Spin-texture of three-dimensional topological insulators: Bi$_2$Te$_3$, Bi$_2$Se$_3$ and Sb$_2$Te$_3$

We have investigated the nature of surface states in the Bi$_2$Te$_3$, Bi$_2$Se$_3$ and Sb$_2$Te$_3$ family of 3D topological insulators using first-principles calculation as well as $k\cdot p$ scheme [1]. Recent spin-resolved photoemission experiments suggest that electrons on the surface of a topological insulator behave as massless relativistic particles with an intrinsic angular momentum (spin) which is locked to their translational momentum [2,3]. We have computed the in-plane spin-textures of all three aforementioned compounds to demonstrate the `spin-helical' nature of the 2D fermions. In addition, the spin must acquire a finite out-of-the-plane component to preserve the bulk topological invariant [1]. We study this quantity in particular since there are possibilities of observing new quantum effects. Work supported by the US DOE.\\[4pt] [1] L. Fu, Phys. Rev. Lett. {\bf 103}, 266801, (2009). \\[0pt] [2] D. Hsieh {\it et al.}, Science {\bf 323}, 919 (2009). \\[0pt] [3] D. Hsieh {\it et al.}, Nature {\bf 460}, 1101 (2009).