Layer-By-Layer Entangled Spin-Orbital Texture of the Topological Surface State in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

We study ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ by polarization-dependent angle-resolved photoemission spectroscopy and density-functional theory slab calculations. We find that the surface state Dirac fermions are characterized by a layer-dependent entangled spin-orbital texture, which becomes apparent through quantum interference effects. This explains the discrepancy between the spin polarization obtained in spin and angle-resolved photoemission spectroscopy—ranging from 20% to 85%—and the 100% value assumed in phenomenological models. It also suggests a way to probe the intrinsic spin texture of topological insulators, and to continuously manipulate the spin polarization of photoelectrons and photocurrents all the way from 0 to $\pm 100\%$ by an appropriate choice of photon energy, linear polarization, and angle of incidence.