Symmetry rules shaping spin-orbital textures in surface states

Abstract

Strong spin-orbit coupling creates exotic electronic states such as Rashba and topological surface states, which hold promise for technologies involving the manipulation of spin. Only recently has the complexity of these surface states been appreciated: they are composed of several atomic orbitals with distinct spin textures in momentum space. A complete picture of the wave function must account for this orbital dependence of spin. We discover that symmetry constrains the way orbital and spin components of a state coevolve as a function of momentum, and from this, we determine the rules governing how the two degrees of freedom are interwoven. We directly observe this complexity in spin-resolved photoemission and ab initio calculations of the topological surface states of Sb(111), where the photoelectron spin direction near $\overline{\mathrm{\ensuremath{\Gamma}}}$ is found to have a strong and unusual dependence on photon polarization. This dependence unexpectedly breaks down at large $|k|$, where the surface states mix with other nearby surface states. However, along mirror planes, symmetry protects the distinct spin orientations of different orbitals. Our discovery broadens the understanding of surface states with strong spin-orbit coupling, demonstrates the conditions that allow for optical manipulation of photoelectron spin, and will be highly instructive for future spintronics applications.