We investigate the surface Rashba effect for a surface of reduced in-plane symmetry. Formulating a k.p perturbation theory, we show that the Rashba splitting is anisotropic, in agreement with symmetry-based considerations. We show that the anisotropic Rashba splitting is due to the admixture of bulk states of different symmetry to the surface state, and it cannot be explained within the standard theoretical picture supposing just a normal-to-surface variation of the crystal potential. Performing relativistic ab initio calculations we find a remarkably large Rashba anisotropy for an unreconstructed Au(110) surface that is in the experimentally accessible range.
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