Valley spin polarization of Tl/Si(111)

The metal/semiconductor hybrid system Tl/Si(111)-$\left(1\times 1\right)$ exhibits a unique Tl-derived surface state with remarkable properties. It lies within the silicon band gap and forms spin-momentum-locked valleys close to the Fermi energy at the $\overline{K}$ and ${\overline{K}}^{\prime }$ points. These valleys are completely spin polarized with opposite spin orientation at $\overline{K}$ and ${\overline{K}}^{\prime }$ and show a giant spin splitting of more than 0.5 eV. We present a detailed preparation study of the surface system and demonstrate that the electronic valleys are extremely robust, surviving exposure to 100 L hydrogen and 500 L oxygen. We investigate the influence of additional Tl atoms on the spin-polarized valleys. By combining photoemission and inverse photoemission, we prove the existence of fully spin-polarized valleys crossing the Fermi level. Moreover, these metallic valleys carry opposite Berry curvature at $\overline{K}$ and ${\overline{K}}^{\prime }$, very similar to ${\mathrm{WSe}}_2$, promising a large spin Hall effect. Thus, Tl/Si(111)-$\left(1\times 1\right)$ possesses all necessary key properties for spintronic applications.

Figure 1

(a) Top view and side view of the structural model of the Tl/Si(111)-$\left(1\times 1\right)$ surface. (b) LEED image (inverted contrast) of the clean Tl/Si(111)-$\left(1\times 1\right)$ surface for a primary electron beam energy $E_p=85$ eV. The corresponding surface Brillouin zone with the relevant high-symmetry points is indicated in red. (c) STM image of the Tl/Si(111)-$\left(1\times 1\right)$ surface (preparation A, $150\times 150{\mathrm{nm}}^2,U=-1$ V, $I=0.1$ nA). Large terraces with a width of about 50 nm are observed. (d) STM image of the Tl/Si(111)-$\left(1\times 1\right)$ surface with about 1.1 ML Tl (preparation A, $140\times 140{\mathrm{nm}}^2,U=1$ V, $I=0.1$ nA).

Figure 2

SRIPE spectra of Tl/Si(111)-$\left(1\times 1\right)$ around $\overline{K}$ obtained for preparation A (open purple up-pointing and orange down-pointing triangles) and B (filled purple up-pointing and orange down-pointing triangles). The spectra were measured at an incidence angle of $\theta ={60}^{\circ }$ with sensitivity to the out-of-plane spin-polarization direction.

Figure 3

Surface electronic structure of Tl/Si(111)-$\left(1\times 1\right)$ around $\overline{K}$ (a) and ${\overline{K}}^{\prime }$ (d). Filled and open triangles were obtained for preparations A and B, respectively. Solid lines represent the calculated surface-state bands and gray-shaded areas denote the projected bulk bands [23]. Blue dashed lines indicate where the constant-energy maps shown in Fig. 4 were measured. (b) and (e) SRIPE spectra (preparation B) with sensitivity to the out-of-plane spin polarization around $\overline{K}$ and ${\overline{K}}^{\prime }$, respectively, with corresponding out-of-plane spin asymmetry shown in (c) and (f).

Figure 4

Constant-energy maps for the two out-of-plane spin directions of Tl/Si(111)-$\left(1\times 1\right)$ (preparation B) around $\overline{K}$ at (a) $E-E_F=0.75$ eV and (d) $E-E_F=0.35$ eV. The open circles show the calculated contour of the lower lying surface-state component $S_3$ [see (c) and (f)]. (b) and (e) The corresponding spin-asymmetry data. Calculated constant-energy maps at (c) $E-E_F=0.75$ eV and (f) $E-E_F=0.35$ eV.

Figure 5

(a) Illustration and (b) results of a constant-$k_{\parallel }$ $\left(k_{\parallel }\approx 1.1\AA \right)$ measurement of Tl/Si(111)-$\left(1\times 1\right)$ (preparation B) at a constant energy of $E-E_F=0.2$ eV for $\theta ={60}^{\circ }$. $k_{\parallel }=\sqrt{{k_x^2+k_y^2}^{\phantom{0}}}$ is fixed, while $k_x$ and $k_y$ are varied by changing the sample azimuthal angle $\phi =arctan\frac{k_y}{k_x}$. The measurement crosses the lower-lying surface-state component $S_3$ at $\overline{K}$ and ${\overline{K}}^{\prime }$. The experiment is sensitive to the out-of-plane spin-polarization direction (purple up-pointing and orange down-pointing triangles).

Figure 6

SRIPE spectra around $\overline{K}$ on preparation B for a surface exposed to 100 L of ${\mathrm{H}}_2$, 500 L of ${\mathrm{O}}_2$, and air at ambient pressure (filled purple up-pointing and orange down-pointing triangles). Spectra for the clean surface are shown as solid lines (same data as in Fig. 2, preparation B).

Figure 7

Left: ARPES measurements $(\hslash \omega =21.22$ eV) around $\overline{K}$ of 1 ML Tl/Si(111)-$\left(1\times 1\right)$ (preparation B) and Tl/Si(111)-$\left(1\times 1\right)$ surfaces with more than 1 ML Tl. Right: Corresponding SRIPE measurements with sensitivity to the out-of-plane spin-polarization direction.

Figure 8

Visualization of the Fermi surface of the doped Tl/Si(111)-$\left(1\times 1\right)$ surface. Completely out-of-plane but oppositely spin-polarized valleys are formed at $\overline{K}$ and ${\overline{K}}^{\prime }$ (after Ref. [22]).