  We theoretically show that two distinctive spin textures manifest themselves
around saddle points of energy bands in a monolayer NbSe$_2$ under external
gate potentials. While the density of states at all saddle points diverge
logarithmically, ones at the zone boundaries display a windmill-shaped spin
texture while the others unidirectional spin orientations. The disparate
spin-resolved states are demonstrated to contribute an intrinsic spin Hall
conductivity significantly while their characteristics differ from each
other.Based on a minimal but essential tight-binding approximation reproducing
first-principles computation results, we established distinct effective Rashba
Hamiltonians for each saddle point, realizing the unique spin textures
depending on their momentum. Energetic positions of the saddle points in a
single layer NbSe$_2$ are shown to be well controlled by a gate potential so
that it could be a prototypical system to test a competition between various
collective phenomena triggered by diverging density of states and their spin
textures in low-dimension.
