Quasicrystalline Lattice Research Articles

Modulational instability of a Yukawa fluid excitation under the Quasi-localized charged approximation (QLCA) framework

Collective response of a strongly coupled system departs from that in continuum phase upon transition to the quasi-crystalline phase, or a Wigner lattice. The nonlinearity driven modulational instability, for example, of a quasi-crystalline dusty plasma lattice wave, is predicted to inevitably grow macroscopic envelope structures at the expense of a mesoscopic carrier wave. The modulational instability in the dimensionally extended quasi-crystalline or amorphous phase of a strongly coupled system, uniquely accessed by the quasi-localized charge approximation (QLCA) formulation, is shown to offer conditional stability over the entire range of spectral scales by prescribing a narrower instability regime. In distinction from the excitations of linear one-dimensional chain of strongly coupled dust grains, the longitudinal modes of a quasi-crystalline phase incorporated by means of a pair correlation function in the present QLCA based treatment shows the lattice excitations to be stable for arbitrarily long wavelengths beyond a finite value of screening parameter κ = a/λ D = 0.182 at low enough temperature, where a is the inter dust separation and λ D is the plasma Debye length. However, this unstable domain of the parameter space does grow with increase in the dust temperature which invokes the weak coupling-like effect. The present results show that in comparison to the one-dimensional chains, the dimensionally extended strongly coupled lattice are potentially stable with respect to the macroscopic amplitude modulations. Results offer a greater handle over the macroscopic structures growing from the mesoscopic fluctuations, a mechanism which underlies a variety of processes, ranging from the barrier formation in strongly coupled turbulence to the highly localized modification, induced by collective excitation, of the ultracold ions trapped in strong electromagnetic fields. The existence of the growth rate of instability as well as the maximum modulational growth rate of instability has been investigated for a wide range of values of the screening parameter.

Cardiac Sarcomere Signaling in Health and Disease.

The cardiac sarcomere is a triumph of biological evolution wherein myriad contractile and regulatory proteins assemble into a quasi-crystalline lattice to serve as the central point upon which cardiac muscle contraction occurs. This review focuses on the many signaling components and mechanisms of regulation that impact cardiac sarcomere function. We highlight the roles of the thick and thin filament, both as necessary structural and regulatory building blocks of the sarcomere as well as targets of functionally impactful modifications. Currently, a new focus emerging in the field is inter-myofilament signaling, and we discuss here the important mediators of this mechanism, including myosin-binding protein C and titin. As the understanding of sarcomere signaling advances, so do the methods with which it is studied. This is reviewed here through discussion of recent live muscle systems in which the sarcomere can be studied under intact, physiologically relevant conditions.

Bulk localized transport states in infinite and finite quasicrystals via magnetic aperiodicity

Topological edge states can form when a charged particle confined to a crystalline lattice interacts with a magnetic field. These edge states are localized to the boundary and can support transport along the edge even with an insulating bulk. Here, the authors show that a different state that supports transport in the bulk can emerge when the charged particle is on a quasicrystalline lattice. Utilizing a recently developed spectral computation technique, they show that these new bulk localized transport (BLT) states survive in the infinite-size limit.

Interlaced wire medium with quasicrystal lattice

We propose a design of an interlaced wire medium with a quasicrystalline lattice based on fivefold rotation symmetry Penrose tiling. The transport properties of this structure are studied. We distinguish two transport regimes, namely, a propagation regime related to the low-frequency interval and localization regime in the high-frequency interval. While the former is observed in structures both with and without the translation symmetry property, the latter is exclusive for aperiodic structures only. We show that the localization regime is promising for many applications, including the engineering of effective multichannel devices for telecommunication and imaging systems.

Higher-order topological Anderson insulators in quasicrystals

The disorder effects on higher-order topological phases in periodic systems have attracted much attention. However, in aperiodic systems, such as quasicrystalline systems, the interplay between disorder and higher-order topology is still unclear. In this paper, we investigate the effects of disorder on two types of second-order topological insulators, including a quasicrystalline quadrupole insulator and a modified quantum spin Hall insulator, in a two-dimensional Amman-Beenker tiling quasicrystalline lattice. We demonstrate that the higher-order topological insulators are robust against weak disorder in both models. More striking, the disorder-induced higher-order topological insulators called higher-order topological Anderson insulators are found at a certain region of disorder strength in both models. Our paper extends the study of the interplay between disorder and higher-order topology to quasicrystalline systems.

Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal

Recent research on disorder effects in topological phases in quasicrystalline systems has received much attention. In this work, by numerically computing the (spin) Bott index and the thermal conductance, we reveal the effects of disorder on a class D chiral topological superconductor and a class DIII time-reversal-invariant topological superconductor in a two-dimensional Ammann-Beenker tiling quasicrystalline lattice. We demonstrate that both the topologically protected chiral and helical Majorana edge modes are robust against weak disorder in the quasicrystalline lattice. More fascinating is the discovery of disorder-induced topologically nontrivial phases exhibiting chiral and helical Majorana edge modes in class D and DIII topological superconductor systems, respectively. Our findings open the door for the research on disorder-induced Majorana edge modes in quasicrystalline systems.

The mean-field Bose glass in quasicrystalline systems

We confirm the presence of a mean-field Bose glass (BG) in 2D quasicrystalline Bose–Hubbard models. We focus on two models where the aperiodic component is present in different parts of the problem. First, we consider a 2D generalisation of the Aubry–André (AA) model, where the lattice geometry is that of a square with a quasiperiodic onsite potential. Second, we consider the randomly disordered vertex model, which takes aperiodic tilings with non-crystalline rotational symmetries, and forms lattices from the vertices and lengths of the tiles. For the disordered vertex models, the mean-field BG forms across large ranges of the chemical potential, and we observe no significant differences from the case of a square lattice with uniform random disorder. Small variations in the critical points in the presence of random disorder between quasicrystalline and crystalline lattice geometries can be accounted for by the varying coordination number and the different rotational symmetries present. In the 2D AA model, substantial differences are observed from the usual phase diagrams of crystalline disordered systems. We show that weak modulation lines can be predicted from the underlying potential and may stabilise or suppress the mean-field BG in certain regimes. This results in a lobe-like structure for the mean-field BG in the 2D AA model, which is significantly different from the case of random disorder. Together, the two quasicrystalline models studied in this work show that the mean-field BG phase is present, as expected for 2D quasiperiodic models. However, a quasicrystalline geometry is not sufficient to result in differences from crystalline realisations of the BG, whereas a quasiperiodic form of disorder can result in different physics, as we observe in the 2D AA model.

Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal

The quest for the topological phases of matter in an aperiodic system has been greatly developed recently. Here we investigate the effects of disorder on topological phases of a two-dimensional Ammann-Beenker tiling quasicrystalline lattice. For comparison purposes, we also consider the case of a periodic snub-square crystalline lattice, which has the same primitive tiles as the Ammann-Beenker tiling quasicrystalline lattice. By calculating the spin Bott index and the two-terminal conductance, we confirm that the topological phases with disorder share the similar properties in the two systems which possess different symmetry and periodicity. It is shown that the quantum spin Hall states are robust against weak disorder in both the quasicrystalline lattice and the crystalline lattice. More interesting is that topological Anderson insulator phases induced by disorder appear in the two systems. Furthermore, the quantized conductance plateau contributed by the topological Anderson insulator phase is verified by the distribution of local currents.

Dynamics of rotating spin–orbit-coupled Bose–Einstein condensates in a quasicrystalline optical lattice

We investigate the dynamics of rotating pseudo-spin-1/2 Bose–Einstein condensates (BECs) with Rashba spin–orbit coupling (SOC) in a quasicrystalline optical lattice (QOL). For given parameters, the system evolves from an initial heliciform-stripe phase into a final visible vortex necklace with a giant vortex and a hidden vortex necklace. Simultaneously, the corresponding spin texture undergoes a transition from a meron–antimeron pair to a half-antiskyrmion necklace. During the dynamic evolution process, the angular momentum increases gradually, and then approaches to a convergent value. Furthermore, typical quantum phases of rotating two-component BECs with SOC in different external potentials are summarized.

Critical fluid density obtained from the theory of generalized charges in accordance with the hypothesis on the first coordination number

In this article, a model of hard spheres for critical fluid, based on the hypothesis on the coordination number of molecules in minimally bound infinite clusters, is considered. Variants of homogeneous (quasi-crystalline lattice) and heterogeneous (“Cayley tree forest”) molecular packings at the vertices of a uniform graph of order 3 are described. Using the theory of generalized charges and taking into account the found structures, the dependences of the critical molar volume on electronic structure parameters, which have the character of non-empirical laws, are derived. A priori calculations of molar volumes by the critical state model are in good agreement with the reference data for simple gases and linear hydrocarbons.

Emergent Periodic and Quasiperiodic Lattices on Surfaces of Synthetic Hall Tori and Synthetic Hall Cylinders.

