Controlling Rashba spin splitting in Au(111) surface states through electric field

Combining density-functional theory (DFT) calculations and theoretical analyses, we demonstrate the high-order Rashba spin-orbit coupling in the Au(111) surface and the electric field manipulation of the Rashba splitting energy. A good linear relationship between the Rashba splitting energy and applied electric field is revealed by DFT calculations. The effect is attributed to the linear response of the first-order Rashba parameter to the applied electric field. The nonlinear relationship between Rashba splitting energy and the wave vectors identifies the higher-order Rashba components, which, however, are found to be less influenced by the external electric field. Our investigation provides an in-depth understanding of the tunability of Rashba splitting in a metal surface, which is of great interest in the area of electrical control of spin states.