Erratum: Atomic and Electronic Structure of Ultrathin Bi(111) Films Grown on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Te</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>111</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Substrates: Evidence for a Strain-Induced Topological Phase Transition [Phys. Rev. Lett.<b>109</b>, 227401 (2012)]

Hirahara, Toru; Fukui, Naoya; Shirasawa, Tetsuroh; Aitani, Masaki; Miyazaki, Hideki T.; Matsunami, Masaharu; Kimura, S.; Takahashi, Takashi; Hasegawa, Shuji; Kobayashi, Kaya

doi:10.1103/physrevlett.110.149901

Cited by 33 publications

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“…A combination of SOC and several symmetries produces topologically protected electronic states with inherent spin splitting. Despite the essential role in topological studies, a pure Bi crystal itself had long been believed topologically trivial based on several calculations [20][21][22][23][24][25][26], which had been considered to agree with transport [27] and angleresolved photoelectron spectroscopy (ARPES) measurements [22,28,29]. However, a recent high-resolution ARPES result suggests the surface bands are actually different from previously calculated ones and Bi possesses a nontrivial topology [30,31].…”

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Proving Nontrivial Topology of Pure Bismuth by Quantum Confinement

et al. 2016

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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. [5]. Even now, numbers of novel quantum phenomena have been intensively reported on this system [6][7][8][9][10][11][12][13]. In spite of the enormous amount of research, one fundamental property of Bi has been controversial: its electronic topology. Because of its huge spin-orbit coupling (SOC) [14], Bi has also been a central element in designing topological materials such as Bi 1−x Sb x , Bi 2 Se 3 , Na 3 Bi, and β-Bi 4 I 4 [15][16][17][18][19]. A combination of SOC and several symmetries produces topologically protected electronic states with inherent spin splitting. Despite the essential role in topological studies, a pure Bi crystal itself had long been believed topologically trivial based on several calculations [20][21][22][23][24][25][26], which had been considered to agree with transport [27] and angleresolved photoelectron spectroscopy (ARPES) measurements [22,28,29]. However, a recent high-resolution ARPES result suggests the surface bands are actually different from previously calculated ones and Bi possesses a nontrivial topology [30,31]. New transport measurements also imply the presence of topologically protected surface states [32,33].Nevertheless, the recent ARPES result has not yet been conclusive because it lacks clear peaks of bulk bands [30,31]. In principle, surface-normal bulk dispersions can be measured by changing the incident photon energy, where the momentum resolution is determined from the uncertainty relation ∆z · ∆k z ≥ 1/2 (Ref.[34]). (∆z is an escape depth of photoelectrons.) However, the Dirac dispersion of Bi is so sharp against this resolution that hν-dependent spectra show no clear peak [29][30][31]. This is a serious problem because Bi has a very small (∼10 meV [21,26]) band gap and a slight energy shift in bulk bands can easily transform a nontrivial case [ Fig. 1(d)] into a trivial case [ Fig. 1(e)]. In short, to unambiguously identify the topology of Bi, one must precisely determine both the surface and bulk electronic structures. One promising approach is using a thin film geometry, where quantumwell state (QWS) subbands are formed inside bulk band projections [35,36]. Although QWSs originate from bulk states, they possess a two-dimensional character and can be clearly observed in ARPES measurements.In this Letter, we performed high-resolution ARPES

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Proving Nontrivial Topology of Pure Bismuth by Quantum Confinement

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“…A single bilayer Bi(111) film has been predicted to be a 2d TI with a large band gap of about 0.5 eV [5][6][7], while other 2d TIs, such as HgTe/CdTe quantum wells [8] and InAs/GaSb quantum wells [9], have gaps of only several tens of meV at best. Recently, Bi(111) bilayer has been readily grown on Bi 2 Te 3 or Bi 2 Se 3 substrates [10][11][12][13][14][15]. Therefore, it is very promising for room-temperature TI-based devices.…”

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Edge engineering of a topological Bi(111) bilayer

