Tetragonal bismuth bilayer: a stable and robust quantum spin hall insulator

Kou, Liangzhi; Tan, Xin; Ma, Yandong; Tahini, Hassan A.; Zhou, Liujiang; Sun, Ziqi; Du, Aijun; Chen, Changfeng; Smith, Sean C.

doi:10.1088/2053-1583/2/4/045010

Cited by 40 publications

(59 citation statements)

References 58 publications

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“…Table 1 lists the optimized structural parameters of 2D T-Ge and T-Sn at the PBE level, including the lattice constants a 0 , the bond length l 1 that constitutes the square ring, the bond length l 2 that links two square rings, and the buckling height d. Similar to their honeycomb counterparts, the lattice constants a 0 , the buckling height d and the bond lengths l 1 and l 2 monotonously increase along with increasing of the atomic indices from Ge to Sn, as listed in table 1. Moreover, the bond length l 1 is slightly larger than l 2 , which is similar to tetragonal allotrope of group V elements [26] and MoS 2 [21].…”

Section: Computational Detailsmentioning

confidence: 67%

“…Interestingly, tetragonal allotrope of single layer MX 2 (M=Mo, W; T=S, Se, Te) were proposed to be QSH insulator [18][19][20]. Moreover, it was theoretically proposed that except for single layer puckered and buckled honeycomb lattice structures [22], group V elements, including P, As, Sb and Bi, can form a stable 2D tetragonal allotrope composed of buckled square and octagon rings [23][24][25][26]. Remarkably, 2D tetragonal allotrope of Bi was predicted to be QSH insulator with a sizable band gap about 0.41 eV [25,26].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, it was theoretically proposed that except for single layer puckered and buckled honeycomb lattice structures [22], group V elements, including P, As, Sb and Bi, can form a stable 2D tetragonal allotrope composed of buckled square and octagon rings [23][24][25][26]. Remarkably, 2D tetragonal allotrope of Bi was predicted to be QSH insulator with a sizable band gap about 0.41 eV [25,26]. It is therefore imperative to investigate 2D tetragonal allotrope of Ge and Sn.…”

Section: Introductionmentioning

confidence: 99%

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Topological node line semimetal state in two-dimensional tetragonal allotrope of Ge and Sn

Wang

Han

et al. 2019

New J. Phys.

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Realizing semimetal states in two-dimensional (2D) materials are of great importance for their future application in novel quantum devices at the nanoscale. Using first-principles calculations based on density functional theory, we propose a new 2D tetragonal allotrope of Ge and Sn, 2D T-Ge and T-Sn, which consists of repeated square and octagon rings. The calculated cohesive energy, ab initio molecular dynamic simulations and phonon dispersions indicate that 2D T-Ge and T-Sn are stable at room temperature and possibly synthesized in the experiments under appropriate growth conditions. In the absence of spin-orbital coupling (SOC), 2D T-Ge and T-Sn are node line semimetals and the nodal loop in 2D T-Ge and T-Sn are protected by the combination of the spatial inversion P and timereversal T symmetries. Remarkably, when SOC is included, 2D T-Ge and T-Sn are still node line semimetals although small gap is opened along the nodal loop, which are identified by nontrivial Z 2 invariant and topological edge states at the sample boundaries. Furthermore, our calculations show that node line semimetal states in 2D T-Ge and T-Sn are robust with the biaxial strains in the range of −3% to 3%. Our results provide a new 2D material platform for realization of 2D topological node line semimetals and innovative applications of topological node line semimetals.

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Section: Computational Detailsmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topological node line semimetal state in two-dimensional tetragonal allotrope of Ge and Sn

Wang

Han

et al. 2019

New J. Phys.

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“…Values of the fundamental band gaps calculated using the PBE method together with the band gaps of the b-X, w-X, and aw-X structures calculated earlier are listed in Table III. The fundamental band gap calculated using PBE is indirect and is 2. [45] Since the fundamental band gaps are normally underestimated by DFT, the band structures are also calculated using the HSE correction. After HSE correction to the PBE bands, the fundamental band gaps of s/o-X structures generally increase, but the direct/indirect character of the fundamental band gaps is unaltered.…”

Section: Electronic Propertiesmentioning

confidence: 99%

“…However, neither dynamical, thermal, nor other stability analysis of these structures was performed to show whether they are really stable, and no relevant structural parameters, such as buckling distance, short and long bonds, bond angles, pertinent mechanical properties, critical energetics, etc., were provided to characterize the s/o structure. Recently, Kou et al [45] pointed out that the buckled s/o structure (which they named the tetragonal bilayer) of Bi is stable and exhibits topological insulator features.…”

Section: Introductionmentioning

confidence: 99%

Stable single-layer structure of group-V elements

2016

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In addition to stable single-layer buckled honeycomb and washboard structures of group-V elements (or pnictogens P, As, Sb, and Bi) we show that these elements can also form two-dimensional, single-layer structures consisting of buckled square and octagon rings. An extensive analysis comprising the calculation of mechanical properties, vibration frequencies, and finite-temperature ab initio molecular dynamics confirms that these structures are dynamically and thermally stable and suitable for applications at room temperature and above. All these structures are semiconductors with a fundamental band gap, which is wide for P but decreases with increasing row number. The effect of the spin-orbit coupling decreases the band gap and is found to be crucial for Sb and Bi. These results are obtained from first-principles calculations based on density functional theory.

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Emerging topological states in quasi‐two‐dimensional materials

Huang

Wang

et al. 2016

WIREs Comput Mol Sci

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Inspired by the discovery of graphene, various two-dimensional (2D) materials have been experimentally realized, which exhibit novel physical properties and support promising applications. Exotic topological states in 2D materials (including quantum spin Hall and quantum anomalous Hall insulators), which are characterized by nontrivial metallic edge states within the insulating bulk gap, have attracted considerable attentions in the past decade due to their great importance for fundamental research and practical applications. They also create a surge of research activities and attract extensive efforts to search for new topological materials in realistic 2D/quasi-2D systems. This review presents a comprehensive survey of recent progress in designing of topological states in quasi-2D materials, including various quantum well heterostructures and 2D atomic lattice structures. In particular, the possibilities of constructing topological nontrivial states from commonly used materials are discussed and the ways of enlarging energy gaps of topological states and realizing different topological states in a single material are presented.

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Tetragonal bismuth bilayer: a stable and robust quantum spin hall insulator

Cited by 40 publications

References 58 publications

Topological node line semimetal state in two-dimensional tetragonal allotrope of Ge and Sn

Topological node line semimetal state in two-dimensional tetragonal allotrope of Ge and Sn

Stable single-layer structure of group-V elements

Emerging topological states in quasi‐two‐dimensional materials

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