Endohedral gallide cluster superconductors andsuperconductivity in ReGa5Weiwei 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-clusters as a favorable structural motif for superconductivity anddevelop empirical, molecule-based, electron counting rules thatgovern the hierarchical architectures that the clusters assume inbinary phases. Among the binary T@Gan endohedral cluster systems,Mo8Ga41, Mo6Ga31, Rh2Ga9, and Ir2Ga9 are all previously knownsuperconductors. The well-known exotic superconductor PuCoGa5and related phases are also members of this endohedral gallidecluster family. We show that electron-deficient compounds likeMo8Ga41 prefer architectures with vertex-sharing gallium clusters,whereas electron-rich compounds, like PdGa5, prefer edge-sharingcluster architectures. The superconducting transition temperaturesare highest for the electron-poor, corner-sharing architectures. Basedon this analysis, the previously unknown endohedral cluster com-pound ReGa5 is postulated to exist at an intermediate electroncount and a mix of corner sharing and edge sharing cluster archi-tectures. The empirical prediction is shown to be correct and leadsto the discovery of superconductivity in ReGa5. The Fermi levels forendohedral gallide cluster compounds are located in deep pseudo-gaps in the electronic densities of states, an important factor in de-termining their chemical stability, while at the same time limitingtheir superconducting transition temperatures.

superconducitivity | endohedral cluster | solid state chemistry

The prediction of new superconductors remains an elusive goal.Although one can analyze the superconductivity, once dis-

covered, through materials physics-based “k-space” picturesbased on Fermi surfaces, energy band dispersions, and effec-tive interactions, often it is chemists, whose viewpoint is insteadfrom “real space” rather than k-space, who find such super-conductors in the first place (1, 2). Given the difficulty inmaking extrapolations between the physics of superconductivityand the chemical stability of compounds that will be super-conducting, there are as many strategies for finding new su-perconductors as there are researchers looking for them (3–5).Most such search strategies fail, because the interactions thatgive rise to superconductivity can also lead to competing elec-tronic states or can be strong enough to tear potential com-pounds apart (6, 7).One chemical perspective for increasing the odds of finding

superconductivity is to postulate that it runs in structural fami-lies. The perovskites are a well-known example of this in metaloxides, and in intermetallic compounds, the “122” ThCr2Si2structure type is a good example (8–10). It is the discovery ofthese new structural families of superconductors that often leads,sometimes slowly or sometimes quickly, to advances in newsuperconducting materials. Here we show that a previously un-appreciated chemical family, the endohedral gallium clusterphases, is a favored chemical family for superconductivity. Fur-ther, we analyze the occurrence and hierarchical structures ofsuch phases from a molecular perspective and then use thatperspective to predict the existence and structure of a pre-viously unreported compound, ReGa5. We find that compoundand discover it to be superconducting.

Endohedral Gallium Clusters and SuperconductivityElemental gallium, in group 13, is located at the Zintl border inthe periodic table and is known in solid state chemistry for itstendency, due to its moderate electronegativity, to form com-pounds based on gallium clusters (11). (The Zintl border separatesgroups 13 and 14. In combination with electropositive metals, theelements in group 14 and to the right usually form compoundswhose electronic structures are consistent with filled bonding, fil-led nonbonding, and empty antibonding levels, and therefore areelectron precise, which is not generally the case for group 13 andto the left.) Previous investigations of binary alkali metal-Ga (A-Ga)solid state systems have resulted in the discovery of many new Zintlcompounds, in which Gan clusters or molecules use the electronsdonated from the alkali metals to satisfy their valence requirements(12). The large electronegativity differences between alkali metalsand Ga always makes these AmGan Zintl compounds valence-precisesemiconductors, i.e., they display a relatively large band gap betweenoccupied and unoccupied states, motivating the investigation of Zintlcompounds as good thermoelectric materials above ambient tem-perature (13). Structurally, the Ga atoms in AmGan systems formicosahedral (Ga12) or octahedral (Ga6) clusters, analogous tothose found in borane chemistry (14). The gallium clusters in theZintl phases are analogs to borane clusters and follow the samerules for the number of skeletal electrons required for stability.When replacing alkali metals with lanthanides or actinides (R) toform Ga-rich RmGan compounds, the electronegativity differencesbetween R and Ga are smaller than those between the alkalis andGa, and the semiconducting band gap diminishes—sometimes tozero to yield metallic conductivity. The formation of exo-bonds toother clusters in vertex-sharing, edge-sharing, or face-sharing cluster

