Topological spin-polarized electron layer above the surface of Ca-terminated Bi${}_2$Se${}_3$

Spin-polarized gapless surface states on the boundary of topological insulators are of interest for spintronic applications. First-principles calculations show that adsorption of a Ca monolayer on films of the prototypical topological insulator, Bi${}_2$Se${}_3$, yields a substantial enhancement of the surface-state spin polarization, despite the low atomic mass of Ca and its weak spin-orbit coupling. Much of the topological surface electron distribution is transferred outside the Ca to form a polarized electron layer out in vacuum; this spatial separation from the substrate minimizes scattering by defects in Bi${}_2$Se${}_3$ and can be a useful feature for device engineering.

Figure 1

Top views of the atomic structures of (a) Bi${}_2$Se${}_3$, (c) Bi${}_2$Se${}_3$-Ca, and (e) Bi${}_2$Se${}_3$-Cl. The corresponding side views are shown in (b), (d), and (f), respectively; only the topmost quintuple layer is included. A quintuple layer unit cell is indicated in (b) with the dotted rectangle.

Figure 2

Band dispersions with normalized charge moment $M$ (upper row) and spin polarization ${\sigma }_y$ (lower row) indicated by color coding for the surface states and nearby quantum-well states. (a) and (e) are for the top surface states of a pristine 6-QL film, while (b) and (f) are for the bottom surface states of the same film. (c) and (g) are for Ca chemisorption on the top face of the film, and (d) and (h) are for Cl chemisorption on the top face of the film. The green- and yellow-shaded areas indicate the projected bulk band regions and gaps, respectively. The maximum ±${\sigma }_y$ for the topological surface states of the pristine film are shown with triangles next to the lower color scale bar.

Figure 3

(a) Spin-resolved charge distributions for the upper state near each Dirac point indicated in Fig. 2 for pristine and Ca- and Cl-chemisorbed 6-QL Bi${}_2$Se${}_3$ films. The curves indicate the total charge density, and the red-white-blue color coding indicates the spin polarization ${\sigma }_y\left(z\right)$. The boundaries of the quintuple layers are marked by vertical dashed-dotted lines. The positions of the atomic planes of Ca and Cl are marked by solid vertical lines. The red triangle indicates the interference minimum in the charge density. (b) Same as (a) except that the Bi${}_2$Se${}_3$ film thickness is 2 QLs. (c) Three-dimensional isosurface of charge distribution of state $A_1$ for a Ca-adsorbed 2-QL Bi${}_2$Se${}_3$ film in a 3 × 3 unit cell. The atomic positions are indicated. The charge layer above the Ca atoms is evident.

Figure 4

Same as Fig. 2 except that the Bi${}_2$Se${}_3$ film has a thickness of 2 instead of 6 QLs.

Figure 5

Band structure and charge moment of Ca-adsorbed Bi${}_2$Se${}_3$ for each Bi${}_2$Se${}_3$ film thickness in the 2–6 QL range. The green- and yellow-shaded areas indicate the projected bulk band regions and the bulk gap, respectively. The color coding indicates the charge moment $M$. The Bi${}_2$Se${}_3$ substrate thicknesses for (a)–(d), (e), and (f) are 2–5, 5, and 6 QLs, respectively. (a)–(d) are based on the optimized geometrical structure of 2-QL Bi${}_2$Se${}_3$-Ca; (e) and (f) are based on the optimized geometrical structure of 6-QL Bi${}_2$Se${}_3$-Ca. Dirac points $P_0^{\prime }$ and $A_1$ are indicated.