Effects of orbital composition in a pair of spin-orbit-split surface bands at Tl/Ge(111)

The spin texture of the unoccupied surface electronic structure of the metal-semiconductor hybrid system $\mathrm{Tl}/\mathrm{Ge}(111)\ensuremath{-}(1\ifmmode\times\else\texttimes\fi{}1)$ is investigated by spin- and angle-resolved inverse photoemission as well as quasiparticle band-structure calculations. Spin-polarized surface bands with rotating spin and giant energy splitting are found along $\overline{\mathrm{\ensuremath{\Gamma}}}\overline{K}({\overline{K}}^{\ensuremath{'}})$, forming valleys with alternating out-of-plane spin polarization at $\overline{K}$ and ${\overline{K}}^{\ensuremath{'}}$. This behavior is known from the equivalent hybrid system on Si(111). Along $\overline{\mathrm{\ensuremath{\Gamma}}}\overline{M}$, a pair of surface bands appears within a projected bulk band gap, whose equivalent on Tl/Si(111) is a surface resonance because, there, it overlaps with bulk states. Surprisingly, the spin splitting of these bands on Tl/Ge(111) is much smaller than on Tl/Si(111) despite the stronger surface localization and the heavier substrate. Our detailed analysis of the band structure and a tight-binding model including all relevant interactions show that a remarkable interplay between spin-orbit coupling and hybridization is responsible for this unexpected result. The comparison between the two similar hybrid systems demonstrates that the strength of the spin-orbit coupling alone, based on the atomic number of the respective elements, is not sufficient to estimate spin splittings of spin-orbit-influenced surface states.