Microscopic origin of the relativistic splitting of surface states

Spin-orbit splitting of surface states is analyzed within and beyond the Rashba model using as examples the (111) surfaces of noble metals, Ag2Bi surface alloy, and topological insulator Bi2Se3. The ab initio analysis of relativistic velocity proves the Rashba model to be fundamentally inapplicable to real crystals. The splitting is found to be primarily due to a spin-orbit induced in-plane modification of the wave function, namely to its effect on the nonrelativistic Hamiltonian. The usual Rashba splitting -- given by charge distribution asymmetry -- is an order of magnitude smaller.