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Distinct Tamm and Shockley surface states on Re(0001) mixed by spin-orbit interaction

Phys. Rev. B 105, L241412 (2022).
Tamm and Shockley states, these two paradigmatic concepts are used to describe surface states not only in electronic systems but also in photonic and phononic crystals. The Re(0001) surface hosts both types of electronic surface states in neighboring but qualitatively different energy gaps. Interestingly, spin-orbit interaction generates a double W-shaped energy vs k dispersion by mixing both types of states and lifting their spin degeneracy. By combining spin- and angle-resolved photoemission, tight-binding model calculations, as well as density functional theory including the photoemission process, we develop verifiable criteria to distinguish between the two types of surface states and arrive at a consistent picture of the role of spin-orbit interaction in such a scenario.

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

Phys. Rev. B 105, 155419 (2022).
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 ΓK and ΓM, we identify transitions into d-derived bulk states as well as different types of surface states. The Rashba-type spin-split hole pocket around Γ finds continuation in empty spin-split surface states for higher k, thereby forming W-shaped states whose lower parts are partially occupied. A large energy gap below and above the vacuum energy around Γ hosts image-potential-induced surface states. The n=1 member of the Rydberg-like series exhibits a free-electron-like E(k) 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 αR=105±33meVÅ.
 

Rashba-split surface state and spin-dependent photon emission from Re(0001) at Γ

Phys. Rev. B 104, 205425 (2021).
The unoccupied electronic structure of the Re(0001) surface is investigated by spin- and angle-resolved inverse photoemission, experimentally and theoretically. The work is focused on the states around the center of the surface Brillouin zone Γ, where a hole pocket of a surface state with Rashba-type spin splitting is detected. Furthermore, we observe spin-dependent photon emission from unpolarized surface and bulk states at Γ. The size and sign of the spin asymmetry depends on experimental parameters such as the direction of the electron spin polarization and the photon detection angle. Maximum (zero) spin asymmetry is detected if the electron spin polarization and the plane of photon emission are perpendicular (parallel). The effect is traced back to spin-orbit-induced hybridization of the involved states.
 

Rashba-type splitting of the Au(110) surface state: A combined inverse and direct photoemission study

Phys. Rev. B 104, L161101 (2021).
The Shockley surface state located at Y on the (1×2)-reconstructed Au(110) surface is predicted to exhibit
a Rashba-type spin splitting. Previous photoemission experiments searched for this splitting but it could not be
resolved yet. In order to uncover a possible splitting, the unoccupied surface state on Au(110) is examined with
spin- and angle-resolved inverse photoemission, whereas Na-covered Au(110) allows for investigation of the
now occupied surface state by means of spin- and angle-resolved direct photoemission. Our data show clear spin
splittings in the order of 100 meV with a sign reversal at Y in the surface state’s in-plane spin components which
is characteristic for a Rashba-type behavior. Furthermore, we deduce an effective mass of m = (0.27 ± 0.02)me
and a Rashba parameter of αR = (0.46 ± 0.04) eVÅ from direct photoemission measurements.