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.
More than 35 years and 11 000 publications after the discovery of quasicrystals by Dan Shechtman, quite a bit is known about their occurrence, formation, stability, structures and physical ...properties. It has also been discovered that quasiperiodic self‐assembly is not restricted to intermetallics, but can take place in systems on the meso‐ and macroscales. However, there are some blank areas, even in the centre of the big picture. For instance, it has still not been fully clarified whether quasicrystals are just entropy‐stabilized high‐temperature phases or whether they can be thermodynamically stable at 0 K as well. More studies are needed for developing a generally accepted model of quasicrystal growth. The state of the art of quasicrystal research is briefly reviewed and the main as‐yet unanswered questions are addressed, as well as the experimental limitations to finding answers to them. The focus of this discussion is on quasicrystal structure analysis as well as on quasicrystal stability and growth mechanisms.
The state of the art of quasicrystal research is critically reviewed. Fundamental questions that are still unanswered are discussed and experimental limitations are considered.
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.
The artificial stacking of atomically thin crystals suffers from intrinsic limitations in terms of control and reproducibility of the relative orientation of exfoliated flakes. This drawback is ...particularly severe when the properties of the system critically depends on the twist angle, as in the case of the dodecagonal quasicrystal formed by two graphene layers rotated by 30°. Here we show that large-area 30°-rotated bilayer graphene can be grown deterministically by chemical vapor deposition on Cu, eliminating the need of artificial assembly. The quasicrystals are easily transferred to arbitrary substrates and integrated in high-quality hexagonal boron nitride-encapsulated heterostructures, which we process into dual-gated devices exhibiting carrier mobility up to 105 cm2/(V s). From low-temperature magnetotransport, we find that the graphene quasicrystals effectively behave as uncoupled graphene layers, showing 8-fold degenerate quantum Hall states. This result indicates that the Dirac cones replica detected by previous photoemission experiments do not contribute to the electrical transport.
Quasicrystals are long-range ordered and yet nonperiodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher ...dimensions, and the presence of nontrivial structure on all scales. Here, we report on the first experimental demonstration of an eightfold rotationally symmetric optical lattice, realizing a two-dimensional quasicrystalline potential for ultracold atoms. Using matter-wave diffraction we observe the self-similarity of this quasicrystalline structure, in close analogy to the very first discovery of quasicrystals using electron diffraction. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. These measurements pave the way for quantum simulations in fractal structures and higher dimensions.
Topological Corner States in Photonic Quasicrystals
Higher‐order topological quasicrystalline insulators (HOTQIs) in photonic systems are theoretically and experimentally observed by Fei Gao, Jianjun ...Liu, and co‐workers (see article number 2300956). It is found that HOTQIs possess topological corner state (TCS) arrays, with each TCS array containing several TCSs. This work introduces new ideas for investigating highly integrated, multi‐region localized TCSs and is expected to provide novel approaches for exploring topological phenomena and the applications of photonic quasicrystals.
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