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Proving Nontrivial Topology of Pure Bismuth by Quantum Confinement

S. Ito, B. Feng, M. Arita, A. Takayama, R.-Y. Liu, T. Someya, W.-C. Chen, T. Iimori, H. Namatame, M. Taniguchi, C.-M. Cheng, S.-J. Tang, F. Komori, K. Kobayashi, T.-C. Chiang, and I. Matsuda
Phys. Rev. Lett. 117, 236402 – Published 2 December 2016
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    Abstract

    The topology of pure Bi is controversial because of its very small (∼10  meV) band gap. Here we perform high-resolution angle-resolved photoelectron spectroscopy measurements systematically on 14–202 bilayer Bi films. Using high-quality films, we succeed in observing quantized bulk bands with energy separations down to ∼10  meV. Detailed analyses on the phase shift of the confined wave functions precisely determine the surface and bulk electronic structures, which unambiguously show nontrivial topology. The present results not only prove the fundamental property of Bi but also introduce a capability of the quantum-confinement approach.

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    • Received 1 August 2016

    DOI:https://doi.org/10.1103/PhysRevLett.117.236402

    © 2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Topological phases of matter
    1. Physical Systems
    Bilayer filmsQuantum wellsThin films
    1. Techniques
    Angle-resolved photoemission spectroscopy
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    S. Ito1, B. Feng1, M. Arita2, A. Takayama3, R.-Y. Liu1, T. Someya1, W.-C. Chen4, T. Iimori1, H. Namatame2, M. Taniguchi2, C.-M. Cheng4, S.-J. Tang4,5, F. Komori1, K. Kobayashi6, T.-C. Chiang7, and I. Matsuda1

    • 1Institute for Solid State Physics (ISSP), The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
    • 2Hiroshima Synchrotron Radiation Center (HSRC), Hiroshima University, Higashi-Hiroshima, Hiroshima 739-0046, Japan
    • 3Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
    • 4National Synchrotron Radiation Research Center (NSRRC), Hsinchu, Taiwan 30076, Republic of China
    • 5Department of Physics and Astronomy, National Tsing Hua University, Hsinchu, Taiwan 30013, Republic of China
    • 6Department of Physics, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan
    • 7Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

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    Issue

    Vol. 117, Iss. 23 — 2 December 2016

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    Images

    • Figure 1
      Figure 1

      Schematic representation of (a) the bulk and surface Brillouin zone of Bi crystal in the [111] direction and (b) the Fermi surface. (c) Near-EF structure of the bulk projections at M¯. (d)–(g) Possible band structures along the Γ¯M¯ direction on the Bi(111) surface. The blue and red lines indicate the two spin-splitting surface bands, SS1 and SS2, respectively.

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    • Figure 2
      Figure 2

      (a),(b) The Fermi surface and the band structures measured along the Γ¯M¯ direction in a 14 BL Bi(111) film at hν=21  eV. Solid lines in (b) indicate bulk projections calculated by a tight-binding method [21]. (c) Band structures obtained by the first-principles calculations for a 14 BL Bi slab. (d) Plane-averaged electron densities within the film calculated at the four k points marked in (c). (e),(f) Possible band assignments in an ultrathin Bi film. Gray areas illustrate positions of the VB maximum (VBM) and CB minimum (CBM).

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    • Figure 3
      Figure 3

      (a) Wide-range band structures measured along the Γ¯M¯ direction in 14, 18, and 79 BL Bi(111) films at hν=21  eV. The colored images were produced using a curvature method for better visualization [49]. (b) Near-EF band structures measured at hν=8.437  eV inside the red box in (a). The thickness is systematically increased from 14 to 202 BL.

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    • Figure 4
      Figure 4

      (a) EDCs extracted at M¯ (k=0.8  Å−1). The triangles show peak positions fitted by Lorentzian functions (inset). (b) E−k⊥ dispersion experimentally obtained using Eq. (2). The solid line represents a linear fit. (c) E−k⊥ dispersion obtained from a tight-binding calculation [21]. (d) Total phase shifts experimentally derived using Eq. (1). (e) A plot of the N−E relation in QWSs (a structure plot). Solid lines are drawn using Eq. (3).

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    • Figure 5
      Figure 5

      (a) EDCs at M¯ magnified around EF. (b) Evolutions of peak positions extracted in (a) and those of VBM (n=1 QWS in VB) against an inverse thickness 1/N. The meanings of the solid lines are discussed in the text. (c) Schematic representation of the evolution in electronic structures of Bi films approaching the bulk limit.

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