  We show that the spin-orbit coupling (SOC) in alpha-MnTe impacts the
transport behavior by generating an anisotropic valence-band splitting,
resulting in four spin-polarized pockets near Gamma. A minimal k-dot-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 upper limit of the PHE
percentage is shown to be fundamentally determined by the band shape, and is
quantitatively estimated to be roughly 31% by first principles.
