Two-dimensional Quasicrystals Research Articles

Self-consistent study of topological superconductivity in two-dimensional quasicrystals

Self-consistent study of topological superconductivity in two-dimensional quasicrystals

Thermoelastic fracture of two-dimensional hexagonal quasicrystal media weakened by a penny-shaped crack subjected to uniformly antisymmetric heat fluxes

This study focuses on the thermoelastic fracture behavior of quasicrystals, a class of solids that exhibit unique properties between traditional crystals and amorphous materials. The complex atomic structure of quasicrystals poses challenges in understanding their fracture mechanisms under thermoelastic loading conditions. Central to our investigation is an analytical examination of a penny-shaped crack in an infinite three-dimensional body composed of two-dimensional hexagonal quasicrystals, where the upper and lower crack surfaces are applied to a pair of uniformly antisymmetric heat fluxes. This crack problem requires simultaneous consideration of thermal-phason-phonon multiple field coupling. According to the symmetry of field variables with respect to the crack plane, the thermal-phason-phonon coupled crack problem is transformed into a mixed boundary value problem in the upper half space. The extended displacement discontinuities, encompassing both phonon and phason displacement discontinuities, as well as the temperature discontinuity, are chosen as the basic unknown variables to construct the boundary integral-differential equations governing the mixed boundary value problem. Based on these boundary governing equations and Fabrikant's potential theory method, the problem with the crack surface subjected to uniform antisymmetric heat fluxes is solved. The solutions of thermal-phason-phonon fields on the crack plane, and in the full space are given in closed-form. Numerical results are employed to validate the obtained analytical solutions and visually illustrate the spatial distribution of thermal-phonon-phason coupling fields in the vicinity of the crack. The study provides fundamental insights into the behavior of cracks in quasicrystals under thermal loading, with potential implications for the design of new materials and structures.

Analytical solutions to Mode I penny-shaped crack problems in two-dimensional hexagonal quasicrystals with piezoelectric effect

The paper studies a penny-shaped crack in an infinite three-dimensional body of two-dimensional hexagonal quasicrystal media with piezoelectric effect. The crack surfaces are applied combined electric and normal phonon loadings. Such a Model I crack problem is transformed into a mixed boundary value problem in the upper half-space, which is analytically solved using Fabrikant's potential theory method. The boundary integral-differential equations governing Model I crack problems are presented for two-dimensional hexagonal piezoelectric quasicrystals. The normal phonon displacement discontinuity and electric potential discontinuity across crack surfaces are taken as the unknown variables of boundary governing equations. Analytical solutions of all field variables are derived not only for the crack plane but also for the full space. Solutions in integral form are provided for the penny-shaped crack under arbitrarily distributed electric and normal phonon loadings. Closed-form solutions in terms of elementary functions are given for concentrated point loadings and uniformly distributed loadings, respectively. Key fracture mechanics parameters, such as crack surface extended displacements (i.e., normal phonon displacement, electric potential), crack tip extended stresses (i.e., normal phonon stress, electric displacement) distribution, and corresponding extended stress intensity factors, are clearly derived. Numerical results are utilized to verify the present analytical solutions and graphically illustrate the distribution of phonon-phason-electric coupling fields around the crack. The present solution can serve as a benchmark for both experimental and numerical investigations.

Hamiltonian System for Three-Dimensional Problem of Two-Dimensional Decagonal Piezoelectric Quasicrystals and Its Symplectic Analytical Solutions

Hamiltonian System for Three-Dimensional Problem of Two-Dimensional Decagonal Piezoelectric Quasicrystals and Its Symplectic Analytical Solutions

Higher-order topological states in acoustic two-dimensional Penrose quasicrystals

Higher-order topological states in acoustic two-dimensional Penrose quasicrystals

Chebyshev polynomial approach to Loschmidt echo: Application to quench dynamics in two-dimensional quasicrystals.

