Comparison of quantum spin Hall states in quasicrystals and crystals

Huang, Huaqing; Liu, Feng

doi:10.1103/physrevb.100.085119

Cited by 38 publications

(21 citation statements)

References 43 publications

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“…Apparently, the NI and TI phases are divided by a curve of zero energy gap. In order to confirm the TPT, we calculated the spin Bott index, a topological 3 Research invariant we developed recently for TI systems with disorder [20][21][22]. It is found that there is a concomitant sharp jump in the spin Bott index B s across the phase boundary, confirming a TPT.…”

Section: Tpts In Crystals With Disordermentioning

confidence: 82%

“…We emphasize that the calculations cover almost all kinds of 2D crystalline lattices with different symmetries. More interestingly, the linear scaling is even applicable to quasicrystal lattices, as demonstrated by examples of Penrose-type pentagonal [20,21] and Ammann-Beenker-type octagonal [22] quasicrystalline lattices, as also shown in Figure 3. This points to a general linear scaling of TPT in all the 2D systems, regardless of not only lattice symmetry but also periodicity.…”

Section: Tpts In Crystal and Quasicrystal Latticesmentioning

confidence: 91%

“…Generally, topological states are insensitive to a smooth change of material parameters unless the system passes through a TPT. So far, various TIs with different band inversion mechanisms have been theoretically proposed and/or experimentally verified, either periodic [16,17] or aperiodic [18][19][20][21][22]. The critical condition of TPTs is determined on a case-by-case basis, but there is no unified view on the TPT among different systems.…”

Section: Introductionmentioning

confidence: 99%

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A Unified View of Topological Phase Transition in Band Theory

Huang

Liu

2020

Research

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We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Reevaluating the band evolution from an “atomic crystal” (a normal insulator (NI)) to a solid crystal, such as a semiconductor, we demonstrate that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory. The validity of the scaling relation is verified in various two-dimensional (2D) lattices regardless of lattice symmetry, periodicity, and form of electron hoppings, based on a generic tight-binding model. Significantly, this linear scaling is shown to set an upper bound for the degree of structural disorder to destroy the topological order in a crystalline solid, as exemplified by formation of vacancies and thermal disorder. Our work formulates a simple framework for understanding the physical nature of TPTs with significant implications in practical applications of topological materials.

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Section: Tpts In Crystals With Disordermentioning

confidence: 82%

Section: Tpts In Crystal and Quasicrystal Latticesmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

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A Unified View of Topological Phase Transition in Band Theory

Huang

Liu

2020

Research

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“…1(b). In the previous works by Huang and Liu [28][29][30] , based on the Penrosetype quasicrystal lattice model described by the Hamiltonian (1), they proposed that the quantum spin Hall effect can be realized in quasicrystal lattices.…”

Section: Model and Methodsmentioning

confidence: 99%

Topological Anderson insulator phase in a quasicrystal lattice

Chen

Zhou

2019

Phys. Rev. B

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Motivated by the recent experimental realization of the topological Anderson insulator and research interest on the topological quasicrystal lattices, we investigate the effects of disorder on topological properties of a two-dimensional Penrose-type quasicrystal lattice that supports the quantum spin Hall insulator (QSHI) and normal insulator (NI) phases in the clean limit. It is shown that the helical edge state of the QSHI phase is robust against weak disorder. Most saliently, it is found that disorder can induce a phase transition from NI to QSHI phase in the quasicrystal system. The numerical results based on a two-terminal device show that a quantized conductance plateau can arise inside the energy gap of NI phase for moderate Anderson disorder strength. Further, it is confirmed that the local current distributions of the disorder-induced quantized conductance plateau are located on the two edges of sample. Finally, we identify this disorder-induced phase as topological Anderson insulator phase by computing the disorder-averaged spin Bott index. *

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“…Recently, the QSH effect is also explored in quasicrystals [39][40][41] by one of the authors. As shown in Fig.…”

Section: Quantum Spin Hall Statesmentioning

confidence: 99%

Topological states in quasicrystals

Fan,

Huang

2021

Preprint

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With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.

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Comparison of quantum spin Hall states in quasicrystals and crystals

Cited by 38 publications

References 43 publications

A Unified View of Topological Phase Transition in Band Theory

A Unified View of Topological Phase Transition in Band Theory

Topological Anderson insulator phase in a quasicrystal lattice

Topological states in quasicrystals

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