Rashba-split image-potential state and unoccupied surface electronic structure of Re(0001)

The influence of spin-orbit interaction on the unoccupied electronic structure of the Re(0001) surface is investigated by spin- and angle-resolved inverse photoemission and density-functional theory calculations. In the two high-symmetry azimuths ?? K and P M, we identify transitions into d-derived bulk states as well as different types of surface states. The Rashba-type spin-split hole pocket around ?? finds continuation in empty spin-split surface states for higher k11, thereby forming W-shaped states whose lower parts are partially occupied. A large energy gap below and above the vacuum energy around ?? hosts image-potential-induced surface states. The n = 1 member of the Rydberg-like series exhibits a free-electron-like E(kp) dispersion with an effective mass of m*/me = 1.2 ?? 0.1. Careful spin-resolved measurements for several angles of electron incidence allow us to detect Rashba-type spin-dependent energy splittings of this state with a Rashba parameter of ??R = 105 ?? 33 meV ??.