Spin textures of topological surface states at side surfaces of Bi2Se3 from first principles

We investigate the spin and spin-orbital textures and electronic structures of topologically protected surface states at side surfaces of Bi2Se3 by using slab models within density-functional theory. This is motivated by recent experiments on nanowires, nanoribbons, and nanoplates of Bi2Se3 with side surfaces. In particular, two representative surfaces normal to the (111) surface, such as (11¯0) and (112¯) surfaces, are examined, in the presence of time-reversal symmetry and inversion symmetry. The (11¯0) surface lying in the mirror plane has twofold (C2) rotational symmetry, whereas the (112¯) surface has only mirror symmetry. For the (11¯0) surface, we find that a Dirac cone with strongly anisotropic Fermi velocity is formed at Γ with the Dirac point at the Fermi level, and that the spin texture reveals features of Rashba-type combined with Dresselhaus-type spin-orbit coupling. For the (112¯) surface, a Dirac cone is found at either Γ or the Y point (along the mirror symmetry axis) below the Fermi level. In this case, the spin texture of the surface states strikingly differs from that of the (111) and (11¯0) surfaces: (i) the in-plane spin polarization dominantly aligned perpendicular to the [111] direction or the mirror symmetry axis, (ii) the Dresselhaus-type spin texture, and (iii) significant out-of-plane spin polarization away from the mirror symmetry axis. Our findings distinctively differ from the previous works based on the effective bulk model Hamiltonian. Our calculated spin and spin-orbital textures and band structures can be observed by spin-resolved angle-resolved photoemission spectroscopy.