Endohedral gallide cluster superconductors and PNAS PLUS superconductivity in ReGa5 Weiwei Xiea, Huixia Luoa, Brendan F. Phelana, Tomasz Klimczukb, Francois Alexandre Cevallosa, and Robert Joseph Cavaa,1 aDepartment of Chemistry, Princeton University, Princeton, NJ 08540; and bFaculty of Applied Physics and Mathematics, Gdansk University of Technology, 80-233 Gdansk, Poland Contributed by Robert Joseph Cava, November 11, 2015 (sent for review October 12, 2015; reviewed by Malcolm R. Beasley and Danna Freedman) We present transition metal-embedded (T@Gan) endohedral Ga- Endohedral Gallium Clusters and Superconductivity clusters as a favorable structural motif for superconductivity and Elemental gallium, in group 13, is located at the Zintl border in develop empirical, molecule-based, electron counting rules that the periodic table and is known in solid state chemistry for its govern the hierarchical architecturesthattheclustersassumein tendency, due to its moderate electronegativity, to form com- T binary phases. Among the binary @Gan endohedral cluster systems, pounds based on gallium clusters (11). (The Zintl border separates Mo8Ga41,Mo6Ga31,Rh2Ga9,andIr2Ga9 are all previously known groups 13 and 14. In combination with electropositive metals, the superconductors. The well-known exotic superconductor PuCoGa5 elements in group 14 and to the right usually form compounds and related phases are also members of this endohedral gallide whose electronic structures are consistent with filled bonding, fil- cluster family. We show that electron-deficient compounds like led nonbonding, and empty antibonding levels, and therefore are Mo8Ga41 prefer architectures with vertex-sharing gallium clusters, electron precise, which is not generally the case for group 13 and whereas electron-rich compounds, like PdGa5, prefer edge-sharing to the left.) Previous investigations of binary alkali metal-Ga (A-Ga) cluster architectures. The superconducting transition temperatures solid state systems have resulted in the discovery of many new Zintl are highest for the electron-poor, corner-sharing architectures. Based compounds, in which Gan clusters or molecules use the electrons on this analysis, the previously unknown endohedral cluster com- donated from the alkali metals to satisfy their valence requirements pound ReGa5 is postulated to exist at an intermediate electron (12). The large electronegativity differences between alkali metals SCIENCES count and a mix of corner sharing and edge sharing cluster archi- and Ga always makes these AmGan Zintl compounds valence-precise APPLIED PHYSICAL tectures. The empirical prediction is shown to be correct and leads semiconductors, i.e., they display a relatively large band gap between to the discovery of superconductivity in ReGa5.TheFermilevelsfor occupied and unoccupied states, motivating the investigation of Zintl endohedral gallide cluster compounds are located in deep pseudo- compounds as good thermoelectric materials above ambient tem- gaps in the electronic densities of states, an important factor in de- perature (13). Structurally, the Ga atoms in A Ga systems form termining their chemical stability, while at the same time limiting m n icosahedral (Ga12)oroctahedral(Ga6) clusters, analogous to their superconducting transition temperatures. those found in borane chemistry (14). The gallium clusters in the Zintl phases are analogs to borane clusters and follow the same superconducitivity | endohedral cluster | solid state chemistry rules for the number of skeletal electrons required for stability. When replacing alkali metals with lanthanides or actinides (R)to he prediction of new superconductors remains an elusive goal. form Ga-rich RmGan compounds, the electronegativity differences TAlthough one can analyze the superconductivity, once dis- between R and Ga are smaller than those between the alkalis and covered, through materials physics-based “k-space” pictures Ga, and the semiconducting band gap diminishes—sometimes to based on Fermi surfaces, energy band dispersions, and effec- zero to yield metallic conductivity. The formation of exo-bonds to tive interactions, often it is chemists, whose viewpoint is instead other clusters in vertex-sharing, edge-sharing, or face-sharing cluster from “real space” rather than k-space, who find such super- conductorsinthefirstplace(1,2).Giventhedifficultyin Significance making extrapolations between the physics of superconductivity and the chemical stability of compounds that will be super- conducting, there are as many strategies for finding new su- The prediction of new superconductors remains an elusive goal. perconductors as there are researchers looking for them (3–5). It is often chemists who find new superconductors, although it is