Strongly Spin-Orbit Coupled Two-Dimensional Electron Gas Emerging near the Surface of Polar Semiconductors

We investigate the two-dimensional highly spin-polarized electron accumulation layers commonly appearing near the surface of $n$-type polar semiconductors $\mathrm{BiTe}X$ ($X=\mathrm{I}$, Br, and Cl) by angular-resolved photoemission spectroscopy. Because of the polarity and the strong spin-orbit interaction built in the bulk atomic configurations, the quantized conduction-band subbands show giant Rashba-type spin splitting. The characteristic 2D confinement effect is clearly observed also in the valence bands down to the binding energy of 4 eV. The $X$-dependent Rashba spin-orbit coupling is directly estimated from the observed spin-split subbands, which roughly scales with the inverse of the band-gap size in $\mathrm{BiTe}X$.

Figure 1

Crystal structures of BiTeI, BiTeBr (a) and BiTeCl (b). Brillouin zones of BiTeI, BiTeBr (c) and BiTeCl (d). (e) Temperature-dependent electrical resistivity of $\mathrm{BiTe}X$. (f)–(h) Band dispersions of $\mathrm{BiTe}X$ obtained from first-principles calculations.

Figure 2

(a) Laser-ARPES spectral image of BiTeBr along the $k_y$ direction. (b) Constant energy cross-sectional views of the subband structure at intervals of 80 meV. (c), (d) Depth ($z$)-dependent potential energy $V(z)$ and electron density $n(z)$ of near-surface $\mathrm{BiTe}X$ calculated by the PS method.

Figure 3

(a)–(c) Laser-ARPES spectral images of $\mathrm{BiTe}X$. The peak positions of ARPES intensity corresponding to $n=1$, 2, and 3 subbands are plotted by red ●, blue ■, and green ◆ markers. (d)–(f) Corresponding subband structures obtained by PS method. (g)–(i) Intensity mappings at $E_F$ obtained by laser ARPES, which correspond to the 2D Fermi surfaces near the surface. Black triangle markers in (g) indicate the possible contributions of the bulk bands. (j)–(l) Corresponding Fermi surfaces calculated by PS method. $z$-dependent potential energy and electron density obtained are shown in Figs. 2c, 2d.

Figure 4

(a)–(c) Second-derivative ARPES images of BiTeI along the $k_x$ direction at $k_z=\pi /c$, $1.51\pi /c$, and 0 ($2\pi /c$), respectively. The peak positions of ARPES intensity corresponding to the $k_z$-dependent bulk bands ($k_z$-independent subbands for $n=1$ and 2) are plotted by green ◇ (red ● and blue ■) markers. (d), (e) Electronic structures for the topmost Te-Bi-I trilayer and the projection of the electronic structures from all trilayers into the bulk, obtained by PS calculation.