Significance

The prediction of new superconductors remains an elusive goal.It is often chemists who find new superconductors, although it isdifficult to translate the physics of superconductivity into chemicalrequirements for discovering new superconducting compounds.There are many strategies for finding new superconductors, onebeing to postulate that superconductivity runs in structural fam-ilies. Here we show that a previously unappreciated structuralfamily, the endohedral gallium cluster phases, is favored for su-perconductivity, and then use the understanding we develop tofind a superconductor. More broadly, our work shows that mol-ecule-based electron counting and stability rules can provide auseful chemistry-based design paradigm for finding new super-conductors. Using these ideas to search for new superconductorswill be of significant future interest.

Author contributions: W.X. and R.J.C. designed research; W.X., H.L., and F.A.C. performedresearch; W.X., T.K., and R.J.C. analyzed data; and W.X., B.F.P., and R.J.C. wrote the paper.

Reviewers: M.R.B., Stanford University; and D.F., Northwestern University.

The authors declare no conflict of interest.1To whom correspondence should be addressed. Email: rcava@princeton.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1522191112/-/DCSupplemental.

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hierarchies and the distortion of the clusters away from idealdeltahedral symmetries can also stabilize RmGan compounds (15).Examples of the Ga clusters in these compounds can be seen inFig. 1A.The introduction of transition metals (T) to the centers of the

gallium clusters to create T@Gan endohedral clusters reducesthe cluster charge and is an important path to gallide chemicalstability. For example, the Ni-centered Ni@Ga10 cluster (Fig.1A) yields the chemical stability of Na10NiGa10 (11). Of greatinterest for their electronic properties are the large number ofthus-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 inthis 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 criticaltemperature 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

architecture is more complex in this compound (17). Also im-portant as heavy fermion superconductors are the In analogs ofthese phases, the CeMIn5 (M = Co, Rh, Ir) family of compounds,which are iso-structural with PuCoGa5; their study has consid-erably illuminated the understanding of the interplay betweensuperconductivity and magnetism (18). Fig. 1 summarizes thestructural relationships described here.The electron transfer between cations and anions in the A-Ga

or R-Ga systems is clearly primarily ionic due to the large elec-tronegativity differences (19). It is much less obvious, however,to tell a priori how the electrons are transferred in Ga-rich T-Ga(T = transition metal) binary phases such as Mo8Ga41 andPdGa5, because the electronegativities for late transition metalsand gallium are similar (20, 21). Nonetheless, we can define herea set of electron counting rules and the relationships betweenelectron counting and the hierarchical architectures of theendohedral clusters required for chemical stability through ob-servation of the known phases. Further, we can establish an

Fig. 1. Schematic structural relationships among different kinds of Ga-cluster compounds. (A) Ga metal reacts with alkali and alkali earth elementsto yield Zintl phases such as K3Ga13, which has isolated Ga12 icosahedralclusters, and Ba5Ga6, which has Ga6 octahedral clusters. In Na10NiGa10, atransition metal (Ni)-centered endohedral Ni@Ga10 cluster is found (19).(B) The combination of Ga plus R (R = lanthanide and actinide elements)leads to the formation of polar intermetallics, for example, PuGa6, which con-tains Pu@Ga12 clusters (15). (C) Centering Ga-clusters with transition metalsstabilizes Ga-cluster compounds such as CoGa3, which contains Co@Ga8square antiprism clusters (38). (D) Combining T-centered and R-centeredclusters forms the unconventional superconductor PuCoGa5, in which Pu@Ga12cuboctahedra share faces with neighboring Pu@Ga12 and Co@Ga8 (cube)clusters (16). (E) Adding more Ga atoms to T-Ga systems forms other Ga-richcompounds, such as the superconductor Mo8Ga41. In this compound, Mo@Ga10clusters are found (23).

Table 1. Selected Binary Phases with Endohedral Ga-clusters

Binarycompounds

Structuretype

Pearsonsymbol 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 workRh2Ga9 Co2Al9 mP22 2.0 Shibayama et al. (22)Ir2Ga9 Co2Al9 mP22 2.3 Shibayama et al. (22)PdGa5 PdGa5 tI24 — Grin et al. (29)

Fig. 2. Electronic structures of Ga-cluster–based binary phases from a mo-lecular perspective. (Left) The isolated clusters, showing for each: above, theGan clusters and then below, the TGan endohedral clusters. (Center) Themolecular 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 functionsfor s and p orbitals and double-zeta functions for d orbitals were used.)(Right) The electronic DOS generated by VASP based on the optimized crystalstructures of Mo8Ga41, Rh2Ga9, and PdGa5.