Liu

Jiang

et al. 2014

Phys. Rev. B

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A topological insulator is a novel quantum state, characterized by symmetry-protected non-trivial edge/surface states. Our first-principle simulations show the significant effects of the chemical decoration on edge states of topological Bi(111) bilayer nanoribbon, which remove the trivial edge state and recover the Dirac linear dispersion of topological edge state. By comparing the edge states with and without chemical decoration, the Bi(111) bilayer nanoribbon offers a simple system for assessing conductance fluctuation of edge states. The chemical decoration can also modify the penetration depth and the spin texture of edge states. A low-energy effective model is proposed to explain the distinctive spin texture of Bi(111) bilayer nanoribbon, which breaks the spin-momentum orthogonality along the armchair edge.PACS numbers: 71.15. Mb, 73.43.Nq, 73.20.Fz, As an insulating state with symmetry-protected gapless interface electronic modes, the topological insulator (TI) has received considerable attention recently [1][2][3]. The edge conduction channels of two-dimensional (2d) TI exhibits quantum spin Hall effect within bulk gap [4]. A single bilayer Bi(111) film has been predicted to be a 2d TI with a large band gap of about 0.5 eV [5][6][7], while other 2d TIs, such as HgTe/CdTe quantum wells [8] and InAs/GaSb quantum wells [9], have gaps of only several tens of meV at best. Recently, Bi(111) bilayer has been readily grown on Bi 2 Te 3 or Bi 2 Se 3 substrates [10][11][12][13][14][15]. Therefore, it is very promising for room-temperature TI-based devices. However, the native edges of Bi bilayer suffer from the simultaneous presence of both trivial and non-trivial edge modes [6,12], which complicate the fundamental investigation of its topological properties and eventual applications. Similar complication had perplexed the interpretation of surface states in threedimensional (3d) TI Bi 1−x Sb x [16,17]. Although localization in Anderson's sense will suppress trivial conducting channels, quantitively localizing trivial channels will still be an experimental challenge. A wide distribution of conductance induced by multiple edge states is not desirable for accurate transport measurement [6,18,19].The complicated edge or surface states may be a generic problem associated with dangling bond states at the termination of 2d or 3d TIs. In this Letter, we report a first-principle analysis of chemical decoration of the edge states of Bi(111) bilayer, which, as we show, is an effective route for precise engineering of conducting edge states. We demonstrate that chemical passivation quantitatively removes the trivial edge bands in Bi bilayer nanoribbons, restoring the desired Dirac dispersion of the non-trivial edges. We further compute transport and optical signatures of the chemical decoration of the Bi bilayer edges, which can be assessed experimentally. In particular, we suggest that the Bi bilayer nanoribbons, with and without chemical passivation, offer a simple system for assessing conductance fluctuation of edge states...

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“…[16][17][18] Motivated by these recent experiments, we have carried out a systematic study of the electronic properties of BL-Bi focusing on the effects of strain and perpendicular electric field (as a major consequence of interface charge transfer), based on first-principles calculations.…”

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confidence: 99%

“…Among them, 2D TIs [7][8][9][10][11][12][13][14][15][16] exist naturally in the thin-film form. So far, theoretical predictions of 2D TI thin films, such as Bi(111) 10,11 and Sb(111) 12 films have mostly been done for freestanding films assuming a bulk lattice constant, whose topological and electronic properties show a very strong thickness dependence.…”

Section: Introductionmentioning

confidence: 99%

Robustness of two-dimensional topological insulator states in bilayer bismuth against strain and electrical field

2013

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Using first-principles and Wannier function methods, we systematically calculate the electronic band structure and topological edge states of single bilayer Bi (111) film (BL-Bi) as a function of strain and perpendicular electric field, to investigate the effects induced by lattice mismatch and interfacial charge transfer when BL-Bi is epitaxially grown on a substrate. We found that the BL-Bi remains with a finite band gap and a nontrivial band topology for strains up to ±6% and electric filed up to 0.8eV/Å. This indicates that the BL-Bi is a robust 2D topological insulator against strain and electrical field on a substrate. PACS number(s): 68.35. Gy, 73.20.At

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Erratum: Atomic and Electronic Structure of Ultrathin Bi(111) Films Grown onBi2Te3(111)Substrates: Evidence for a Strain-Induced Topological Phase Transition [Phys. Rev. Lett.109, 227401 (2012)]

Cited by 33 publications

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Proving Nontrivial Topology of Pure Bismuth by Quantum Confinement

Proving Nontrivial Topology of Pure Bismuth by Quantum Confinement

Edge engineering of a topological Bi(111) bilayer

Robustness of two-dimensional topological insulator states in bilayer bismuth against strain and electrical field

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