Band structure ofTl/Ge(111)−(3×1): Angle-resolved photoemission and first-principles prediction of giant Rashba effect

Abstract

We have investigated the atomic and electronic structure of the $\text{Tl}/\text{Ge}(111)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}1)$ surface using angle-resolved photoelectron spectroscopy (ARPES) and first-principles total-energy-band calculation. The experimental surface bands exhibit semiconducting electronic structure and are well reproduced by the band calculation based on the honeycomb-chain channel structure with Tl adsorbed at ${H}_{3}$ site. Electron density maps of the surface-related states show the formation of the $\text{Ge}=\text{Ge}$ double-bond-like state as observed on the alkali-metal-induced $\text{Si}(111)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}1)$ surfaces. In our scalar-relativistic all-electron calculation, the Tl-derived surface bands show a Rashba-type spin splitting in the projected bulk band gap, which is not clearly resolved by ARPES due to a limited energy resolution. They show complicated dispersion due to the hybridization with the bulk states in the projected bulk band region. The lowest unoccupied surface band, which is an antibonding state formed between $\text{Tl}\text{ }6p$ and Ge dangling bonds and is highly localized in the topmost surface layer, shows a large spin-orbit splitting of $\ensuremath{\sim}200\text{ }\text{meV}$.