Importance of spin-orbit coupling in power factor calculations for half-Heusler ANiB (AÂ =Â Ti, Hf, Sc, Y; BSn, Sb, Bi)

We investigate the spin-orbit coupling (SOC) effects on the electronic structures and semi-classic transport coefficients of half-Heusler ANiB (A = Ti, Hf, Sc, Y; BSn, Sb, Bi) by using generalized gradient approximation (GGA). Calculated results show that SOC splits the valence bands at high symmetry Γ point, and modifies the outline of Γ-centered valence bands, which has remarkable effects on the electron transport properties. Thermoelectric properties are performed through solving Boltzmann transport equations within the constant scattering time approximation. It is found that the compounds containing Sn atom have larger power factor in p-type doping than ones in n-type doping, and it is just the opposite for compounds containing Sb and Bi elements. The SOC has obvious detrimental influence on power factor in p-type doping, while has a negligible effect in n-type doping. These can be understood by considering the effects of SOC on the valence bands and conduction bands. The maximum power factors (MPF) are extracted in n-type and p-type doping with GGA and GGA + SOC, and the MPF at 300 K with SOC is predicted to be about 4.25%∼ 44.13% smaller than that without SOC in the case of p-type doping for ANiB (A = Ti, Hf, Sc, Y; BSn, Sb, Bi). Therefore, it is crucial to consider SOC effects for theoretical analysis in the case of p-type doping in half-Heusler compounds composed of heavy elements.