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empirical relationship between electron counting and super-conducting transition temperature in these compounds; we findthat as the number of electrons per formula unit decreases, thecritical temperature for superconductivity first increases andthen decreases. Among the previously reported binary endohe-dral Ga cluster phases, Mo8Ga41 is a superconductor with Tc =9.8 K (1); Mo6Ga31 is a superconductor with Tc = 8.0 K (1);Rh2Ga9 is a superconductor with Tc = 2.0 K; and Ir2Ga9 is asuperconductor with Tc = 2.3 K (22).Based on this understanding, we designed and synthesized

the previously unreported binary endohedral cluster compoundReGa5 and found it to be superconducting at a critical temper-ature Tc = 2.3 K. Our electronic structure calculations showthat the Fermi level of ReGa5 is located within a pseudogapin density of electronic states (DOS), which, as is seen in theother binary endohedral gallium cluster superconductors, isrequired for the chemical stability of the compound. Given thatsuperconducting transition temperatures should be higher formaterials with a higher density of electronic states and that thelocation of the Fermi energy within a deep pseudogap is arequirement for chemical stability in the endohedral gallidephases, superconductivity and structural stability can be seen tocompete in this family. Nonetheless, a compromise is clearlymet between the two competing factors in the real materials,resulting in a large family of superconducting endohedral galliumcluster compounds.

Electron Counting Rules for Ga-Rich Compounds and aMolecular Perspective on Ga-Clusters in SolidsMo8Ga41 and Mo6Ga31. In the crystal structure of Mo8Ga41, themost striking features are Mo atoms inside 10-atom Ga clusters,i.e., Mo@Ga10 endohedral clusters (23, 24). These endohedralclusters are arranged such that an almost regular cube of Moatoms is found. The Mo@Ga10 clusters share all their vertex Ga,an architecture that creates a Ga cuboctahedron in the intersti-tial space between clusters that is itself centered by a Ga atom inMo8Ga41; this compound can thus be written as Ga(MoGa5)8.The whole architecture is strongly reminiscent of an A-site de-ficient perovskite oxide, i.e., Ga1/8Mo@Ga10/2 ∼ AxTO6/2, althoughwith 10-vertex-connected dodecahedral Mo@Ga10 clusters ratherthan 6-vertex-connected M@O6 octahedral clusters. The perovskitestructure is known to host many important superconductors, rang-ing from the high Tc copper oxides to low Tc Na0.23WO3, and inanalogy Mo8Ga41 is also superconducting (25). The overall sym-metry of the thus-arranged endohedral clusters in Mo8Ga41 isrhombohedral, which is one of the variants of the many possibledistortions of the simple cubic lattice found in oxide perovskites (8).

In the crystal structure of the related superconducting clusterphase Mo6Ga31, two of the Mo@Ga10 endohedral clusters arefused together, such that 4 of the 10 Ga are shared between twoMo, in an edge sharing motif (23). The four peripheral Ga’s sharedbetween endohedral clusters are on the vertices of a square, cre-ating an overall face sharing motif of double clusters. Thesedouble clusters share vertices with other double clusters to createa mixed corner sharing plus edge sharing architecture. This kind ofdouble cluster architecture in Mo6Ga31 is again reminiscent of themotif found in other superconducting phases: in this case, thefamily of Chevrel structure-derived phases made from corner andface-sharing Mo6S8 clusters (26).To investigate the electronic factors behind the vertex-sharing

Mo@Ga10 cluster architecture in Mo8Ga41, we begin with theelectronic structure of the hypothetical model compound Mo8Ga40,which is based on removing the Ga that is in the interstitial re-gion between the Mo@Ga10 clusters in Mo8Ga41. HypotheticalMo8Ga40 (i.e., MoGa5) made only of the endohedral clusterssharing corner Ga, was then subject to complete structural op-timization using Vienne Ab Initio Simulation Package (VASP)(27). The electronic structure of this compound is shown in Fig.2A. We find that the Fermi level of MoGa5, which has 21e-(6 from Mo and 3 × 5 from Ga) is located in a pseudogap in theelectronic DOS. An important question to next consider is howthe endohedral Mo atom affects the stability of the Ga10-cluster.To get further insight, then, extended Hückel theory was used toanalyze isolated molecular “Ga10” and “MoGa10” clusters (28).

