Fig. 1. Representative semiconducting electrides.^19–21

Fig. 2. (a) Crystal structure of Ae₅X₃. (b) Structural prototypes of A₅B₃ compounds as a function of the radius ratio r_M/r_X and the electronegativity difference E_diff. The red, brown, and purple spheres represent compounds that adopt the β-Yb₅Sb₃ prototype, coexistence of β-Yb₅Sb₃ and Mn₅Si₃ prototypes, and the Mn₅Si₃ prototype, respectively. The gray spheres represent phases that have not yet been reported. (c) Volume of Ae₆ octahedron as a function of Ae ionic radius. (d) Spin polarization energies ΔE of Ae₅X₃ with AFM configuration.

Fig. 3. (b) ELF of Ba₅Sb₃. (b) ELF maps of interstitial electrons in Ba₅Sb₃ and the intermetallic electride α-Yb₅Sb₃, calculated with and without spin polarization, respectively. (c) Spin charge density of Ba₅Sb₃. (d) Maximum spin charge density in the voids of Ae₅X₃ compared with α-Yb₅Sb₃.

Fig. 4. Spin-polarized band structures of Ba₅Sb₃ calculated (a) with the HSE06 functional, (b) without Coulomb interaction correction (U = 0 eV), (c) with U = 3 eV, and (d) with U = 5 eV. The calculations were performed for an AFM configuration.

Fig. 5. (a) and (b) Weighted band structures of Ba₅Sb₃ in sites A and B, respectively. (c) Schematic illustrations of the interaction between anionic electrons distributed in sites A and B. (d) Partial charge density of interstitial states.

Fig. 6. (a) Bandgap and spin polarization energy of Ba₅Sb₃ under isotropic strain. (b) ELF maps of Ba₅Sb₃ with (−5% and +5%) and without (0%) lattice deviation. (c) Bandgaps of Ba₅Sb₃ under pressure; the inserts are ELF maps of Ba₅Sb₃ at 2 and 6 GPa. (d) Band structure of Ba₅Sb₃H.