Fig. 3

a Schematic diagram of orbital engineering to realize three-fold degenerate p orbitals in CaAl₂Si₂-type compounds. Nondegenerate band Γ(p_z) and doubly degenerate band Γ(p_x,y) are mainly composed of p_z and p_x,y orbitals from the anions, respectively. Δ denotes the crystal field splitting energy between p_x,y and p_z orbitals at the Γ point. b Band structure of Mg₃Sb₂ by TB-mBJ potential without spin–orbit coupling. The p orbitals of Sb are projected on the band structure. c, d Partial charge densities of the valence bands c Γ(p_z) (isovalue: 0.06 e Å⁻³) and d Γ(p_x,y) (isovalue: 0.13 e Å⁻³) at the Γ point in Mg₃Sb₂. e The theoretical power factor at 300 K versus Δ of Mg₃Sb₂ at various hole concentrations p. The red curve shows the best values corresponding to the optimum carrier concentrations. Data points for unoptimized carrier concentrations fill up the pink area right below the red curve. f The experimental power factors^{14,15,17,18,19,20,21,22,23,24,25,26,27,39,40,41} of reported CaAl₂Si₂-type compounds at 600 K as a function of Δ. Red points represent the alloys^18,21 with zT larger than unity at high temperatures. a, b, e, f are adapted with permission from ref. ¹⁰⁵, CC-BY-4.0