Higher-order topological insulator in a dodecagonal quasicrystal

Hua, Chun-Bo; Chen, Rui; Zhou, Bin; Xu, Dong-Hui

doi:10.1103/physrevb.102.241102

Cited by 58 publications

(26 citation statements)

References 114 publications

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“…Comparing our results to similar work on higher-order topological insulators in quasicrystals protected by eight and twelvefold rotation symmetry [23,34,35] raises a natural question: can the amorphous phases protected by continuous rotation symmetry be described as a limit of systems with increasingly fine discrete rotation symmetry? It also remains an open question how to extend the topological classification to materials with multiple atom species.…”

Section: Conclusion and Discussionsupporting

confidence: 59%

Amorphous topological phases protected by continuous rotation symmetry

2021

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Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. We show that the edge remains protected from localization in the topological phase, and the local disorder caused by the amorphous structure results in critical scaling of the transport in the system. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.

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Section: Conclusion and Discussionsupporting

confidence: 59%

Amorphous topological phases protected by continuous rotation symmetry

2021

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“…As an extension of TCIs, the recently proposed HOTIs are also related to lattice symmetry and have been extensively investigated in crystals. Recently, the concept of HOTIs were extended to quasicrystals, which results in quasicrystalline symmetry-protected higher-order topological phases [47][48][49][50].…”

Section: Quasicrystalline Symmetry-protected Topological Statesmentioning

confidence: 99%

“…Although higher-order topological phases were extended to octagonal quasicrystals [47,48] (as elucidated above) as well as dodecagonal quasicrystals, [49,50] the argument for the existence of eight corner Majorana zero modes relies on an alternating sign of the mass terms at the boundary. It fails in quasicrystals with odd-rotational symmetries, e.g., C 5 .…”

Section: Quasicrystalline Symmetry-protected Topological Statesmentioning

confidence: 99%

“…More interestingly, beyond the classical crystallographic restriction of periodicity, quasicrystals contain unique symmetries (such as five-fold and eight-fold rotations) that are forbidden in conventional crystals [66][67][68]. These novel symmetries can lead to new types of topological states that have no crystalline counterparts [47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

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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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“…In 2-dimensional (2D) systems, the second order topological phases are characterized by 0D in-gap corner states, while a 3D HOTI may host 1D gapless hinge states or in-gap corner states 5 . Up to now, HOTIs have been reported in various systems [9][10][11][12][13][14][15][16][17] , including quasicrystals [18][19][20] and Anderson insulators 21,22 .…”

Section: Introductionmentioning

confidence: 99%

Transport features of topological corner states in honeycomb lattice with multihollow structure

Wang,

Xu,

Wang

et al. 2021

Preprint

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Higher-order topological phase in 2-dimensional (2D) systems is characterized by in-gap corner states, which are hard to detect and utilize. We numerically investigate transport properties of topological corner states in 2D honeycomb lattice, where the second-order topological phase is induced by an in-plane Zeeman field in the conventional Kane-Mele model. Through engineering multihollow structures with appropriate boundaries in honeycomb lattice, multiple corner states emerge, which greatly increases the probability to observe them. A typical two-probe setup is built to study the transport features of a diamond-shaped system with multihollow structures. Numerical results reveal the existence of global resonant states in bulk insulator, which corresponds to the resonant tunneling of multiple corner states and occupies the entire scattering region. Furthermore, based on the well separated energy levels of multiple corner states, a single-electron source is constructed.

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Higher-order topological insulator in a dodecagonal quasicrystal

Cited by 58 publications

References 114 publications

Amorphous topological phases protected by continuous rotation symmetry

Amorphous topological phases protected by continuous rotation symmetry

Topological states in quasicrystals

Transport features of topological corner states in honeycomb lattice with multihollow structure

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