  We study the electronic spin relaxation effect in the hole-doped monolayer
and bilayer transition-metal dichalcogenides in the presence of the crystal
defects. We consider realistic models of the lattice vacancy and actually
estimate the spin relaxation rate using the multi-orbital tight-binding model.
In the monolayer, the spin-relaxation time is found to be extremely long
compared to the momentum relaxation time, and this is attributed to the fact
that the spin hybridization in the band structure is suppressed by the mirror
reflection symmetry. The bilayer TMD has a much shorter spin relaxation time in
contrast, and this is attributed to stronger spin hybridization due to the
absence of the mirror symmetry.