Fig. 3. Motivation for searching for superconductors in the Re-Ga systems based on electron counting and cluster architectures. Mo8Ga41 contains vertex-sharing 10-coordinate Ga-clusters; Rh2Ga9 and PdGa5 contain both vertex-sharing and edge-sharing clusters. Before the current work there were no knowncompounds in this family with 22 electrons per transition metal.

Fig. 4. The crystal structure of ReGa5. ReGa5 crystalizes in an orthorhombicstructure with space group Cmce (S.G. 64). (green, Ga; pink, Re.) (A) This viewemphasizes the shapes of the clusters. (B) This view emphases the vertex-sharing of the clusters and the square faces with four-corner Ga atoms thatare shared to create the double cluster architecture.

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Fig. 2 (Top Left) illustrates the crystal orbital energy diagramsfor the two cases evaluated (the primitive unit cell used containsone 10-atom Ga-cluster or one 11-atom Mo-centered Ga-clusterat the corners of the cell) at the Γ-point in the Brillouin zone,with the orbital energies given relative to the correspondingFermi levels. We find that after inserting the Mo atom into theGa10 cluster to create an endohedral cluster, the degenerate or-bitals at EF in the Ga10 cluster are split significantly in energy,resulting in EF (the Fermi energy) for Mo@Ga10 being in anenergy gap rather than in a partially occupied state with a signif-icant DOS, and stabilizing the cluster. These crystal orbital energydiagrams provide a rationale for how Ga10-clusters are stabilizedthrough the presence of endohedral transition metal elements.

Rh2Ga9 (Ir2Ga9) and PdGa5. Superconducting Rh2Ga9 and Ir2Ga9both crystalize in the Co2Al9-type structure (22). The Ga clustersin these compounds are single-capped square antiprismatic Ga9

(or Al9) clusters with endohedral transition metal atoms, creat-ing T@Tr9 (T = Co, Rh, or Ir and Tr = Al or Ga) endohedralclusters. These endohedral clusters are assembled in edge-shar-ing zig-zag strands along one crystallographic axis (the c axis inthe monoclinic unit cell) and share corners between strands. Thus,in this Co2Al9 structure type, the T@Tr9 clusters share both cor-ners and edges. As was the case for Mo8Ga41, we calculated theelectronic structure of Rh2Ga9 and find that the Fermi level isagain located in a pseudogap in the density of states at an electroncount of 22.5 e- per RhGa4.5 (Rh2Ga9/2) unit (Fig. 2, Middle Right).A sharp, deep pseudogap is seen about 0.25 eV below the Fermilevel, associated with 22 e- per RhGa4.5. Similarly to what weobserved for Mo@Ga10 clusters from molecular orbitals calcu-lations, we find that the Rh-centered Ga9 cluster is more stablethan the empty Ga9 cluster due to the splitting in energy ofdegenerate orbitals at the Fermi level (Fig. 2, Middle Left).PdGa5 crystalizes in a tetragonal crystal structure (29). In bi-

nary PdGa5, each palladium atom is coordinated by 10 galliumatoms in the form of a bicapped tetragonal antiprism, formingPd@Ga10 clusters. The Pd@Ga10 clusters share edges (8 Ga)and vertices (2 Ga). The Fermi level in the electronic structure ofPdGa5 is located in a pseudogap with 25 e-/PdGa5, again inanalogy to what is seen in the other gallate cluster compounds. Asharp narrow gap about 1.5 eV above the Fermi level is associ-ated with 26 e- per Pd. Thus, just as we find in the other endo-hedral cluster compounds, the Pd atoms play an important rolein splitting the orbitals of Ga10 to place the Fermi level in the gapand thus yield chemical stability.From these and similar analyses, considering Ga-rich binary

phases, we find that electron-deficient compounds such asMo8Ga41 prefer vertex-sharing of the Ga clusters, whereaselectron-rich (26e-) compounds like PdGa5 favor edge-sharing ofthe clusters. A single formula for the formation of stable T-Gacompounds can therefore be found. The formula is TGa(n-1/2*m+l)(n = number vertices of the T-centered cluster;m = shared vertices;l = isolated Ga atoms in interstitial positions). Moreover, thesuperconducting transition temperature changes for the endohe-dral cluster compounds as one progresses in the transition metalseries fromMo, to Rh/Ir, to Pd. Noting the missing members of theseries in both electron count and structure, we thus postulated the

Fig. 5. The calculated electronic structure for ReGa5: the physics-basedpicture. (Left) The total DOS as a function of energy near the Fermi energy (E =0) obtained from LDA calculations in WEIN-2k with spin-orbit coupling (SOC)included. (Right) The corresponding energy dispersion of the bands in selecteddirections in the orthorhombic Brillouin zone.

