Quantum well states in ultrathin Bi films: Angle-resolved photoemission spectroscopy and first-principles calculations study

T. Hirahara, T. Nagao, I. Matsuda, G. Bihlmayer, E. V. Chulkov, Yu. M. Koroteev, and S. Hasegawa

Phys. Rev. B 75, 035422 – Published 24 January 2007

Abstract

Quantum well states (QWSs) in ultrathin Bi(001) films grown on $Si (111) - 7 \times 7$ with thicknesses up to several tens of nanometers were studied by angle-resolved photoemission spectroscopy and first-principles calculations. We observed QWSs at various points in $k$ -space; those located near $\bar{Γ}$ are very difficult to distinguish while the QWS peaks at off-normal emission $(\bar{M})$ are clearly resolved and show highly anisotropic features due to the saddle-point-like band dispersion near the Fermi level of bulk Bi along the $L − X$ direction. The features of the QWSs are well-reproduced by ab initio calculations for free-standing Bi slabs. The standard method of the phase-shift accumulation model is applied to the QWSs and the bulk band dispersion perpendicular to the surface at finite parallel momentum is experimentally obtained for the first time. The phase shifts at the film interfaces are discussed in detail. The QWSs have little contribution to the electronic structure near the Fermi level and this suggests that the macroscopic physical properties of the films in the thickness of several atomic layers are likely determined by the highly metallic surface states.

Received 25 July 2006

DOI:https://doi.org/10.1103/PhysRevB.75.035422

Authors & Affiliations

T. Hirahara^1,*, T. Nagao², I. Matsuda¹, G. Bihlmayer³, E. V. Chulkov^4,5, Yu. M. Koroteev^4,6, and S. Hasegawa¹

¹Department of Physics, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
²Nano System Functionality Center, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
³Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich, Germany
⁴Donostia International Physics Center (DIPC), 20018 San Sebastián/Donostia, Basque Country, Spain
⁵Departamento de Física de Materiales and Centro Mixto CSIV-UPV/EHU, Facultad de Ciencias Químicas, UPV/EHU, Apartado 1072, 20080 San Sebastián, Basque Country, Spain
⁶Institute of Strength Physics and Materials Science, Russian Academy of Sciences, 634021, Tomsk, Russia

^*Electronic address: hirahara@surface.phys.s.u-tokyo.ac.jp

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Issue

Vol. 75, Iss. 3 — 15 January 2007

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Images

Figure 1
(a) The bulk and surface Brillouin zone of $Bi {(001)}_{hex}$ , or ${(111)}_{rhom}$ . (b) Schematic drawing of the bulk band structure of Bi near the Fermi level projected on the (001) surface Brillouin zone. The hole pocket is located at the $\bar{Γ}$ $(T)$ point and the electron pocket is located at the $\bar{M}$ $(L)$ point. The shaded areas indicate electron-filled regions. (c),(d) Calculated bulk band structure along the trigonal axis for the $Γ − T$ $(k_{‖} = 0)$ and $L − X$ direction $(k_{‖} \neq 0)$ [dark lines in (a)] based on the tight-binding calculation of Liu and Allen (Ref. 17).Reuse & Permissions
Figure 2
(Color online) (a)–(d) The angle-resolved photoemission spectra of ultrathin $Bi (001)$ films on $Si (111) − 7 \times 7$ along the $\bar{Γ} - \bar{M}$ direction for the 6.8 BL (a), 14.7 BL (b), and 19.5 BL (c) films and that along the $\bar{Γ} - \bar{K}$ direction for the 14.7 BL (d) film. Each spectrum was recorded in 0.5° steps. The dotted spectra represent the high symmetry points in the surface Brilluoin zone [ $\bar{Γ}$ , $\bar{M}$ , and $\bar{K}$ shown in Fig. 3e]. (e)–(h) The band dispersion image derived from (a)–(d) by taking the second derivatives for the 6.8 BL (e), 14.7 BL (f), 19.5 BL (g), and 14.7 BL (h) films, respectively. The white arrows indicate Fermi level crossings. The white dotted lines, the white dotted boxes, and the feature A are discussed in the text. The solid lines in (g) and (h) near $E_{F}$ represent the edge of the bulk band projection in the tight-binding calculation (Ref. 17). (i),(j) The bulk band projection along the $\bar{Γ} - \bar{M}$ direction for the tight-binding model (i) and first-principles calculations (j), respectively.Reuse & Permissions
Figure 3
(Color online) (a),(b) The band structure of the 10.0 BL (a) and 17.0 BL (b) ultrathin Bi (001) films for the $\bar{M} - \bar{K}$ direction. The red filled circles are the results of the first-principles calculations for free-standing Bi slabs. (c),(d) The Fermi surface of the 19.5 BL (c) and 40.0 BL (d) Bi (001) films. The white line indicates the surface Brillouin zone boundary. (e) The schematic drawing of the Fermi surface in the surface Brillouin zone. The high symmetry points are also indicated. A hexagonal electron pocket is located at the $\bar{Γ}$ point while six hole lobes are seen along the $\bar{Γ} - \bar{M}$ direction. There is also a faint needlelike electron pocket around the $\bar{M}$ point.Reuse & Permissions
Figure 4
(a) ARPES spectra for 6.8, 10.0, 14.7, 17.0, 19.5, and 40.0 BL Bi(001) films at 4° off $\bar{Γ}$ . The surface states (SS) just below $E_{F}$ are marked with filled squares and the QWSs are marked with triangles. (b) ARPES spectra at the $\bar{M}$ point for the same film thicknesses as shown in (a). The filled triangles pointing up represent the surface resonance state forming the electron pocket at L while the rest of the QWSs originating from the bulk band below $E_{F}$ are shown by triangles facing down.Reuse & Permissions
Figure 5
(a) The solid circles with error bars are the bulk band dispersion obtained from the QWS peaks in Fig. 4b. The solid lines are the calculated band dispersion using the tight-binding parameters of Liu and Allen (Ref. 17). The solid circles with error bars are the total reflection phase shift $Φ = ϕ_{s u b} + ϕ_{vac}$ obtained for the QWS peaks in Fig. 4b using Eq. (4). The solid lines are the least-squares linear fits. (c) The solid circles are the total reflection phase shift $Φ (E)$ obtained using Eq. (7) for the QWSs of free-standing Bi slabs in the ab initio calculations. The solid line indicates the analytically calculated results of $Φ (E) = 2 \times ϕ_{vac}$ using Eq. (6).Reuse & Permissions
Figure 6
The so-called structure plot, showing the energy positions of the experimentally obtained QWSs (solid circles with error bars) for various thicknesses. The solid lines are the predictions calculated with Eq. (5) using the bulk band dispersion in Fig. 5a and phase shifts of the solid line in Fig. 5b. The solid triangles represent the positions of the QWSs obtained for the first-principles calculation.Reuse & Permissions

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