Interplay of Spin–Orbit Coupling and Anharmonicity in Governing High-Temperature Thermoelectric Performance of A ₃ Sn (A = Pt, Pd) Intermetallics

Topological semimetals A 3 Sn (A = Pt, Pd), exhibiting nontrivial band inversion and weak topological Dirac/Weyl band crossings, are investigated for the first time with a focus on their thermoelectric (TE) performance through electronic band structure calculation from the viewpoint of spin–orbit coupling (SOC) and finite temperature ( T ) anharmonicity. Both compounds show semimetallic character with flat or near-flat bands along the Γ– X line of the L1 2 structure Brillouin zone, promoting carrier asymmetry and improved Seebeck coefficient. A sharp feature in the total electronic density-of-states (e-DOS) near the Fermi level ( E F ) induces a subtle thermal redistribution of occupancies at low temperatures, producing changes in electronic pressure and affecting transport. SOC splits Pt/Pd d and p orbitals, respectively, into j = 3/2, 5/2 and j = 1/2, 3/2 (in terms of ℏ) sublevels, smoothing out e-DOS features. Beyond perturbative effects, SOC also modulates anharmonicity, where directional Pt/Pd d orbitals and spin (S⃗) interact to modulate the nonharmonic character of interaction potential, which at elevated temperatures enhances TE performance. These observations are analyzed and confirmed by systematic study of projected electronic density-of-states (PDOS) and various TE parameters. The ZT and power factor (PF) maxima of Pt 3 Sn occur within a narrow energy window around E F, reflecting its more metallic character. For Pd 3 Sn, ZT is almost zero in the vicinity of E F and has finite values deep in conduction and valence bands, reflecting its broader energy range for effective carrier asymmetry. At 1000 K, the ZT and PF values reach 3.326 and 7.912 for Pt 3 Sn and 4.030 and 7.071 for Pd 3 Sn, respectively, at optimal carrier concentrations, highlighting the superior performance of p-type Pd 3 Sn. These findings demonstrate that SOC, orbital hybridization, and anharmonicity collectively govern electronic transport and TE efficiency, making these L1 2 -type intermetallics promising candidates for high- T TE applications.