The surface Rashba effect: ak·pperturbation approach

For surface systems, the Rashba effect is studied by using a k·p perturbation method. It is shown that the velocity-operator term in the perturbation gives the generalized Rashba Hamiltonian, of which a group-theoretical analysis is given to explain variations in the spin splitting and spin structure expected for typical surface symmetry. The matrix elements of the velocity and spin-angular-momentum operators play a key role in determining the characteristic features of the surface Rashba effect. Whether a surface system shows isotropic spin splitting and vortical spin structure as given by the original Rashba Hamiltonian or not depends on the group of k appearing in the corresponding two-dimensional Brillouin zone. It is especially emphasized that the ideal Rashba effect may be realized even for a wavevector k without time reversal, which is usually believed to be a necessary condition.