Spin-dependent hybridization of image-potential states and overlayer states: One monolayer of Tl on Ag(111)

We present a study of the unoccupied electronic states of one monolayer (ML) Tl epitaxially grown on Ag(111) in a moir\'e superstructure. This two-dimensional atomic-layer material is investigated by scanning tunneling microscopy/spectroscopy, spin-resolved inverse photoemission, and calculations based on density functional theory. The unoccupied band structure exhibits characteristic spin-dependent hybridization between overlayer states influenced by the substrate. Most of the experimentally observed bands, their $E({\mathbf{k}}_{\ensuremath{\parallel}})$ behavior, and their Rashba-type spin dependence can be qualitatively described by a simple model for a Tl/Ag bilayer. A more realistic superstructure model reflecting the moir\'e structure provides deeper insight into the hybridization mechanisms for states of different orbital composition, further elucidated by calculations of the charge densities. Experimentally, $E({\mathbf{k}}_{\ensuremath{\parallel}})$ measurements as well as the analysis of spin-dependent spectral intensities allow us to distinguish different orbital contributions in the respective spin-up and spin-down components leading to hybridization gaps with spin-dependent size. Most interestingly, spin-dependent hybridization with overlayer states was discovered for an image-potential-induced surface band, which is mainly located in front of the sample surface.