Most such search strategies fail, because the interactions that difficult to translate the physics of superconductivity into chemical give rise to superconductivity can also lead to competing elec- requirements for discovering new superconducting compounds. tronic states or can be strong enough to tear potential com- There are many strategies for finding new superconductors, one pounds apart (6, 7). being to postulate that superconductivity runs in structural fam- One chemical perspective for increasing the odds of finding ilies. Here we show that a previously unappreciated structural superconductivity is to postulate that it runs in structural fami- family, the endohedral gallium cluster phases, is favored for su- lies. The perovskites are a well-known example of this in metal perconductivity, and then use the understanding we develop to find a superconductor. More broadly, our work shows that mol- oxides, and in intermetallic compounds, the “122” ThCr Si 2 2 ecule-based electron counting and stability rules can provide a structuretypeisagoodexample(8–10). It is the discovery of useful chemistry-based design paradigm for finding new super- these new structural families of superconductors that often leads, conductors. Using these ideas to search for new superconductors sometimes slowly or sometimes quickly, to advances in new will be of significant future interest. superconducting materials. Here we show that a previously un- appreciated chemical family, the endohedral gallium cluster Author contributions: W.X. and R.J.C. designed research; W.X., H.L., and F.A.C. performed phases, is a favored chemical family for superconductivity. Fur- research; W.X., T.K., and R.J.C. analyzed data; and W.X., B.F.P., and R.J.C. wrote the paper. ther, we analyze the occurrence and hierarchical structures of Reviewers: M.R.B., Stanford University; and D.F., Northwestern University. such phases from a molecular perspective and then use that The authors declare no conflict of interest. perspective to predict the existence and structure of a pre- 1To whom correspondence should be addressed. Email: [email protected]. viously unreported compound, ReGa5. We find that compound This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. and discover it to be superconducting. 1073/pnas.1522191112/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1522191112 PNAS Early Edition | 1of7 Downloaded by guest on September 23, 2021 Table 1. Selected Binary Phases with Endohedral Ga-clusters Binary Structure Pearson compounds type symbol Tc (K) Reference V8Ga41 V8Ga41 hR147 — Girgis et al. (36) Mo8Ga41 V8Ga41 hR147 9.8 Yvon (23) Mo6Ga31 Mo6Ga31 mS148 8 Yvon (23) ReGa5 ReGa5 oS48 2.3 This work Rh2Ga9 Co2Al9 mP22 2.0 Shibayama et al. (22) Ir2Ga9 Co2Al9 mP22 2.3 Shibayama et al. (22) PdGa5 PdGa5 tI24 — Grin et al. (29) hierarchies and the distortion of the clusters away from ideal deltahedral symmetries can also stabilize RmGan compounds (15). Examples of the Ga clusters in these compounds can be seen in Fig. 1A. The introduction of transition metals (T)tothecentersofthe gallium clusters to create T@Gan endohedral clusters reduces the cluster charge and is an important path to gallide chemical stability. For example, the Ni-centered Ni@Ga10 cluster (Fig. 1A) yields the chemical stability of Na10NiGa10 (11). Of great interest for their electronic properties are the large number of thus-derived ternary A/R-T-Ga (A = alkali or alkali-earth; R = lanthanide or actinide; and T = late transition metal) compounds. An important class of superconductors has been discovered in this group. The actinide-based compound PuCoGa5, for example, is assembled from metal-centered endohedral clusters: Pu-cen- tered Ga cuboctahedra (Pu@Ga12) and Co-centered Ga cubes (Co@Ga8) (Fig. 1 B and C) and displays a very high critical temperature Tc= 18.5 K that increases to 22 K under pressure (16). The Tc= 2.8 K superconductor Sm4Co3Ga16 similarly con- tains Sm@Ga12 and Co@Ga8 endohedral clusters that are iso- structural with the Pu@Ga12 and Co@Ga8 clusters in PuCoGa5; because the clusters are not present in a 1:1 ratio, the hierarchical Fig. 2. Electronic structures of Ga-cluster–based binary phases from a mo- lecular perspective. (Left) The isolated clusters, showing for each: above, the Gan clusters and then below, the TGan endohedral clusters. (Center) The molecular energy level diagrams for the isolated Ga-clusters and the T-cen- tered endohedral Ga-clusters, obtained using the extended Hückel theory. (Two different minimal basis sets involving Slater-type single-zeta functions for s and p orbitals and double-zeta functions for d orbitals were used.) (Right) The electronic DOS generated by VASP based on the optimized crystal structures of Mo8Ga41,Rh2Ga9,andPdGa5.