Synthetic spaces allow physicists to bypass constraints imposed by certain physical laws in experiments. Here, we show that a synthetic torus, which consists of a ring trap in the real space and internal states of ultracold atoms cyclically coupled by Laguerre-Gaussian Raman beams, could be threaded by a net effective magnetic flux through its surface-an impossible mission in the real space. Such a synthetic Hall torus gives rise to a periodic lattice in real dimensions, in which the periodicity of the density modulation of atoms fractionalizes that of the Hamiltonian. Correspondingly, the energy spectrum is featured by multiple bands grouping into clusters with nonsymmorphic-symmetry-protected band crossings in each cluster, leading to swaps of wave packets in Bloch oscillations. Our scheme allows physicists to glue two synthetic Hall tori such that localization may emerge in a quasicrystalline lattice. If the Laguerre-Gaussian Raman beams and ring traps were replaced by linear Raman beams and ordinary traps, a synthetic Hall cylinder could be realized and deliver many of the aforementioned phenomena.

Phasonic Spectroscopy of a Quantum Gas in a Quasicrystalline Lattice.

Phasonic degrees of freedom are unique to quasiperiodic structures and play a central role in poorly understood properties of quasicrystals from excitation spectra to wave function statistics to electronic transport. However, phasons are challenging to access dynamically in the solid state due to their complex long-range character and the effects of disorder and strain. We report phasonic spectroscopy of a quantum gas in a one-dimensional quasicrystalline optical lattice. We observe that strong phasonic driving produces a nonperturbative high-harmonic plateau strikingly different from the effects of standard dipolar driving. Tuning the potential from crystalline to quasicrystalline, we identify spectroscopic signatures of quasiperiodicity and interactions and map the emergence of a multifractal energy spectrum, opening a path to direct imaging of the Hofstadter butterfly.

Bulk spectrum and K-theory for infinite-area topological quasicrystals

The bulk spectrum of a possible Chern insulator on a quasicrystalline lattice is examined. The effect of being a 2D insulator seems to override any fractal properties in the spectrum. We compute that the spectrum is either two continuous bands, or that any gaps other than the main gap are small. After making estimates on the spectrum, we deduce a finite system size, above which the K-theory must coincide with the K-theory of the infinite system. Knowledge of the spectrum and K-theory of the infinite-area system will control the spectrum and K-theory of sufficiently large finite systems. The relation between finite volume K-theory and infinite volume Chern numbers is only proven to begin, for the model under investigation here, for systems on Hilbert space of dimension around 17 × 106. The real-space method based on the Clifford spectrum allows for computing Chern numbers for systems on Hilbert space of dimension around 2.7 × 106. New techniques in numerical K-theory are used to equate the K-theory of systems of different sizes.

The order-disorder evolution in quasicrystals through phason flips

Abstract The problem of incorporating phason flips in the structural investigation of aperiodic systems is still an open question and a challenge in crystallography. Phasons are understood both as atomic fluctuation and positional disorder of the quasicrystalline lattice. Popular correction to diffraction peaks' intensities takes the form of generalized Debye-Waller factor, assuming Gaussian distribution of fluctuations in the perpendicular space of higher-dimensional periodic lattice. Although proven to work in case of random tiling types of structures recent evidence indicates improper handling of peaks with high perpendicular space scattering vector whenever structure is far from random tiling regime. We introduce the concept of a series expansion of the characteristic function of the statistical distribution to properly correct the peaks' intensities with respect to phasonic fluctuations. Calculations are performed upon Penrose tiling. Such approximation of the structure factor works correctly even in cases for which the Debye-Waller correction fails. Even more we investigate transition to random tiling through phason flips by means of the statistical approach which results in interesting scaling properties (ordered → disordered → random → amorphous structure).

Broadband multiple responses of surface modes in quasicrystalline plasmonic structure.

We numerically study the multiple excitation of surface modes in 2D photonic quasicrystal/metal/substrate structure. An improved rigorous coupled wave analysis method that can handle the quasicrystalline structure is presented. The quasicrystalline lattice, which refers to Penrose tiling in this paper, is generated by the cut-and-project method. The normal incidence spectrum presents a broadband multiple responses property. We find that the phase matching condition determines the excitation frequency for a given incident angle, while the depth of the reflection valley depends on the incident polarization. The modes will split into several sub-modes at oblique incidence, which give rise to the appearance of more responses on the spectrum.