The understanding of quantum phase transitions in disordered or quasicrystal media is a central issue in condensed matter physics. In this paper we investigate localization properties of the two-dimensional Aubry-André model. We find that the system exhibits self-duality for the transformation between position and momentum spaces at a critical quasiperiodic potential, leading to an energy-independent Anderson transition. Most importantly, we present the implementation of an efficient and accurate algorithm based on the Chebyshev polynomial expansion of the Loschmidt echo, which characterizes the nonequilibrium dynamics of quantum quenched quasiperiodic systems. We analytically prove that the system under quench dynamics displays dynamical quantum phase transitions and further provide numerical verification by computing the polynomial expansion of the Loschmidt echo. Our results may provide insight into the realization of electronic transport in experiments.

On the Thermally Induced Interfacial Behavior of Thin Two-Dimensional Hexagonal Quasicrystal Films with an Adhesive Layer

The mechanical response of a quasicrystal thin film is strongly affected by an adhesive layer along the interface. In this paper, a theoretical model is proposed to study a thin two-dimensional hexagonal quasicrystal film attached to a half-plane substrate with an adhesive layer, which undergoes a thermally induced deformation. A perfect non-slipping contact condition is assumed at the interface by adopting the membrane assumption. An analytical solution to the problem is obtained by constructing governing integral–differential equations for both single and multiple films in terms of interfacial shear stresses that are reduced to a linear algebraic system via the series expansion of Chebyshev polynomials. The solution is compared to that without adhesive layers, and the effects of the aspect ratio of films, material mismatch, and the adhesive layer, as well as the interaction between films, are discussed in detail. It is found that the adhesive layer can soften the localized stress concentration. This study is instructive to the accurate safety assessment and functional design of a quasicrystal film system.

Superconductivity in a van der Waals layered quasicrystal

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 Ta1.6Te. 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. This discovery can promote new research on assessing the physical properties of novel van der Waals layered quasicrystals as well as two-dimensional quasicrystals; moreover, it paves the way toward new frontiers of superconductivity in thermodynamically stable quasicrystals.

Hybrid Skin-Topological Effect Induced by Eight-Site Cells and Arbitrary Adjustment of the Localization of Topological Edge States

Hybrid skin-topological effect (HSTE) in non-Hermitian systems exhibits both the skin effect and topological protection, offering a novel mechanism for localization of topological edge states (TESs) in electrons, circuits, and photons. However, it remains unclear whether the HSTE can be realized in quasicrystals, and the unique structure of quasicrystals with multi-site cells may provide novel localization phenomena for TESs induced by the HSTE. We propose an eight-site cell in two-dimensional quasicrystals and realize the HSTE with eight-site nonreciprocal intracell hoppings. Furthermore, we can arbitrarily adjust the eigenfield distributions of the TESs and discover domain walls associated with effective dissipation and their correlation with localization. We present a new scheme to precisely adjust the energy distribution in non-Hermitian quasicrystals with arbitrary polygonal outer boundaries.

Critical states and anomalous mobility edges in two-dimensional diagonal quasicrystals

We study the single-particle properties of two-dimensional quasicrystals where the underlying geometry of the tight-binding lattice is crystalline but the on-site potential is quasicrystalline. We will focus on the two-dimensional (2D) generalized Aubry-André model which has a varying form to its quasiperiodic potential, through a deformation parameter and varied irrational periods of cosine terms, which allows a continuous family of on-site quasicrystalline models to be studied. We show that the 2D generalized Aubry-André model exhibits many single-particle mobility edges which we confirm for finite systems and supports critical states across large parameter regions. Critical states are neither fully localized nor extended. We observe that diagonal quasicrystalline models can support many energy intervals of critical states in the spectrum while stabilizing both localized and extended states in other energy intervals; we refer to these as anomalous mobility edges. We show that critical states are present independent of system size through a scaling analysis of the inverse participation ratio and that they are present in spectra that also contain extended and localized states, confirming that at least one anomalous mobility edge is present. Due to this, these models exhibit anomalous diffusion of initially localized states across the majority of parameter regions, including deep in the normally localized regime. The presence of critical states in large parameter regimes and throughout the spectrum will have consequences for the many-body properties of quasicrystals, including the formation of the Bose glass and the potential to host a many-body localized phase. Published by the American Physical Society 2024

