Orbit- and atom-resolved spin textures of intrinsic, extrinsic, and hybridized Dirac cone states

Combining first-principles calculations and spin- and angle-resolved photoemission spectroscopy measurements, we identify the helical spin textures for three different Dirac cone states in the interfaced systems of a two-dimensional (2D) topological insulator (TI) of a Bi(111) bilayer and a three-dimensional (3D) TI Bi${}_2$Se${}_3$ or Bi${}_2$Te${}_3$. The spin texture is found to be the same for the intrinsic Dirac cone of Bi${}_2$Se${}_3$ or Bi${}_2$Te${}_3$ surface states, the extrinsic Dirac cone of Bi bilayer induced by the Rashba effect, and the hybridized Dirac cone between the former two states. Further orbit- and atom-resolved analysis shows that $s$ and $p_z$ orbits have a clockwise (counterclockwise) spin rotation tangent to the iso-energy contour of the upper (lower) Dirac cone, while $p_x$ and $p_y$ orbits have radial spin components. The Dirac cone states may reside on different atomic layers, but have the same spin texture. Our results suggest that the unique spin texture of Dirac cone states is a signature property of spin-orbit coupling, independent of topology.

Figure 1

(a) Bi/Bi${}_2$Se${}_3$ spectral function projected onto a top Bi bilayer plus upper 2QL Bi${}_2$Se${}_3$. (b) Percentage contribution of different atoms to the Dirac cone states marked by labels I, II, and III with different colors and symbols in (a). Upper (lower) denotes upper (lower) Dirac cone states and the atomic layer index is shown in (c). (c) Atomic structure of the optimized Bi/Bi${}_2$Se${}_3$. A Bi bilayer and upper 3QL Bi${}_2$Se${}_3$ are labeled with numbers to denote their atomic layer index. (d) and (e) Orbit-resolved spin textures of the iso-energy contour Dirac cone state at the energy marked by labels I and II in (a).

Figure 2

(a) Bi/Bi${}_2$Te${}_3$ spectral function projected onto the top Bi bilayer plus upper 1QL Bi${}_2$Te${}_3$. (b) Percentage contribution of different atoms to the Dirac cone states marked by labels I, II, and III with different colors and symbols in (a). (c) Orbit-resolved spin textures of the iso-energy contour Dirac cone state at the energy marked by label II in (a). The scaling factor of the arrow length is the same as that in Fig. [1].

Figure 3

(a) Spin-integrated ARPES spectra of Bi/Bi${}_2$Se${}_3$ and (b) Bi/Bi${}_2$Te${}_3$. The dashed blue and yellow lines show the position of the intrinsic and extrinsic Dirac cones. Experimentally, the relative intensity of two Dirac cones can be tuned by incident photon energy. (c) and (d) The experimental momentum dependent spin polarization and fitting data of Bi/Bi${}_2$Se${}_3$ and Bi/Bi${}_2$Te${}_3$. (e) and (f) Spin textures of intrinsic, extrinsic Dirac cones, and hybridized Dirac cone. The images in (f) are the constant energy contours of ARPES intensity.

Figure 4

Atom- and orbit-resolved spin textures of the iso-energy contour Dirac cone state at the energy marked by label II in Figs. 1 and 2. (a) and (b) The spin textures of the first (Bi-1) and second (Bi-2) atom in Bi/Bi${}_2$Se${}_3$. (c) and (d) The spin textures of the first (Bi-1) and second (Bi-2) atom in Bi/Bi${}_2$Te${}_3$. The scaling factor of the arrow length is twice that in Fig. [1].