Splitting of Shockley surface states in thin films of noble metals

Abstract

The splitting of the surface bands of Cu(1 1 1), Ag(1 1 1), and Au(1 1 1) films is studied by means of relativistic density-functional theory (DFT) calculations. It is found that the splitting of the bands of clean films obtained in semirelativistic approximation, in agreement with previous studies, stems from the interaction between the surfaces and hence depends on the thickness of the slabs. Since the Kramers’ degeneracy is not broken by the presence of the surface, the spin-orbit coupling does not lead to the spin-splitting of the bands. An H monolayer, deposited on one face of the film, breaks the inversion symmetry and results in the appearance of the Rashba-type splitting of the bands.