Topological states in quasicrystals

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.     

Optics design of a top-cut prism interferometer for holographic photonic quasicrystals

Optical interference holography has been proved to be a useful technique in fabricating periodic photonic crystals in which electromagnetic waves are forbidden in certain frequency band-gaps. Compared to periodic crystals, quasicrystals have higher point group symmetry and are more favorable in achieving complete band-gaps. In this report, a top-cut prism interferometer is designed and optimized for photonic quasicrystals. By changing the prism parameters and characteristics of different beams, different quasicrystalline structures can be obtained. At the same time, the diffraction patterns of the designed structures are also provided and reveal the ten-fold symmetry of the structures more clearly. Furthermore, the effect of the intensity threshold on the quasicrystalline structures is also investigated. This will provide guidance for the large-area and fast production of ten-fold quasicrystalline structures with high quality.     

Lithium Storage Property of Graphite/AlCuFe Quasicrystal Composites

Quasicrystals have long-range quasi-periodic translational ordering and non-crystallographic rotational symmetry.Al-Cu-Fe quasicrystals have great potential for lithium storage because of their high Al content and a large number of defects in the structure.In our previous study(J.Alloys Compd.805(2019)942)we showed that Al-Cu-Fe quasicrystals have good initial capacity whereas its cycle stability is poor.In the present study,graphite/AlCuFe is prepared by the mechanical alloying method.The results show that graphite/AlCuFe quasicrystal composites are successfully synthesized by planetary ball milling at 550 rpm for 80 h.The quasicrystal particle size decreases and the amorphous graphite forms onion-like carbon(OLC)when the two phases mix evenly.OLC forms on the surface of the Al-Cu-Fe quasicrystalline powder.Charge and discharge tests show that graphite/AlCuFe quasicrystal composites have high-stability capacity of 480 mAh/g after 20 cycles,which is larger than the sum of capacities of graphite and Al-Cu-Fe quasicrystals.     

Emergent rotational symmetries in disordered magnetic domain patterns

Uniaxial systems often form labyrinthine domains that exhibit short-range order but are macroscopically isotropic and would not be expected to exhibit precise symmetries. However, their underlying frustration results in a multitude of metastable configurations of comparable energy, and driving such a system externally might lead to pattern formation. We find that soft x-ray speckle diffraction patterns of the labyrinthine domains in CoPd/IrMn heterostructures reveal a diverse array of hidden rotational symmetries about the magnetization axis, thereby suggesting an unusual form of emergent order in an otherwise disordered system. These symmetries depend on applied magnetic field, magnetization history, and scattering wave vector. Maps of rotational symmetry exhibit intriguing structures that can be controlled by manipulating the applied magnetic field in concert with the exchange bias condition.     

Elastic theory of icosahedral quasicrystals - application to straight dislocations

In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three- and fivefold straight screw- and edge-dislocations in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three- and fivefold symmetry of the elastic fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which can be seen from the contributions of all orders. Received 21 February 2001 and Received in final form 27 June 2001     

Ferromagnetism in quasicrystals: Symmetry aspects

Magnetic-group analysis of the symmetries typical of quasicrystals shows that ferromagnetism is incompatible with the icosahedral symmetry. Depending on the magnetic field direction, the icosahedral symmetry in the magnetic field is reduced to pentagonal, trigonal or rhombic symmetries.     

An affine extension of non-crystallographic Coxeter groups with applications in the theory of quasicrystals and integrable systems

Similarly as in the theory of Kac-Moody algebras, affine extensions of the non-crystallographic Coxeter groupsH _k, (k=2, …, 4) can be derived via an appropriate extension of the Cartan matrix. These groups lead to novel applications in the theory of quasicrystals and integrable models. In the former case, a new model for quasicrystals with five-fold symmetries could be established; in the latter case, subgroups have been used to obtain a Calogero model related to a non-integrally laced group. Presented at the DI-CRM Workshop held in Prague, 18–21 June 2000. Financial support through a European-Union Marie Curie fellowship is gratefully acknowledged.     

Magnetic rotation and chiral symmetry breaking

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.     

Phase diagram of a random tiling quasicrystal

We study the phase diagram of a two-dimensional random tiling model for quasicrystals. At proper concentrations the model has 8-fold rotational symmetry. Landau theory correctly gives most of the qualitative features of the phase diagram, which is in turn studied in detail numerically using a transfer matrix approach. We find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first-order or continuous transitions. Exact solutions are given in all phases except for the quasicrystal phase, and for the phase boundaries between them. We calculate numerically the phason elastic constants and entropy density, and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8-fold rotational symmetry. In addition to the obvious application to quasicrystals, this study generalizes certain surface roughening models to two-dimensional surfaces in four dimensions.     