Fig. 6. Characterization of the superconducting transition of ReGa5. (A) χv (T) measured in a 10 Oe applied magnetic field from 1.8 to 6 K with zero-fieldcooling. (Inset) Resistivity vs. temperature over the range of 2–50 K measured in different applied magnetic fields. (B) Temperature dependence of theelectronic specific heat Cel of ReGa5. The sample was measured with (μ0H = 5T) and without magnetic field, presented in the form of Cp/T (T), and theelectronic part was obtained from heat capacity at μ0H = 5T. (Inset) Temperature dependence of specific heat Cp of ReGa5 sample measured with (5T) andwithout magnetic field, presented in the form of Cp/T (T2).

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existence of several possible new compounds and set out to syn-thesize them and test their properties.

Structural and Physical Properties of the PreviouslyUnreported Superconductor ReGa5The Synthesis of ReGa5 and Phase Information. Based on the un-derstanding above, we realized that that there were no compoundsknown with 22 electrons per T atom and we thus attempted theirsynthesis. Loading compositions of Re1.5Ga98.5 and Re3Ga97 (Re:powder, 99.999%, Alfa Aesar; Ga: sponge, 99.995%, Alfa Aesar)about 1 g total mass, were sealed into evacuated SiO2 jackets(<10−5 Torr) to protect them from air during heating. Thesamples were heated to 900 °C for 24 h at a speed of 3 °C/min,followed by cooling to 500 °C at a rate of 4 °C/h, and annealed atthis temperature for 2 d, after which the containers were spun inthe centrifuge at 1,200 × g for 10 s. Both loading compositionsgive the same previously unreported compound, ReGa5 accordingour subsequent analysis, with Ga-flux as a minor impurity. Look-ing for the analogous cluster compound based on Ru was notsuccessful; Ru1.5Ga98.5 and Ru3Ga97 reacted using the sameprocedure yielded only the known compound RuGa3. This 17electron per cluster compound is semiconducting with extensiveedge-sharing of Ru@Ga9 endohedral clusters; the Fermi energyfalls in a deep, wide gap in the density of states (Fig. S2).

The Crystal Structure of ReGa5 and Comparison with PdGa5 and MoGa5.To obtain insights into the detailed structure of the new Re-basedGa-rich compound found, single crystals were investigated. Theresults of single crystal X-ray diffraction characterization of aspecimen extracted from a single crystal sample of nominal com-position ReGa5 are summarized in Tables S1 and S2 and thecrystal structure of ReGa5 is shown in Fig. 5. ReGa5 crystallizesin an orthorhombic crystal structure in space group Cmce (spacegroup 64) and displays a previously unobserved structure type. Itcan be described in terms of single-capped square antiprismatic co-ordination polyhedra of Ga around the transition metal atoms,forming Re@Ga9 endohedral clusters. These clusters are structurallyanalogous to those found for Ru@Ga9 in RuGa3. The architectureof the new compound is different, however, from those previously

observed. Four neighboring Ga atoms on one of the square facesof a Re@Ga9 cluster are shared with a neighboring Re@Ga9cluster, creating an overall double cluster architecture. EachRe@Ga9 double cluster then also shares 4 vertex Ga with neigh-boring clusters in a corner sharing geometry, and, finally, a“capping” Ga is left coordinated to only a single Re.

