Weak topological insulators induced by the interlayer coupling: A first-principles study of stacked Bi<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow /><mml:mn>2</mml:mn></mml:msub></mml:math>TeI

Tang, Peizhe; Yan, Binghai; Cao, Wendong; Wu, Shu-Chun; Felser, Claudia; Duan, Wenhui

doi:10.1103/physrevb.89.041409

Cited by 56 publications

(53 citation statements)

References 54 publications

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“…The first proposal of graphene as a QSH insulator [3] is practically useless because of its extremely small gap (10 −3 meV) induced by spin-orbit coupling (SOC) [8], although, so far, graphene is the best 2D material and that be easily made even by the scotch-tape method [9]. Recently, Bi 2 TeI has been proposed as another candidate for a QSH insulator [10], but its energy gap is also small. The bismuth (111) bilayer is potentially a large-gap (about 0.2 eV) QSH insulator [11].…”

Section: Introductionmentioning

confidence: 99%

Transition-Metal PentatellurideZrTe5andHfTe5: A Paradigm for Large-Gap Quantum Spin Hall Insulators

2014

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Quantum spin Hall (QSH) insulators, a new class of quantum matter, can support topologically protected helical edge modes inside a bulk insulating gap, which can lead to dissipationless transport. A major obstacle to reaching a wide application of QSH is the lack of suitable QSH compounds, which should be easily fabricated and have a large bulk gap. Here, we predict that single-layer ZrTe 5 and HfTe 5 are the most promising candidates for large-gap insulators, with a bulk direct (indirect) band gap as large as 0.4 eV (0.1 eV) and which are robust against external strains. The three-dimensional crystals of these two materials are good layered compounds with very weak interlayer bonding, and they are located near the phase boundary between weak and strong topological insulators, paving a new way for future experimental studies on both the QSH effect and topological phase transitions.

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Section: Introductionmentioning

confidence: 99%

Transition-Metal PentatellurideZrTe5andHfTe5: A Paradigm for Large-Gap Quantum Spin Hall Insulators

2014

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“…There are many proposed TCI phases depending on different crystal symmetries [4][5][6][7][8][9], yet those relying on mirror symmetry [10] are of particular interest as they have been experimentally observed in, for example, IV-VI semiconductors SnTe, Pb 1−x Sn x Te, and Pb 1−x Sn x Se [11][12][13][14][15]. More materials are theoretically proposed to realize the TCI phases such as rocksalt semiconductors [16,17], pyrochlore iridates [18], graphene systems [19], heavy fermion compounds [20,21], and antiperovskites [22], including two-dimensional (2D) materials such as SnTe thin films [23,24] and a (001) monolayer of PbSe [25].…”

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confidence: 99%

Layered Topological Crystalline Insulators

et al. 2015

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Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a threedimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the inter-layer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) (µ1, µ2) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) Mirror-symmetric TCIs are mathematically characterized by mirror Chern numbers (MCNs). The MCN is a topological invariant defined by µ 1 ≡ (µ + − µ − )/2 where µ + and µ − are Chern numbers of Bloch states with the opposite eigenvalues of a mirror operator (M z ) calculated on the mirror-invariant plane at k z = 0 in the Brillouin zone (BZ). In a three-dimensional (3D) crystal, there is a second MCN (µ 2 ) defined on the mirror-invariant plane at the boundary of the BZ k z = π (in units of 1/a, where a is the length of the primitive lattice vector along the z-axis) [26]. Moreover, considering different mirror symmetries, multiple pairs of MCNs (µ 1 , µ 2 ) can be simultaneously present in three dimensions. A complete characterization of 3D TCIs requires consideration of all the MCNs, which may allow for the possibility of new states of matter, where MCNs are locked together or undergo separate transitions. Nonetheless, previous study based only on µ 1 has not explored this situation.In this paper, by considering MCNs on all inequivalent mirror-symmetric planes in reciprocal space, we study new topological states of matter realized in a 3D layered crystal generated by stacking 2D TCI layers. We show that the layered system realizes a new class of 3D TCIs when inter-layer interaction is weak, which we will refer to as a layered TCI. The layered TCI is characterized by equal and nonzero first and second MCNs µ 1 = µ 2 = 0 with a number of metallic surface states eqaul to |µ 1 | + |µ 2 |. Increasing the inter-layer interaction, we then show that the layered TCI undergoes topological phase transitions that change the MCNs (µ 1 , µ 2 ). Based on first-principles calculations, we predict that a heterostructure consisting of alternating layers of PbSe monolayer and hexagonal BN (h-BN) sheet realizes the layered TCI indexed by (2,2), and that it undergoes distinct topological phase transitions in the sequence (µ 1 , µ 2 ): (2, 2) → (0, 2) → (0, 0) under external uniaxial tensile strain. Our findings shed light on new states of matter allowed by the presence of multiple MCNs in a 3D crystal. They may also help guide the discovery of more topological materials. Before presenting the results, we first briefly explain arXiv:1503.05966v1 [cond-mat.mtrl-sci]

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“…Let us find elementary solutions φ(i) of the eigenvalue equation (19) assuming φ(i) = ρ i v with v = t (v 1 , 0, 0, v 2 ). Under this assumption, the eigenvalue equation is reduced to…”

Section: Discussionmentioning

confidence: 99%

“…Several materials have been proposed as possible * takane@hiroshima-u.ac.jp WTIs. [17][18][19][20] To theoretically describe Dirac electrons on a side surface of WTIs, an effective 2D model consisting of coupled 1D helical channels has been proposed in Refs. 14 and 15.…”

Section: Introductionmentioning

confidence: 99%

Effective Model for Massless Dirac Electrons on a Surface of Weak Topological Insulators

Arita

Takane

2014

J. Phys. Soc. Jpn.

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In a typical situation, gapless surface states of a three-dimensional (3D) weak topological insulator (WTI) appear only on the sides, leaving the top and bottom surfaces gapped. To describe massless Dirac electrons emergent on such side surfaces of a WTI, a two-dimensional (2D) model consisting of a series of onedimensional helical channels is usually employed. However, an explicit derivation of such a model from a 3D bulk Hamiltonian has been lacking. Here, we explicitly derive an effective 2D model for the WTI surface states starting from the Wilson-Dirac Hamiltonian for the bulk WTI and establish a firm basis for the hitherto hypothesized 2D model. We show that the resulting 2D model accurately reproduces the excitation spectrum of surface Dirac electrons determined by the 3D model. We also show that the 2D model is applicable to a side surface with atomic steps.

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Weak topological insulators induced by the interlayer coupling: A first-principles study of stacked Bi2TeI

Cited by 56 publications

References 54 publications

Transition-Metal PentatellurideZrTe5andHfTe5: A Paradigm for Large-Gap Quantum Spin Hall Insulators

Transition-Metal PentatellurideZrTe5andHfTe5: A Paradigm for Large-Gap Quantum Spin Hall Insulators

Layered Topological Crystalline Insulators

Effective Model for Massless Dirac Electrons on a Surface of Weak Topological Insulators

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