Uncovering and tailoring hidden Rashba spin-orbit coupling in centrosymmetric crystals*

Hidden Rashba and Dresselhaus spin-splittings in centrosymmetric crystals having subunits (sectors) with 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 the non-symmorphic symmetry of the wavevectors, 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 non-centrosymmetric Rashba (R-1) effect and the R-2 effect, both originating from the local sector symmetries, rather than from the global crystal symmetry 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.