The Electronic Structure of ReGa5According to the electron counting rules described above, theschematic electronic structure diagram for ReGa5 is shown inFig. 3. We consider two formula units of ReGa5, which are thecontents of the primitive unit cell. The two Re atoms per unit cellbring 10 d orbitals to the electronic system, whereas the two setsof Ga4 on the corners of the shared square faces in the doublecluster bring 32 Ga sp orbitals. Strong interactions occur withinthe Ga4 portion, a reflection of the multiple Ga-Ga contacts inthe structure. In the scheme here, there are 8 + x low-lying Galevels for the two Ga4 and 4 − y low-lying Ga levels for 2 isolatedGa atoms, 12 being the minimum number of Ga levels needed tomake the 22 occupied orbitals per Re2Ga10. For Re2Ga10, then,the total number of electrons is: 2 × 7e-/Re + 10 × 3e-/Ga = 44e-/Re2Ga10. This means that 22 bonding orbitals in the cluster wouldbe fully occupied by electrons, and the Fermi level of ReGa5 shouldbe located in a gap or pseudogap in the DOS. To test whether thesemolecule-like the electron counting rules work for ReGa5 whenconsidered in the context of the electronic structure expected from aphysics-based electronic picture, the electronic structure of ReGa5was calculated by use of the program WIEN2k with spin-orbit cou-pling included. Dramatically, the Fermi level is exactly located inthe deep pseudogap in the DOS, just as expected from our mo-lecular picture. Thus, unlike the case for regular superconduc-tors, where having the Fermi level on a peak in DOS is preferredfor superconductivity, a different kind of electronic structureis found for ReGa5. The WEIN2k calculations allow for theelectronic structure to be described in more detail than isavailable in the molecular picture: the valence and conductionbands barely cross the Fermi energy in ReGa5, at differentplaces in the Brillouin zone (Fig. 5), in an electronic structure

Fig. 7. The structural and electronic characteristics of the binary endohe-dral gallide cluster superconductor family. The horizontal axis is the numberof electrons (e-) per transition metal and the vertical axis is the super-conducting transition temperature (Tc). The formulas of the compounds areshown. The endohedral clusters shown in the insets illustrate the crossoverfrom corner sharing to edge sharing cluster architectures as a function ofelectron count.

Fig. 8. Comparison of the superconducting Tc vs. electron count and thecalculated electronic DOS at EF vs. electron count for the endohedral gallidecluster superconductors. The plot has been scaled so that the peaks for Tcand the calculated DOS near Mo8Ga41 (∼21.4 e- per transition metal) co-incide. If Matthias’ rule for intermetallic superconductors generally held inthis family, then the two curves would coincide over the whole range; theydo for small electron counts but not for high electron counts. (Inset) Calcu-lated DOS near EF (displaced along the vertical axis for clarity) for theendohedral gallide superconductors.

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that is reminiscent of that of the semimetal WTe2 (30). Specif-ically, one conduction band comes down in energy, crossing theFermi level and then increasing in energy again, between theZ-G-X points, whereas one valence band increases in energy,crosses the Fermi level, and then comes down again, again be-tween the Z-G-X points.

Superconductivity in ReGa5. The resistivity of ReGa5 undergoes asudden drop to zero at 2.3 K, characteristic of superconductivity.In correspondence with ρ(T), the magnetic susceptibility [χmol(T)]measured in a field of 10 Oersteds after zero field cooling de-creases from its normal state value at 2.3 K and shows largenegative values, characteristic of an essentially fully super-conducting sample. To prove that the observed superconductivityis intrinsic to the ReGa5 compound the superconducting transi-tion was characterized further, through specific heat (Cp) mea-surements. The Inset of Fig. 6B shows Cp/T vs. T2 in thetemperature range 1.85–4 K under a magnetic field of 5T (opensquares) and 0T (blue circles). The zero field data were fit byusing the formula Cp/T = γ + βT2, yielding the electronic specificheat (Sommerfeld) coefficient γ = 4.68(7) mJ·mol−1·K−2 and thephonon specific heat coefficient β = 0.38(1) mJ·mol−1·K−4. Thelatter quantity is related to the Debye temperature (ΘD) throughΘD = (12π4nR/5β)1/3, and the estimated Debye temperature forReGa5 is thus 314(2) K. This temperature is only 6 K lower thanthe Debye temperature for Ga metal (ΘD = 320 K) (31). Fig. 6Bpresents the temperature dependence of the zero-field electronicspecific heat Cel/T. The good quality of the sample and the bulknature of the superconductivity are strongly supported by thepresence of a large anomaly in the specific heat at Tc = 2.1 K, inexcellent agreement with the Tc determined by ρ(T) and χmol(T).An equal entropy construction gives the specific heat jump ΔCel./γTc = 1.6, which is slightly larger than expected for a weak-coupling BCS superconductor, where it is 1.43 (32, 33). Using theMcMillan equation (34), we calculate the electron-phonon cou-pling constant λep = 0.51. [For this calculation the Coulomb re-pulsion constant was taken as μ* = 0.13 (μ* = 0.13 falls in therange 0.1–0.15 used in the literature) (35).] Having both theelectron-phonon coupling constant λep and the Sommerfeld co-efficient γ, the density of states at the Fermi energy can be cal-culated from N(EF) = 3γ/[π2k2B(1 + λep)]. The N(EF) obtainedfor ReGa5 is low, N(EF) = 1.3 states eV−1 per formula unit andagrees with band structure calculations.

