Spin-orbital Texture in Topological Insulators

Abstract

Relativistic spin-orbit coupling plays an essential role in the field of topological insulators and quantum spintronics. It gives rise to the topological non-trivial band structure and enables electric manipulation of the spin degree of freedom. Because of the spin-orbit coupling, rich spin-orbital coupled textures can exist both in momentum and in real space. For three dimensional topological insulators in the Bi$_2$Se$_3$ family, topological surface states with p$_z$ orbitals have a left-handed spin texture for the upper Dirac cone and a right-handed spin texture for the lower Dirac cone. In this work, we predict a new form of the spin-orbital texture associated with the p$_x$ and p$_y$ orbitals. For the upper Dirac cone, a left-handed (right-handed) spin texture is coupled to the "radial" ("tangential") orbital texture, whereas for the lower Dirac cone, the coupling of spin and orbital textures is the exact opposite. The "tangential" ("radial") orbital texture is dominant for the upper (lower) Dirac cone, leading to the right-handed spin texture for the in-plane orbitals of both the upper and lower Dirac cones. A spin-resovled and photon polarized angle-resolved photoemission spectroscopy experiment is proposed to observe this novel spin-orbital texture.