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Bulk and surface electronic structure of Bi4Te3 from GW calculations and photoemission experiments

Dmitrii Nabok, Murat Tas, Shotaro Kusaka, Engin Durgun, Christoph Friedrich, Gustav Bihlmayer, Stefan Blügel, Toru Hirahara, and Irene Aguilera
Phys. Rev. Materials 6, 034204 – Published 23 March 2022
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  • INTRODUCTION
  • CRYSTAL STRUCTURE
  • COMPUTATIONAL DETAILS
  • EXPERIMENTAL DETAILS
  • RESULTS
  • SURFACE ELECTRONIC STRUCTURE MEASURED BY…
  • SUMMARY
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    We present a combined theoretical and experimental study of the electronic structure of stoichiometric Bi4Te3, a natural superlattice of alternating Bi2Te3 quintuple layers and Bi bilayers. In contrast to the related semiconducting compounds Bi2Te3 and Bi1Te1, density functional theory predicts Bi4Te3 is a semimetal. In this work, we compute the quasiparticle electronic structure of Bi4Te3 in the framework of the GW approximation within many-body perturbation theory. The quasiparticle corrections are found to modify the dispersion of the valence and conduction bands in the vicinity of the Fermi energy, leading to the opening of a small indirect band gap. Based on the analysis of the eigenstates, Bi4Te3 is classified as a dual topological insulator with bulk topological invariants Z2 (1;111) and magnetic mirror Chern number nM=1. The bulk GW results are used to build a Wannier-function-based tight-binding Hamiltonian that is further applied to study the electronic properties of the (111) surface. The comparison with our angle-resolved photoemission measurements shows excellent agreement between the computed and measured surface states and indicates the dual topological nature of Bi4Te3.

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    • Received 12 November 2021
    • Revised 9 February 2022
    • Accepted 1 March 2022

    DOI:https://doi.org/10.1103/PhysRevMaterials.6.034204

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    First-principles calculationsTopological materials
    1. Techniques
    Photoemission spectroscopy
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Dmitrii Nabok1, Murat Tas2, Shotaro Kusaka3, Engin Durgun4, Christoph Friedrich1, Gustav Bihlmayer1, Stefan Blügel1, Toru Hirahara3, and Irene Aguilera1,*

    • 1Peter Grünberg Institut and Institut for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich and JARA, Germany
    • 2Department of Physics, Gebze Technical University, Kocaeli 41400, Turkey
    • 3Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
    • 4UNAM–National Nanotechnology Research Center and Institute of Materials Science and Nanotechnology, Bilkent University, Ankara 06800, Turkey

    • *Present address: Institute of Physics, University of Amsterdam, 1012 WX Amsterdam, Netherlands. i.g.aguilerabonet@uva.nl

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    Vol. 6, Iss. 3 — March 2022

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    Images

    • Figure 1
      Figure 1

      Left: Crystal structure of Bi4Te3, consisting of three quintuple Bi2Te3 layers intercalated with three Bi2 layers, presented in hexagonal (conventional) and rhombohedral (primitive) unit cells. Right: The Brillouin zones of the bulk crystal and the (111) surface. Time-reversal-invariant special k points are shown with red (plus) and blue (minus) dots reflecting the valence-state parity used to compute the topological invariant Z2.

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    • Figure 2
      Figure 2

      (a) RHEED pattern and (b) TEM image of the Bi4Te3(111) film with the QL termination.

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    • Figure 3
      Figure 3

      (a) Electronic band structure of Bi4Te3 in the vicinity of the Fermi energy as computed with different methods: “diag” refers to the standard G0W0 computational approach, and “full” refers to the results obtained by including the off-diagonal matrix elements of the self-energy. The band structures are calculated explicitly on a fine mesh along the k path, not with Wannier interpolation. The bands are aligned with respect to the Fermi energy. The inset shows the behavior of the valence and conduction states in the vicinity of Γ. (b) and (c) The band inversion between the valence and conduction states at the Γ point calculated with PBE and G0W0-full, respectively. The color of the lines represents the contribution of Bi and Te atoms. (d) G0W0-full valence and conduction bands projected onto the BL (blue) and QL (red).

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    • Figure 4
      Figure 4

      Comparison of the explicit and Wannier-interpolated electronic band structures of Bi4Te3 in the vicinity of the Fermi level.

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    • Figure 5
      Figure 5

      GW-TB electronic structure of the semi-infinite Bi4Te3 (111) surface terminated either (a) on the QL or (b) on the BL. The color map corresponds to the density of states projected on the topmost layer in each termination. Emerging surface states are represented as narrow bands arising in different parts of the spectra outside of the wide bulk states. (c) and (d) GW-TB electronic structure of the 18 (QL+BL) layer slab. The surface states with localization on either the topmost (c) QL or (d) BL levels are highlighted with colored circles. The size and color of the circles correspond to the magnitude and sign (red for positive and blue for negative) of the in-plane component of the spin polarization perpendicular to the momentum.

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    • Figure 6
      Figure 6

      PBE electronic structure of the 18 (QL+BL) layer slab in the vicinity of the surface state crossing point along Γ¯−M¯ for the symmetric (left) and deformed (right) Bi4Te3. Only the QL surface states are treated. The color code of the circles is as in Fig. 5.

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    • Figure 7
      Figure 7

      (a) and (b) ARPES spectra of the Bi4Te3 QL terminated (111) surface. (a) shows the raw data, and (b) shows the second derivative with respect to energy to enhance spectral features. (c) The same plot as in Fig. 5 (GW-TB) shifted up 50 meV. (d) Comparison between the experimental and (shifted) theoretical electronic surface structures. Yellow dots represent computed bulk states. As a guide to the eye, solid lines highlight the dispersion of the most intensive ARPES peaks.

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    • Figure 8
      Figure 8

      k||,x versus k||,y (a) experimental and (b) computed (GW-TB) Fermi surface maps. Red dashed lines show constant k||,y scans presented in Fig. 9.

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    • Figure 9
      Figure 9

      Electronic structure of Bi4Te3 along the nonsymmetry lines shown in Fig. 8. Experimental (50 meV shifted theoretical) spectra for (a) ky=0 Å−1, (b) ky=0.1 Å−1, (c) ky=0.14 Å−1, (d) ky=0.18 Å−1, and (e) ky=0.26 Å−1 are shown in the top (bottom) row. The color coding in the theoretical GW-TB spectra is the same as in Fig. 5. Dashed lines indicate the experimental surface band dispersion in the vicinity of the crossing point.

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