Rotating Spin and Giant Splitting: Unoccupied Surface Electronic Structure of $\mathrm{Tl}/\mathrm{Si}(111)$

We present a combined experimental and theoretical study on the unoccupied surface electronic structure of the $\mathrm{Tl}/\mathrm{Si}(111)$ surface. Spin- and angle-resolved inverse-photoemission measurements with sensitivity to both the in-plane and the out-of-plane polarization direction detect a spin-orbit-split surface state, which is well described by theoretical calculations. We demonstrate that the spin polarization vector rotates from the classical in-plane Rashba polarization direction around $\overline{\Gamma }$ to the direction perpendicular to the surface at the $\overline{K}({\overline{K}}^{\prime })$ points—a direct consequence of the symmetry of the 2D hexagonal system. A giant splitting in energy of about 0.6 eV is observed and attributed to the strong localization of the unoccupied surface state close to the heavy Tl atoms. This leads to completely out-of-plane spin-polarized valleys in the vicinity of the Fermi level. As the valley polarization is oppositely oriented at the $\overline{K}$ and ${\overline{K}}^{\prime }$ points, backscattering should be strongly suppressed in this system.

Figure 1

(a) Top view and (b) side view of the structural model of the $\mathrm{Tl}/\mathrm{Si}(111)\mathrm{\text{−}}(1\times 1)$ surface formed by the adsorption of one monolayer of Tl. (c) Corresponding low-energy electron diffraction image and (d) surface Brillouin zone. (e) Quasiparticle band structures including spin-orbit coupling illustrating the in-plane (left-hand side) and out-of-plane (right-hand side) polarization components. The diameter of the circles is proportional to the spin polarization with a maximum degree of 100%, e.g., for $S_4$ at $\overline{K}$. The energy scale refers to the valence-band maximum $E_{\mathrm{VM}}$. The gray shaded area illustrates the projected bulk bands.

Figure 2

Spin- and angle-resolved inverse-photoemission spectra along $\overline{\Gamma }\overline{K}$ and $\overline{\Gamma }{\overline{K}}^{\prime }$ sensitive to the (a),(b) in-plane and (c), (d) out-of-plane spin components. $\theta$ and $\varphi$ denote the angle of incidence and the sample azimuth, respectively. (e) Out-of-plane spin asymmetry at an angle of incidence $\theta =60°$ around $\overline{K}$ and ${\overline{K}}^{\prime }$.

Figure 3

$E$ vs ${\mathbf{k}}_{\parallel }$ plot derived from spectra taken along $\overline{\Gamma }\overline{K}$ with sensitivity to (a) the in-plane and (b) the out-of-plane polarization. Solid lines show the calculated surface-state bands.

Figure 4

Charge distribution plots of the occupied and unoccupied surface-state component $S_1$ and $S_3$ at two points in $\mathbf{k}$ space $\overline{K}/2$ and $\overline{K}$.