quasicrystals

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations...

Industrial emissions, environmental monitoring, and medical fields have put forward huge demands for high-performance and low power consumption sensors. Two-dimensional quasicrystal (2D QC) nanosheets of metallic multicomponent Al70 Co10 Fe5 Ni10 Cu5 have emerged as a promising material for gas sensors due to their excellent catalytic and electronic properties. Herein, we demonstrate highly sensitive and selective NO2 sensors developed by low-cost and scalable fabrication techniques using 2D QC nanosheets and α-Fe2 O3 nanoparticles...

Quasicrystals and their periodic approximants are complex crystalline phases. They have now been observed in many metallic alloys, soft matter systems, and particle simulations. In recent experiments of thin-film perovskites on solid substrates, the type of complex phase was found to change depending on thermodynamic conditions and the type of substrate used. Here, we investigate the effect of a substrate on the relative thermodynamic stability of a two-dimensional model quasicrystal and its approximants. Our simulation model is particles interacting via the Lennard-Jones-Gauss potential...

The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including sixfold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette (ϕ) is half of the flux quantum, zero modes are found localized around the reflected "anti-hats"; and (v) its Hofstadter spectrum is periodic in ϕ, unlike for other quasicrystals...

The binary Cd5.7 Yb phase representing the Tsai-type category of the icosahedral quasicrystals is solved by the assignment of a unique atomic decoration to rhombohedral units in the Ammann-Kramer-Neri tiling. The unique decoration is found for units with an edge length of 24.1 Å and 3m internal point symmetry. The structural refinement was carried out for two underlying tilings generated by the projection method for 6D space. The difference lies in the location of the origin point which for one tiling is in the vertex and for the second one in the center of the 6D unit cell...

Van der Waals layered transition-metal chalcogenides are drawing significant attention owing to their intriguing physical properties. This group of materials consists of abundant members with various elements, having a variety of different structures. However, they are all crystalline materials, and the physical properties of van der Waals layered quasicrystals have never been studied to date. Here, we report on the discovery of superconductivity in a van der Waals layered quasicrystal of Ta1.6 Te. The electrical resistivity, magnetic susceptibility, and specific heat of the quasicrystal unambiguously validate the occurrence of bulk superconductivity at a transition temperature of ~1 K...

The effect of Eu doping in the Tsai quasicrystal (QC) GdCd7.88 and its periodic 1/1 approximant crystal (AC) GdCd6 are investigated. This represents the first synthesis of Eu-containing stable QC samples, where three samples with the final composition Gd1- x Eu x Cd7.6±α at Eu doping concentrations x = 0.06, 0.13, and 0.19 are obtained (α ∼ 0.2). They are compared to two 1/1 ACs with compositions Gd1- x Eu x Cd6 ( x = 0.12, 0.16). In addition, a new type of 1/1 AC, differing only by the inclusion of extra Cd sites unique to the Eu4 Cd25 1/1 AC, has been discovered and synthesized for the concentrations Gd1- x Eu x Cd6+δ ( x = 0...

Anderson localization, i.e., the suppression of diffusion in lattices with a random or incommensurate disorder, is a fragile interference phenomenon that is spoiled out in the presence of dephasing effects or a fluctuating disorder. As a consequence, Anderson localization-delocalization phase transitions observed in Hermitian systems, such as in one-dimensional quasicrystals when the amplitude of the incommensurate potential is increased above a threshold, are washed out when dephasing effects are included...

Because of their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be realized as an exponentially large number of different tilings, resulting in a significant contribution to the quasicrystal entropy. Here, we use free-energy calculations to demonstrate that it is this configurational entropy which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres on a plane...

Soft building blocks, such as micelles, cells or soap bubbles, tend to adopt near-spherical geometry when densely packed together. As a result, their packing structures do not extend beyond those discovered in metallic glasses, quasicrystals and crystals. Here we report the emergence of two Frank-Kasper phases from the self-assembly of five-fold symmetric molecular pentagons. The μ phase, an important intermediate in superalloys, is indexed in soft matter, whereas the ϕ phase exhibits a structure distinct from known Frank-Kasper phases in metallic systems...

Moiré superlattices based on van der Waals bilayers1-4 created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θt ), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θt  = 30° and the commensurate moiré crystals at θt  = 21...

