharing cluster architectures. The empirical prediction is shown to be correct and leads to the discovery of superconductivity in ReGa₅. The Fermi levels for endohedral gallide cluster compounds are located in deep pseudogaps in the electronic densities of states, an important factor in determining their chemical stability, while at the same time limiting their superconducting transition temperatures.