Nontrivial topological electronic structures in a single Bi(111) bilayer on different substrates: A first-principles study

Zhi-Quan Huang, Feng-Chuan Chuang, Chia-Hsiu Hsu, Yu-Tzu Liu, Hua-Rong Chang, Hsin Lin, and Arun Bansil

Phys. Rev. B 88, 165301 – Published 1 October 2013

Abstract

Electronic structures, minimum energy configurations, and band topology of strained Bi(111) single bilayers placed on a variety of semiconducting and insulating substrates are investigated using first-principles calculations. A topological phase diagram of a free-standing Bi bilayer is presented to help guide the selection of suitable substrates. The insulating hexagonal-BN is identified as the best candidate substrate material for supporting nontrivial topological insulating phase of Bi bilayer thin films. A planar hexagonal Bi layer is predicted under tensile strain, which we show could be realized on a SiC substrate. The Bi bilayer becomes metallic under the compressive strain induced by Si and Ge substrates.

Received 30 May 2013

DOI:https://doi.org/10.1103/PhysRevB.88.165301

Authors & Affiliations

Zhi-Quan Huang¹, Feng-Chuan Chuang^1,*, Chia-Hsiu Hsu¹, Yu-Tzu Liu¹, Hua-Rong Chang¹, Hsin Lin^2,†, and Arun Bansil²

¹Department of Physics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan
²Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

^*fchuang@mail.nsysu.edu.tw
^†nilnish@gmail.com

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Vol. 88, Iss. 16 — 15 October 2013

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Images

Figure 1
(a) Total energy of a free-standing Bi single bilayer in the buckled and planar honeycomb structures as a function of lattice constant. Corresponding strain values with respect to the lattice constant of crystalline Bi are marked on the top axis. (b) Band gap at the $Γ$ point and the minimum band gap in the electronic spectrum as a function of lattice constant. (c)–(f) Band structures of free-standing Bi single bilayers in the buckled honeycomb lattice for various values of the lattice constant as marked in the figures. Size of the black circles is proportional to the contribution of the $s$ -type orbital. The even and odd parities of the states are indicated by $+$ and $-$ signs, respectively.Reuse & Permissions
Figure 2
(a) The topological phase diagram for a free-standing Bi single bilayer thin film obtained from the band inversion strength $E_{I}$ as a function of $a_{1}$ and $d_{1}$ . The white dashed line separates the trivial and nontrivial topological phases. Values of $d_{1}$ (black line) as a function of lattice constant have been obtained by relaxing atomic positions of a free-standing Bi bilayer. The values of $a_{1}$ and $d_{1}$ for a Bi single bilayer for several representative substrates are identified. (b)–(e) Band structure evolution of the Bi bilayer as a function of the interlayer distance $d_{1}$ as shown in the figures. The buckled Bi bilayer transforms into the planar structure as $d_{1}$ goes to zero. The lateral lattice constant $a_{1}$ is kept fixed at 4.80 Å.Reuse & Permissions
Figure 3
Atomic structure of the Bi bilayer on (a) $h$ -BN $\sqrt{3}$ $\times$ $\sqrt{3}$ and (b) $h$ -BN $2 \times 2$ substrate. (c) Surface Brillouin zone with high symmetry points marked. Surface band structure of the Bi bilayer on (d) $h$ -BN $\sqrt{3}$ $\times$ $\sqrt{3}$ and (e) $h$ -BN $2 \times 2$ substrate. Red bands are Bi-derived, while the black bands are derived from the substrate.Reuse & Permissions
Figure 4
(a) Band structure of the free-standing Bi thin film in planar honeycomb structure at $a_{1} = 5.35$ Å. (b) Atomic structure of Bi honeycomb on SiC(0001) $\sqrt{3}$ $\times$ $\sqrt{3}$ substrate. (c) Band structure of the Bi honeycomb on SiC(0001) $\sqrt{3}$ $\times$ $\sqrt{3}$ . Red crosses and blue circles identify Bi-derived states with opposite spins. (d) Blow-up of the band structure of (c) around the $K$ point. Red and blue colors refer to opposite spin-polarizations of the bands.Reuse & Permissions
Figure 5
Atomic structure of Bi bilayer on (a) Si(111)- $1 \times 1$ and (b) Ge(111))- $1 \times 1$ substrate. Band structure of the free-standing Bi bilayer at the lattice constant of (c) 3.87 and (d) 4.09 Å. The band structure of Bi bilayer on (e) Si(111)- $1 \times 1$ and (f) Ge(111))- $1 \times 1$ surface. Red bands are Bi derived and the black bands are substrate derived.Reuse & Permissions

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