This Perspective is dedicated to the 25th Anniversary of Biomacromolecules . It provides a personal view on the developing field of the polymer and biology interface over the 25 years since the journal was launched by the American Chemical Society (ACS). This Perspective is meant to bridge an article published in the first issue of the journal and recent bioinspired developments in the laboratory of the corresponding author. The discovery of supramolecular spherical helices self-organizing into Frank-Kasper and quasicrystals as models of icosahedral viruses, as well as of columnar helical assemblies that mimic rodlike viruses by supramolecular dendrimers, is briefly presented...

The material realization of charge-4e/6e superconductivity (SC) is a big challenge. Here, we propose to realize charge-4e SC in maximally-twisted homobilayers, such as 45∘ -twisted bilayer cuprates and 30∘ -twisted bilayer graphene, referred to as twist-bilayer quasicrystals (TB-QC). When each monolayer hosts a pairing state with the largest pairing angular momentum, previous studies have found that the second-order interlayer Josephson coupling would drive chiral topological SC (TSC) in the TB-QC...

Non-Hermitian (NH) quasicrystals have been a topic of increasing interest in current research, particularly in the context of NH topological physics and materials science. Recently, it has been suggested and experimentally demonstrated using synthetic photonic lattices that a class of NH quasicrystals can feature topological spectral phase transitions. Here we consider a NH quasicrystal with a uniformly-drifting (sliding) incommensurate potential and show that, owing to violation of Galilean invariance, the topological phase transition is washed out and the quasicrystal is always in the delocalized phase with an entirely real-energy spectrum...

Quasiperiodic patterns and crystals - having long range order without translational symmetry - fascinate researchers since their discovery. In this study, we report on new p-terphenyl based T-shaped facial polyphiles with two alkyl end-chains and a glycerol-based hydrogen-bonded side-group, self-assembling into an aperiodic columnar liquid quasicrystal with 12-fold symmetry and its periodic liquid-crystalline approximants with complex superstructures. All represent honeycombs formed by self-assembly of the p-terphenyls, dividing space into prismatic cells with polygonal cross-sections...

The flat band system is an ideal quantum platform to investigate the kaleidoscope created by the electron-electron correlation effects. The central ingredient of realizing a flat band is to find its compact localized states. In this work, we develop a systematic way to generate compact localized states by designing destructive interference patterns from 1-dimensional chains. A variety of 2-dimensional new flat band systems are constructed with this method. Furthermore, we show that the method can be extended to generate the compact localized states in multi-orbital systems by carefully designing the block hopping scheme, as well as in quasicrystal and disorder systems...

Since the discovery of the quasicrystal, approximately 100 stable quasicrystals are identified. To date, the existence of quasicrystals is verified using transmission electron microscopy; however, this technique requires significantly more elaboration than rapid and automatic powder X-ray diffraction. Therefore, to facilitate the search for novel quasicrystals, developing a rapid technique for phase-identification from powder diffraction patterns is desirable. This paper reports the identification of a new Al-Si-Ru quasicrystal using deep learning technologies from multiphase powder patterns, from which it is difficult to discriminate the presence of quasicrystalline phases even for well-trained human experts...

In principle, designing and synthesizing almost any class of colloidal crystal is possible. Nonetheless, the deliberate and rational formation of colloidal quasicrystals has been difficult to achieve. Here we describe the assembly of colloidal quasicrystals by exploiting the geometry of nanoscale decahedra and the programmable bonding characteristics of DNA immobilized on their facets. This process is enthalpy-driven, works over a range of particle sizes and DNA lengths, and is made possible by the energetic preference of the system to maximize DNA duplex formation and favour facet alignment, generating local five- and six-coordinated motifs...

The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matter due to its exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties...

The near-field thermal radiation has broad application prospects in micro-nano-scale thermal management technology. In this paper, we report the Dirac semimetal-assisted (AlCuFe quasicrystal) near-field radiative thermal rectifier (DSTR) and thermostat (DST), respectively. The DSTR is made of a Dirac semimetal-covered vanadium dioxide (VO2 ) plate and silicon dioxide (SiO2 ) plate separated by a vacuum gap. The left and right sides of DST are consisted of the SiO2 covered with Dirac semimetal, and the intermediate plate is the VO2 ...