1-D and 2-D NMR of broad-line solids: an application to quasicrystals

Nuclear magnetic resonance (NMR) techniques for measuring one-dimensional absorption spectra and two-dimensional exchange spectra of solids with extremely inhomogeneously broadened lines are discussed. Among various “broad-line” solids, quasicrystals represent alloys of metallic elements, the structures of which include “forbidden” symmetry elements. NMR absorption lines of quasicrystals exhibit a strong electric-quadrupole-induced inhomogeneous broadening that originates from the lack of translational periodicity of the otherwise perfectly long-range-ordered quasiperiodic lattice. Recording an NMR spectrum of a quasicrystalline sample requires a magnetic field-sweep technique. The two-dimensional exchange experiment on quasicrystals can be performed on selectively excited portions of the NMR spectrum only. Due to the off-resonance effects in a selective excitation, the use of a simple three-pulse stimulated-echo exchange sequence is preferred. The²⁷Al spectra of the Al-Pd-Mn and Al-Pd-Re families show interesting features like temperature-dependent frequency shifts and exchange effects due to atomic motion.     

Quasicrystals: A Matter of Definition

It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.     

寻找囚禁在光腔中的玻色-爱因斯坦凝聚体的八重准晶

准晶是一种拥有长程序但不具有周期性结构的一种物质.实验上通过将玻色-爱因斯坦凝聚体(BEC)放置在一个由四个光学腔组成的系统中,通过四个腔中激光照射在凝聚体上从而得到具有八重旋转对称性的准晶.本文结合虚时演化方法和分步傅里叶法从理论上得到了八重准晶体.我们通过这种方法可以实现更为复杂的晶体结构,从而为将来探索新物质提供了可能.     

Experimental demonstration of free-space optical vortex transmutation with polygonal lenses

Vortex transmutation was predicted to take place when vortices interact with systems possessing discrete rotational symmetries of finite order [Phys. Rev. Lett.95, 123901 (2005)]. Here we report what is believed to be the first experimental demonstration of vortex transmutation. We show that in free space, by simply inserting polygonal lenses into the optical path, the central vorticity of a coaxially incident optical vortex can be changed following the modular transmutation rule. We generate the wavefront at the exit face of the lenses with computer generated holograms and measure the output vorticity using the interference patterns at the focal plane. The results agree well with theoretical predictions.     

Occurrence of rotation domains in heteroepitaxy

Heteroepitaxy can involve materials with a misfit of crystal structure. Rotation domains in the epilayer are a fundamental consequence. We derive a general expression for their (minimum) number which is determined by the mismatch of the rotational symmetries of the substrate and epilayer. In the case of a mismatch of rotational symmetry, the number of rotation domains of material A on material B is different from that of B on A. A larger number of rotation domains can occur due to domain structure or nearly fulfilled additional symmetries of the substrate surface.     

Composite lattice pattern formation in a wide-aperture thin-slice solid-state laser with imperfect reflective ends

We observed self-formations of multiple lasing channels and two-dimensional lasing patterns consisting of composite local modes having different lasing frequencies in a laser-diode-pumped wide-aperture thin-slice solid-state laser with imperfect reflective end surfaces. Global patterns resembling higher-order Hermite-Gaussian modes or possessing N-fold rotational symmetries were experimentally shown to appear due to the standard polished surface roughness of closely spaced reflective ends and nonlinear modal interactions.     

D相准晶显示强烈的各向异性电—声子质量增强效应

对ＡｌＮｉＣｏＤ相准晶和热电势测量表明，沿准晶面的电－声子质量增强效应比沿周期方向要大一个数量级以上。     

The symmetry properties of stable polynomial Gaussian beam profiles

We consider the symmetry properties of polynomial Gaussian beam profiles (intensity distributions) that remain stable during propagation, apart from being scaled and possibly rotated. These beams are expressed as special linear combinations of the Laguerre-Gaussian modes. Two kinds of symmetries are present: discreet rotational symmetries and mirror symmetries. The symmetry properties are shown to depend on the particular subset of Laguerre-Gaussian modes that is used to construct the stable beam. We demonstrate the symmetry properties of a few examples of stable beams through numerical simulations.     

Mei Symmetries and Lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.     

Dependence of the Electronic Properties of Quasicrystals on the Nonequilibrium Population of Two-Level Electron Traps

JETP Letters - A new phenomenon is detected in quasicrystals: it is shown that the so-called “exotic” properties of real quasicrystalline materials are due to the presence of metastable...