We show that the spin-orbit coupling (SOC) in α-MnTe impacts the transport behavior by generating an anisotropic valence-band splitting, resulting in four spin-polarized pockets near Γ. A minimal k·p model is constructed to capture this splitting by group theory analysis, a tight-binding model, and ab initio calculations. The model is shown to describe the rotation symmetry of the zero-field planer Hall effect (PHE). The PHE originates from the band anisotropy given by SOC, and is quantitatively estimated to be 25%-31% for an ideal thin film with a single antiferromagnetic domain.