Quasicrystalline-structured light harvesting nanophotonic silicon films on nanoimprinted glass for ultra-thin photovoltaics

We present nanophotonic light harvesting crystalline silicon (c-Si) thin films on glass exhibiting ten-fold transversely quasicrystalline lattice geometry on 6 x 8 mm2 area. The c-Si architectures with a nearest neighbor distance of 650 nm are fabricated by nanoimprinting the desired quasicrystalline geometry into sol-gel coated glass substrates followed by Si deposition of 240 nm to 270 nm thickness, self-organized solid phase crystallization and selective chemical etching. Broadband absorption measurements on these quasicrystalline-structured c-Si architectures yield a very significant improvement in light trapping in the near infrared regime and an enhanced light coupling due to a graded index effect in comparison to the unstructured sample. The average value of maximum achievable short circuit current density jsc, max of solar cells with such quasicrystalline-structured c-Si absorber geometry (19.3 mA/cm2) is more than double in comparison to the jsc, max of unstructured planar films of the same thickness (9.3 mA/cm2) and remains stable for light incident angles up to 60°. In comparison to a 320 nm thick c-Si film on textured ZnO:Al substrate as widely used for light trapping in amorphous-microcrystalline Si thin-film photovoltaics, still a 65% increased jsc, max is observable for the presented quasicrystalline c-Si structures. The nanophotonic light trapping efficiency of these transversely quasicrystalline c-Si nanoarchitectures is among the highest values for experimentally realized structures, revealing their promising influence for broadband and isotropic light trapping for economically viable and efficient ultra-thin solar cells.

Templated Quasicrystalline Molecular Ordering

Quasicrystals are materials with long-range ordering but no periodicity. We report scanning tunneling microscopy (STM) observations of quasicrystalline molecular layers on 5-fold quasicrystal surfaces. The molecules adopt positions and orientations on the surface consistent with the quasicrystalline ordering of the substrate. Carbon-60 adsorbs atop sufficiently separated Fe atoms on icosahedral Al-Cu-Fe to form a unique quasicrystalline lattice, whereas further C60 molecules decorate remaining surface Fe atoms in a quasi-degenerate fashion. Pentacene (Pn) adsorbs at 10-fold symmetric points around surface-bisected rhombic triacontahedral clusters in icosahedral Ag-In-Yb. These systems constitute the first demonstrations of quasicrystalline molecular ordering on a template.

Optical induction of 3D rotational symmetry refractive lattices by combined interferometric-mask method in doped LiNbO3 crystals

A novel combined interferometric–mask method for the formation of micro- and nanometric scale three-dimensional (3D) rotational symmetry quasi-crystalline refractive lattice structures in photorefractive materials is demonstrated experimentally. The method is based on micrometric scale spatial modulation of the light by amplitude mask in the radial directions and along the azimuthal angle and the use of counter-propagating beam geometry building up Gaussian standing wave, which defines the light modulation in the axial direction with half-wavelength periodicity. 3D intensity pattern can be represented as numerous mask-generated 2D quasi-periodic structures located in each anti-node of the standing wave. The formed 3D intensity distributions of the optical beams can be imparted into the photorefractive medium thus creating the micro- and sub-micrometric scale 3D refractive index volume lattices. The used optical scheme allows also the formation of 2D lattices by removing the back-reflecting mirror. 2D and 3D refractive lattices were recorded with the use of 532 nm laser beam and rotational symmetry mask in doped lithium niobate crystals and were tested by the probe beam far-field diffraction pattern imaging and direct observation by phase microscope. The formed rotational symmetry 3D refractive structures have the periods of 20–60 μm in the radial directions, 60 μm along the azimuthal angle and half-wavelength 266 nm in the axial direction.

Wood anomalies in resonant photonic quasicrystals

A theory of light diffraction from a planar quasicrystalline lattice with resonant scatterers is presented. Rich structure, absent in the periodic case, is found in specular reflection spectra, and interpreted as a specific kind of Wood anomaly, characteristic of quasicrystals. The theory is applied to semiconductor quantum dots arranged in Penrose tiling.

Nanocrystalline magnesium oxide stabilized gold nanoparticles: an advanced nanotechnology based recyclable heterogeneous catalyst platform for the one-pot synthesis of propargylamines

A simple and elegant synthesis of gold nanoparticlesvia counter ion stabilization of AuCl4− on nanocrystalline magnesium oxide support followed by sodium borohydride reduction is described here. A thorough characterization of the resulting heterogeneous material revealed the presence of uniformly distributed gold nanoparticles (10–12 nm) deposited on to (111) plane of quasi-crystalline icosahedral lattice of nanocrystalline magnesium oxide which exhibits excellent catalytic activity for the one pot synthesis of structurally divergent propargylamines via a three component coupling of an alkyne, an amine and an aldehyde without requiring any additives or inert atmosphere. The catalyst contains ultra low loading of gold (0.236 mol%), and turnover numbers as high as 400 are obtained. The catalyst can be isolated by simple centrifugation and reused for four cycles.