Superconductivity in the Endohedral Gallide Cluster Family andComparison with Matthias’ Rules. The concepts and results de-scribed here are presented in Fig. 7, which summarizes the structuraland electronic character of the endohedral gallide superconductorfamily. The correlation of the superconducting transition tempera-tures with the chemical and structural characteristics is shown.The plot includes the superconductor discovered here, ReGa5,the previously known superconductors, and the nonsuperconductorsV8Ga41 (36) and PdGa5 (29). The best superconductors are foundfor the endohedral molybdenum gallides, whose hierarchal clusterarchitectures and electron counts are intermediate in the context ofthe full family. To determine whether it is solely the electron count

that governs the superconducting Tc, the Tcs can be compared withthe calculated electronic DOS for the materials in the family. Thiscomparison is shown in Fig. 8, which is essentially an extension ofMatthias’ rules for intermetallic transition metal-based supercon-ductors, where Tc simply tracks the d-state derived electronic den-sity of states at EF (37). The current case is not as straightforwardbecause the chemistry and structures are more complex and allcompounds are required to be near a minimum in the density ofstates to be chemically stable. Nonetheless a fruitful comparison canbe made. Thus, Fig. 8 shows the observed superconducting Tc vs.electron count and the calculated DOS at EF vs. electron count forthe endohedral gallide superconductors. The plot is scaled so thatthe peaks for Tc and the calculated DOS near Mo8Ga41 (∼21.4 e-per transition metal) coincide. If Matthias’ rules for intermetallicsuperconductors generally held in this family, i.e., if Tc were solelydetermined by the electronic density of states, then the two curveswould coincide over the whole range. They do not, coinciding nicelyfor small electron counts but not for high electron counts. Theimplication is that both the electron count and the architecture ofthe endohedral cluster packing play an important role in de-termining Tc, the former at low electron counts and the latter at thehigher electron counts; i.e., if the DOS was the dominant factor indetermining Tc for the gallide cluster superconductors, then the Tcfor PdGa5 should be comparable to that for Mo8Ga41. It is not.

ConclusionThe endohedral gallide cluster compounds are presented as achemical family that is favorable for superconductivity. Based onthe electronic structures of isolated transition metal-centeredendohedral clusters, a molecule-based electronic understandingof the materials is developed that relates their chemical stability,formulas, and the hierarchical architecture of the clusters whenfound in solid compounds. The empirical electron counting rulesdeveloped for the stability of T-Ga binary compounds in thisfamily, TGa(n-1/2*m+l) (T = transition metal, n = vertices of theT-centered cluster; m = shared vertices; l = isolated Ga atom),revealed the lack of superconducting examples at 22 electronsper transition metal. This led to the investigation the Re-Gachemical system. Validating the molecule-based viewpoint of thisfamily of materials, the previously unreported compound ReGa5was found, structurally characterized, and analyzed by electronicstructure calculations. Further, resistivity, heat capacity andmagnetic susceptibility measurements revealed ReGa5 to be asuperconductor with a Tc ∼ 2.3 K. This work shows that selectionof potential superconducting materials based on molecular elec-tron counting rules, here demonstrated in a family of endohedralcluster compounds, is a useful chemistry-based design paradigmfor finding new superconductors. Extension of this concept toadditional materials families will be of significant future interest.

ACKNOWLEDGMENTS. We thank Prof. G. J. Miller (Iowa State University) foroffering the cluster to perform the molecular orbital calculations. Thisresearch was supported by the Gordon and Betty Moore foundation underits EPiQS initiative (Grant GBMF-4412). The Department of Energy, Divisionof Basic Energy Sciences supported some of the chemical synthesis throughGrant DE-FG02-98ER45706.

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