  Hidden Rashba and Dresselhaus spin-splittings in centrosymmetric crystals
with subunits (sectors) having non-centrosymmetric symmetries (the R-2 and D-2
effects) have been predicted and observed experimentally, but the microscopic
mechanism remains unclear. Here we demonstrate that the spin-splitting in R-2
is enforced by specific symmetries (such as the non-symmorphic in the present
example) which ensures that the pertinent spin wavefunctions segregate
spatially on just one of the two inversion-partner sectors and thus avoid
compensation. This finding establishes a common fundamental source for the
conventional Rashba (R-1) effect and the R-2 effect, both originating from the
local sector symmetries, rather than from the global crystal asymmetry alone
for R-1 per se. We further show that the effective Hamiltonian for the R-1
effect is also applicable for the R-2 effect, but applying a symmetry-breaking
electric field to an R-2 compound produces different spin-splitting pattern
than applying a field to a trivial (non-R-2) centrosymmetric compound.
