The generation of a dodecagonal columnar liquid quasicrystal is revealed by Carsten Tschierske, Feng Liu and co‐workers in their Research Article (e202314454). Constructed by the T‐shaped facial ...polyphiles, a special trapezoid tile with three aromatic walls and one flexible aliphatic wall becomes crucial for reaching the delicate balance between steric and entropic effects required by quasiperiodicity.
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the ...subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.
One-dimensional quasiperiodic systems with power-law hopping, 1/r^{a}, differ from both the standard Aubry-André (AA) model and from power-law systems with uncorrelated disorder. Whereas in the AA ...model all single-particle states undergo a transition from ergodic to localized at a critical quasidisorder strength, short-range power-law hops with a>1 can result in mobility edges. We find that there is no localization for long-range hops with a≤1, in contrast to the case of uncorrelated disorder. Systems with long-range hops rather present ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but nonergodic) states. Both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.
The discovery of topological phases in non-Hermitian open classical and quantum systems challenges our current understanding of topological order. Non-Hermitian systems exhibit unique features with ...no counterparts in topological Hermitian models, such as failure of the conventional bulk-boundary correspondence and non-Hermitian skin effect. Advances in the understanding of the topological properties of non-Hermitian lattices with translational invariance have been reported in several recent studies; however little is known about non-Hermitian quasicrystals. Here we disclose topological phases in a quasicrystal with parity-time (PT) symmetry, described by a non-Hermitian extension of the Aubry-André-Harper model. It is shown that the metal-insulating phase transition, observed at the PT symmetry breaking point, is of topological nature and can be expressed in terms of a winding number. A photonic realization of a non-Hermitian quasicrystal is also suggested.
•Magnetocaloric effects of ferromagnetic approximants Au64Al22R14 (R = Gd, Tb, and Dy) investigated.•Magnetic entropy change is from unique spin configuration over second icosahedron shell.•Promising ...approximant and quasicrystal materials design to develop larger magnetocaloric effect.
We report the magnetocaloric effect of the Tsai-type 1/1 quasicrystal approximants Au64Al22R14 (R = Gd, Tb, and Dy) with the space group of Im3̅. These approximants with the electron-per-atom (e/a) ratio of 1.72 exhibit a ferromagnetic transition in bulk at the Curie temperatures of 27, 15, and 9.5 K for R = Gd, Tb, and Dy, respectively, as confirmed by both magnetic susceptibility and specific heat measurements. The magnetic entropy change (ΔSM) of the materials for a field change of 7 T are 6.3, 4.4, and 4.8 J/K mol-R for R = Gd, Tb, and Dy, respectively. Other parameters related to the magnetocaloric effect, the adiabatic temperature change (ΔTad) and the relative cooling power (RCP) are also evaluated. We also discuss the obtained magnetocaloric effect of the approximants with relation to the recently reported unique magnetic order formed on the icosahedral clusters, a building unit of the Tsai-type 1/1 quasicrystal approximants.
The generation of a dodecagonal columnar liquid quasicrystal is revealed by Carsten Tschierske, Feng Liu and co‐workers in their Research Article (e202314454). Constructed by the T‐shaped facial ...polyphiles, a special trapezoid tile with three aromatic walls and one flexible aliphatic wall becomes crucial for reaching the delicate balance between steric and entropic effects required by quasiperiodicity.
Quasicrystals and their Approximants in 2D Ternary Oxides Förster, Stefan; Schenk, Sebastian; Maria Zollner, Eva ...
Physica Status Solidi B-basic Solid State Physics,
July 2020, 2020-07-00, Letnik:
257, Številka:
7
Journal Article
Recenzirano
Odprti dostop
2D oxide quasicrystals (OQCs) are recently discovered aperiodic, but well‐ordered oxide interfaces. In this topical review, an introduction to these new thin‐film systems is given. The concept of ...quasicrystals and their approximants is explained for BaTiO3‐ and SrTiO3‐derived OQCs and related periodic structures in these 2D oxides. In situ microscopy unravels the high‐temperature formation process of OQCs on Pt(111). The dodecagonal structure is discussed regarding tiling statistics and tiling decoration based on the results of atomically resolved scanning tunneling microscopy and various diffraction techniques. In addition, angle‐resolved ultraviolet photoemission spectroscopy and X‐ray photoelectron spectroscopy results prove a metallic character of the 2D oxide.
The recently discovered 2D oxide quasicrystals represent aperiodic, but well‐ordered oxide interfaces. An introduction to these new thin‐film systems is given here. The presence of well‐defined quasicrystalline structures adds another degree of freedom to perovskite oxide interfaces beyond the formation of 2D electron gases, new forms of topology, and new ferroic coupling mechanisms.
Current understanding of higher-order topological insulators (HOTIs) is based primarily on crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals. Specifically, we show ...that two distinct types of second-order topological insulators (SOTIs) can be constructed on the quasicrystalline lattices (QLs) with different tiling patterns. One is derived by using a Wilson mass term to gap out the edge states of the quantum spin Hall insulator on QLs. The other is the quasicrystalline quadrupole insulator (QI) with a quantized quadrupole moment. We reveal some unusual features of the corner states (CSs) in the quasicrystalline SOTIs. We also show that the quasicrystalline QI can be simulated by a designed electrical circuit, where the CSs can be identified by measuring the impedance resonance peak. Our findings not only extend the concept of HOTIs into quasicrystals but also provide a feasible way to detect the topological property of quasicrystals in experiments.
The plane problem of two‐dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of ...stresses and displacements of two‐dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two‐dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.
The plane problem of two‐dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two‐dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two‐dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived.…
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