Different types of Rashba spin-split surface states on Ge(1Â 1Â 1)

In this review article, after a brief account of the early history of the study of the surface Rashba effect is given, a survey is made on an exploration of the Rashba spin-split surface states on a Ge(1 1 1) surface. First, the studies on Pb/Ge(1 1 1) is shown, which was the first surface with Rashba spin-split metallic surface state on a semiconductor established by experiments and first-principles calculation. Second example is Tl/Ge(1 1 1), which exhibits valley-like conduction band minimum at the K¯ points in the surface Brilouin zone. Due to the symmetry of this surface, spins at the bottom of the valleys are completely polarized parallel to the surface normal. In these two cases, the spin splitting is due to the strong spin-orbit interaction (SOI) in the close proximity to the heavy nuclei at the surfaces. On the other hand, the third example demonstrates that a significant Rashba spin splitting is possible also by SOI at the nuclei of the subsurface Ge atoms. This type of spin-split surface states are believed to be ubiquitous on any types of Ge surfaces as well as at the interfaces between Ge and other materials. A personal view of coming developments in this field is given.