Vertex configuration rules to grow an octagonal Ammann–Beenker tiling

Cai, Cheng; Liao, Longguang; Fu, Xiujun

doi:10.1016/j.physleta.2019.04.020

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…As for the AB tiling, a growth algorithm based on three growth rules were proposed and perfect tiling has been obtained. [10] However, this algorithm is applicable only to an eightfold symmetric seed cluster. The present work reveals strong correlations among vertices along Ammann line, which may serve as an arrangement confinement of tiles and improve the growth rule for a perfect AB tiling.…”

Section: Discussionmentioning

confidence: 99%

“…[7] Here we use the Ammann lines proposed by Cai et al in the study of growth algorithm for the AB tiling. [10] Herein we simply draw two diagonal lines for each square and then extend the segments to their AB tilings. After the extension, the Ammann lines pass through diagonals of squares, sides of squares, and sides of rhombuses, but not through any diagonal of rhombuses as shown in Fig.…”

Section: Ab Tiling and Ammann Linesmentioning

confidence: 99%

“…[9] Based on the square and rhombus inflationdeflation, the self-similar transformation of the vertex configuration of the AB tiling was obtained. [10] Guided by the local matching rules and configuration selection, an improved algorithm for aggregation of square and rhombus tiles to generate an octagonal quasilattice was proposed. [11] The novel physical properties in the AB tiling structure have also been discovered recently.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Substitutions of vertex configuration of Ammann–Beenker tiling in framework of Ammann lines

Ye¹,

Huang²,

Fu³

2022

Chinese Phys. B

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The Ammann-Beenker tiling is a typical model for two-dimensional octagonal quasicrystals. The geometric properties of local configurations are the key to understand its formation mechanism. We study the configuration correlations in the framework of Ammann lines, which give a deep inspection on this eightfold symmetric structure. When both the vertex type and the orientation are taken into account, strict confinements on neighboring vertices are found. These correlations reveal the structural properties of the quasilattice and also provide substitution rules of vertex along an Ammann line.

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Section: Discussionmentioning

confidence: 99%

Section: Ab Tiling and Ammann Linesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Substitutions of vertex configuration of Ammann–Beenker tiling in framework of Ammann lines

Ye¹,

Huang²,

Fu³

2022

Chinese Phys. B

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Strip method to construct a two-dimensional quasilattice with eight-fold symmetry

Huang 黄,

Fu 傅

2024

Chinese Phys. B

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Based on the substitution rule and symmetry, we propose a method to generate an octagonal quasilattice consisting of square and rhombus tiles. Local configurations and Ammann lines are used to guide the growth of the tiles in a quasiperiodic order. The structure obtained is a perfect eight-fold symmetric quasilattice which is confirmed by the radial distribution function and the diffraction pattern.

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Topological superconductivity in quasicrystals

et al. 2021

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We propose realization of non-Abelian topological superconductivity in two-dimensional quasicrystals by the same mechanism as in crystalline counterparts. Specifically, we study a two-dimensional electron gas in Penrose and Ammann-Beenker quasicrystals with Rashba spin-orbit coupling, perpendicular Zeeman magnetic field, and conventional s-wave superconductivity. We find that topological superconductivity with broken time-reversal symmetry is realized in both Penrose and Ammann-Beenker quasicrystals at low filling, where the Bott index is unity. The topological nature of this phase is confirmed by the existence of a zero-energy surface bound state and the chiral propagation of a wave packet projected onto the midgap bound state along the surfaces. Furthermore, we confirm the existence of a single Majorana zero mode each in a vortex at the center of the system and along the surfaces, signifying the non-Abelian character of the system when the Bott index is unity.

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Vertex configuration rules to grow an octagonal Ammann–Beenker tiling

Cited by 4 publications

References 14 publications

Substitutions of vertex configuration of Ammann–Beenker tiling in framework of Ammann lines

Substitutions of vertex configuration of Ammann–Beenker tiling in framework of Ammann lines

Strip method to construct a two-dimensional quasilattice with eight-fold symmetry

Topological superconductivity in quasicrystals

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