Role of coupling between surface orbitals in SOC enhanced spin splitting

摘要

In this study we investigate the role of coupling between surface orbitals in a giant spin splitting (GSS) observed in the Pb/Ge(111)-1 x 1 adsorption system along Gamma - M - Gamma'. We report, based on the density functional theory that, the magnitude of the GSS depends on the bonding structure of the Pb/Ge interface, varying from 242 to 667 meV for the metallic surface bands. The splitting is shown to be SOC enhanced, with similar to 93% of the effect being of SOC origin. The split-energy difference observed in the system is a result of a different coupling strength between p(x)/p(y)(Pb) and p(z)(Pb) orbitals, which produces corresponding values of unquenched orbital angular momentum. The described spin-split pattern corresponds to those observed in Tl/Si(111)-1 x 1, Bi/Si(111)-(root 3 x root 3)R30 degrees, and 4/3ML Pb/Ge(111)-(root 3 x root 3)R30 degrees, which suggests that, their GSS may also be SOC enhanced.