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Mode-I Plane Elasticity Problem of Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole in Two-Dimensional Decagonal Quasicrystals

We consider the plane elasticity problem of two asymmetrical edge cracks emanating from an elliptical hole in two-dimensional decagonal quasicrystals (QCs) under remotely uniform tensile stress. A complex variation method of two-dimensional QCs is developed to solve the plane elasticity problem of two-dimensional decagonal QCs containing complex defects. The analytical solutions for the stress field and the stress intensity factors near the crack tip are expressed by using a conformal mapping technique and complex potential theory. Some special cases of the results are also obtained, such as the T-type crack, cross crack, and Griffith crack. The effects of geometrical parameters of crack configuration on the stress intensity factors are presented graphically.

Molecular dynamics simulations for quasicrystals under the Born-Gauss potentials

Molecular dynamics simulations are a tool for the study of the microscopic dynamics in quasicrystals. By choosing suitable potentials, such as the Dzugutov potential and the Lennard-Jones-Gauss potential, two-dimensional quasicrystals with 8-, 10- and 12-fold symmetries have been formed. In this work, we propose a Born-Gauss type potential with more adjusting parameters to do simulations in two dimensions. Decagonal and dodecagonal quasicrystals are successfully obtained. The structural properties are analyzed and the phase transitions between different structures are discussed.

A Phase Field Approach to Two-Dimensional Quasicrystals with Mixed Mode Cracks.

Quasicrystals (QCs) are representatives of a novel kind of material exhibiting a large number of remarkable specific properties. However, QCs are usually brittle, and crack propagation inevitably occurs in such materials. Therefore, it is of great significance to study the crack growth behaviors in QCs. In this work, the crack propagation of two-dimensional (2D) decagonal QCs is investigated by a fracture phase field method. In this method, a phase field variable is introduced to evaluate the damage of QCs near the crack. Thus, the crack topology is described by the phase field variable and its gradient. In this manner, it is unnecessary to track the crack tip, and therefore remeshing is avoided during the crack propagation. In the numerical examples, the crack propagation paths of 2D QCs are simulated by the proposed method, and the effects of the phason field on the crack growth behaviors of QCs are studied in detail. Furthermore, the interaction of the double cracks in QCs is also discussed.

Hubbard models for quasicrystalline potentials

Quasicrystals are long-range ordered, yet not periodic, and thereby present a fascinating challenge for condensed matter physics, as one cannot resort to the usual toolbox based on Bloch's theorem. Here, we present a numerical method for constructing the Hubbard Hamiltonian of nonperiodic potentials without making use of Bloch's theorem and apply it to the case of an eightfold rotationally symmetric two-dimensional optical quasicrystal that was recently realized using cold atoms. We construct maximally localized Wannier functions and use them to extract onsite energies, tunneling amplitudes, and interaction energies. In addition, we introduce a configuration-space representation, where sites are ordered in terms of shape and local environment, that leads to a compact description of the infinite-size quasicrystal in which all Hamiltonian parameters can be expressed as smooth functions. The configuration-space picture serves as an aperiodic analog of the Brillouin zone, and allows one to efficiently describe the quasicrystal in the thermodynamic limit, enabling new analytic arguments on the topological structure and many-body physics of these models. For instance, we use it to conclude that this quasicrystal will host unit-filling Mott insulators in the thermodynamic limit.

