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We investigate the spin-orbit coupling (SOC) effects on the electronicstructures and semi-classic transport coefficients of half-Heusler$\mathrm{ANiB}$ (A=Ti, Hf, Sc, Y; B=Sn, Sb, Bi) by using generalized gradientapproximation (GGA). Calculated results show that SOC splits the valence bandsat high symmetry $\Gamma$ point, and modifies the outline of $\Gamma$-centeredvalence bands, which has remarkable effects on the electron transportproperties. Thermoelectric properties are performed through solving Boltzmanntransport equations within the constant scattering time approximation. It isfound that the compounds containing Sn atom have larger power factor in p-typedoping than ones in n-type doping, and it is just the opposite for compoundscontaining Sb and Bi elements. The SOC has obvious detrimental influence onpower 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 bandsand conduction bands. The maximum power factors (MPF) are extracted in n-typeand p-type doping with GGA and GGA+SOC, and the MPF at 300 K with SOC ispredicted to be about 4.25\%$\sim$44.13\% smaller than that without SOC in thecase of p-type doping for $\mathrm{ANiB}$ (A=Ti, Hf, Sc, Y; B=Sn, Sb, Bi).Therefore, it is crucial to consider SOC effects for theoretical analysis inthe case of p-type doping in half-Heusler compounds composed of heavy elements.

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