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

Abstract

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 ${\mathbf{k}}_{\ensuremath{\parallel}}$ 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.