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In order to explain the anisotropic Rashba-Bychkov effect observed in severalmetallic surface-state systems, we use k.p perturbation theory with a simplegroup-theoretical analysis and construct effective Rashba Hamiltonians fordifferent point groups up to third order in the wavenumber. We performrelativistic ab initio calculations for the Bi/Ag(111) ordered surface alloyand from the calculated splitting of the band dispersion we find evidence ofthe predicted third-order terms. Furthermore, we derive expressions for thecorresponding third-order Rashba parameters to provide a simple explanation tothe qualitative difference concerning the Rashba-Bychkov splitting of thesurface states at Au(111) and Bi/Ag(111).

Higher-order contributions to the Rashba-Bychkov effect with application to Bi/Ag(111) surface alloy