Utilization of two-dimensional multicomponent Quasicrystal for NO2 gas detection

The two-dimensional (2D) materials provide an effective ultra-sensitive response for sensing due to the large surface area available for the analyte. Al70Co10Fe5Ni10Cu5 (Quasicrystal-QC) alloy can be effectively exfoliated into a 2D form consisting of the decagonal quasicrystalline phase. The ultrathin thickness of a few nm (∼6 nm) was achieved, exhibiting anisotropic electron-transport properties. The 2D-QC shows pseudo-conducting behavior in the planar region, which endowed the material in nanosheets to work as ultrasensitive NO2 gas sensors (1–100 ppm) at 100 °C. The fabricated device exhibits a NO2 gas response (ΔR/Ra %) of 46% compared to its bulk counterpart. In addition, the mechanism of gas sensing was further corroborated using density functional theory (DFT) simulations and strongly support the interpretation of the experimental data.

Higher-Order Topological States in Photonic Thue-Morse Quasicrystals: Quadrupole Insulator and the Origin of Corner States

Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here, we systemically study the higher-order topology in the two-dimensional Thue-Morse photonic quasicrystals (TM PQCs). Not only the topological phase transition and the nontrivial CSs with fractional charge induced by multipole moments, but also another type of CSs are found due to the complex structure of TM PQCs near corners. The different origins of these CSs are also analyzed based on the tight-binding model. Our work opens the door to explore richer HOT physics beyond photonic crystals and the robustness of CSs in PQC shows the potential for applications.

Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing

The concrete realization of topological quantum computing using low-dimensional quasiparticles, known as anyons, remains one of the important challenges of quantum computing. A topological quantum computing platform promises to deliver more robust qubits with additional hardware-level protection against errors that could lead to the desired large-scale quantum computation. We propose quasicrystal materials as such a natural platform and show that they exhibit anyonic behavior that can be used for topological quantum computing. Different from anyons, quasicrystals are already implemented in laboratories. In particular, we study the correspondence between the fusion Hilbert spaces of the simplest non-abelian anyon, the Fibonacci anyons, and the tiling spaces of the one-dimensional Fibonacci chain and the two-dimensional Penrose tiling quasicrystals. A concrete encoding on these tiling spaces of topological quantum information processing is also presented by making use of inflation and deflation of such tiling spaces. While we outline the theoretical basis for such a platform, details on the physical implementation remain open.

Spin-wave localization on phasonic defects in a one-dimensional magnonic quasicrystal

We report on the evolution of the spin-wave spectrum under structural disorder introduced intentionally into a one-dimensional magnonic quasicrystal. We study theoretically a system composed of ferromagnetic strips arranged in a Fibonacci sequence. We considered several stages of disorder in the form of phasonic defects, where different rearrangements of strips are introduced. By transition from the quasiperiodic order towards disorder, we show a gradual degradation of spin-wave fractal spectra and closing of the frequency gaps. In particular, the phasonic defects lead to the disappearance of the van Hove singularities at the frequency gap edges by moving modes into the frequency gaps and creating new modes inside the frequency gaps. These modes disperse and eventually can close the gap, with increasing disorder levels. The work reveals how the presence of disorder modifies the intrinsic spin-wave localization existing in undefected magnonic quasicrystals. The paper contributes to the knowledge of magnonic Fibonacci quasicrystals and opens the way to study of the phasonic defects in two-dimensional magnonic quasicrystals.

Intrinsic vortex pinning in superconducting quasicrystals

We numerically show that a vortex pinning occurs in superconducting quasicrystal without impurities and defects. This vortex pinning is intrinsic since the superconducting order parameter in quasicrystal is always inhomogeneous due to the lack of the translational symmetry. We propose that experiments influenced by vortex pinning effects can detect the atomic-scale inhomogeneous superconducting order parameter in quasicrystals. We develop a numerical method to solve the Bogoliubov-de Gennes equations and gap equations in large systems, which is based on the localized-Krylov subspace and a sparse modeling technique. Two two-dimensional quasicrystals, the Penrose and Amman-Beenker tiling, are considered.