Two-dimensional states localized in subsurface layers of Ge(111)

Yoshiyuki Ohtsubo, Koichiro Yaji, Shinichiro Hatta, Hiroshi Okuyama, and Tetsuya Aruga

Phys. Rev. B 88, 245310 – Published 31 December 2013

Abstract

The origin of the two-dimensional surface states localized in subsurface regions of the Ge(111) substrate has been studied by density-functional-theory calculations, which were compared with the experimental results of angle-resolved photoelectron spectroscopy. For the Bi/Ge(111)- $(\sqrt{3} \times \sqrt{3}) R 30^{\circ}$ , Br/Ge(111)-(1 $\times$ 1), and Tl/Ge(111)-(1 $\times$ 1) surfaces, we found that the surface states are classified into three groups. The energy dispersion and the orbital character for each band implies the relationship between the subsurface states and the bulk heavy-hole, light-hole, and spin-orbit split-off bands. These results indicate that the subsurface states originate from the bulk bands that are perturbed due to the truncation of the three-dimensional periodicity at the surface.

Received 21 July 2013
Revised 2 December 2013

DOI:https://doi.org/10.1103/PhysRevB.88.245310

Authors & Affiliations

Yoshiyuki Ohtsubo^1,2, Koichiro Yaji^2,3, Shinichiro Hatta^1,2, Hiroshi Okuyama¹, and Tetsuya Aruga^1,2,*

¹Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
²JST CREST, Saitama 332-0012, Japan
³Synchrotron Radiation Laboratory, Institute for Solid State Physics (SRL-ISSP), The University of Tokyo, Kashiwa 277-8581, Japan

^*aruga@kuchem.kyoto-u.ac.jp

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Vol. 88, Iss. 24 — 15 December 2013

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Images

Figure 1
The LEED patterns [(a), (c), (e)] and schematic structures [(b), (d), (f)] of the Bi/Ge(111)- $(\sqrt{3} \times \sqrt{3}) R 30^{\circ}$ , Br/Ge(111)-(1 $\times$ 1), and Tl/Ge(111)-(1 $\times$ 1) surfaces. Bi atoms form trimers, while Tl and Br are adsorbed in ( $1 \times 1$ ) periodicity. All the LEED patterns were captured at room temperature.
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Figure 2
(a)–(c) Second-derivative ARPES images measured with He I on (a) Bi/Ge, (b) Br/Ge, and (c) Tl/Ge. Panel (a) was reproduced from Ref.[6]. Solid lines are guides to the eyes for the bands $S_{1}$ , $S_{2}$ , and $S_{3}$ . Dashed lines correspond to the upper edges of the HH, SO, and LH bands, which were calculated based on the tight-binding parameters fitted to the experimental bulk bands. Triangle markers in (a) and (b) represent the spin polarization of each band measured by spin-resolved ARPES as reported in Refs.[6] and[7], respectively. Inset in (a) represents the (1 $\times$ 1) (solid) and $(\sqrt{3} \times \sqrt{3}) R 30^{\circ}$ (dashed) SBZ. (d) Schematic of bulk Ge band structure (see text). At $Γ$ the SO band is split by $Δ_{SO} = 0.29$ eV from VBM.
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Figure 3
ARPES energy distribution curves measured on (a) Bi/Ge and (b) Br/Ge. Triangle markers indicate peak positions on each spectrum. Empty ones are not observed as an obvious peak but rather weak features. An emission angle ( $θ_{e}$ ) of 3 $^{\circ}$ corresponds to $k_{∥}$ = 0.1 Å $^{- 1}$ .
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Figure 4
Calculated band structures along [1 $\bar{1}$ 0] for the (a, d) Bi/Ge, (b, e) Br/Ge, and (c, f) Tl/Ge slabs. The radii of the circles, $R_{k_{∥}, E}^{\pm}$ , are defined by Eq. (1). Panels (a–c) are depicted with $R_{k_{∥}, E}^{+}$ and show total contribution of the subsurface layers. Panels (d–f) are depicted with $R_{k_{∥}, E}^{-}$ and show net spin polarization. The contrasts (colors, online) of the circles in (d–f) represent the spin polarization orientations. In the left side, the projected bulk valence bands (thin lines) obtained by the DFT calculation are shown. Solid lines in the right side represent the upper edges of the bulk HH, LH, and SO bands. The arrows in panels (d–f) indicate the states for which partial charge distribution is shown in Fig. 5. Panel (e) is reproduced from Ref.[7].
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Figure 5
Layer- and spin-resolved partial charges of the states belonging to the spin-polarized surface bands on (a, b) Bi/Ge, (c, d) Br/Ge, and (e–g) Tl/Ge at $k_{∥}$ around 0.05 Å $^{- 1}$ (indicated by arrows in Fig. 4). The zeroth layer corresponds to the adsorbate atoms.
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Figure 6
(a) Schematics for bulk band structures around $Γ$ for Ge. Arrows guide the positions of states listed in Table III. (b) The hypothetical surface bands derived from bulk SO and LH bands (solid lines). In this picture, the SOI for the surface bands is ignored for the sake of simplicity. (c) Subsurface-state bands with spin splitting due to SOI. The spin polarization directions are represented by the color of the lines. (d) Same as (c) for HgTe with uniaxial strain. Solid lines represent the topological gapless bands calculated on the surface [5].
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