Comparing light-induced colloidal quasicrystals with different rotational symmetries

Structural studies of local environments in high-symmetry quasicrystals

The statistics of how the local environment of a particle looks like, e.g., given by the distribution of nearest neighbor distances or the sizes of Voronoi cells, is important as a starting point for the calculation of many material properties like electronic or photonic band structures. Here we study local environments that occur in quasicrystals with large rotational symmetry. Both with analytical considerations based on geometric arguments and with an analysis of a large number of numerically created patches of high-symmetry quasicrystals we find that the Voronoi area's distribution reaches a bimodal curve and that in the limit of large rotational symmetries the distribution of nearest neighbor distance converges against a universal curve, where [Formula: see text] of the vertices have their nearest neighbor at a normalized distance equal to 1, while for the other [Formula: see text] the nearest neighbor is at a distance less than 1. Therefore, the statistics of local environments is non-trivial but independent of the specific rotational symmetry. Thus properties that only depend on local environments are expected to be universal for all high-symmetry quasicrystals.

Construction of photorefractive photonic quasicrystal microstructures by twisted square lattices

A convenient method to fabricate two-dimensional photonic quasicrystal microstructures was experimentally demonstrated by using a rotatable four-wedge prism. Two-dimensional eightfold symmetric quasicrystal microstructures are formed by two groups of twisted square lattices in a photorefractive crystal. The experimental devices of this method are simple and stable without complicated optical adjustment equipment. Optical-induced quasicrystal microstructures are analyzed and verified by magnified imaging and far-field diffraction pattern imaging. The method can be extended to fabricate more complex quasicrystal and moiré lattice microstructures. We numerically demonstrate that this method can be used to fabricate other complex photonic microstructures by using different multi-wedge prisms and adjusting the rotation angle properly.

Event-chain Monte Carlo simulations of the liquid to solid transition of two-dimensional decagonal colloidal quasicrystals

In event-chain Monte Carlo simulations, we model colloidal particles in two dimensions that interact according to an isotropic short-ranged pair potential which supports the two typical length scales present in decagonal quasicrystals. We investigate the assembled structures as we vary the density and temperature. Our special interest is related to the transition from quasicrystal to liquid. In contrast to the KTHNY melting theory for quasicrystals which predicts an intermediate pentahedratic phase, we find a one-step first-order melting transition. However, we discover that the slow relaxation of phasonic flips, i.e. rearrangements of the particles due to additional degrees of freedom in quasicrystals, changes the positional correlation functions, to the extent that structures with long-range orientational correlations, but exponentially decaying positional correlations, are observed.

Growth of two-dimensional decagonal colloidal quasicrystals

The growth of quasicrystals, i.e. structures with long-range positional order but no periodic translational symmetry, is more complex than the growth of periodic crystals. By employing Brownian dynamics simulations in two dimensions for colloidal particles that interact according to an isotropic pair potential with two incommensurate lengths, we study the growth of quasicrystalline structures by sequentially depositing particles at their surface. We quantify the occurrence of quasicrystalline order as a function of the temperature and the rate of added particles. In addition, we explore defects like local triangular order or gaps within the quasicrystalline structure. Furthermore, we analyze the shapes of the surfaces in grown structures which tend to build straight lines along the symmetry axes of the quasicrystal. Finally, we identify phasonic flips which are rearrangements of the particles due to additional degrees of freedom. The number of phasonic flips decreases with the distance to the surface.

Dislocation-free growth of quasicrystals from two seeds due to additional phasonic degrees of freedom

We explore the growth of two-dimensional quasicrystals, i.e., aperiodic structures that possess long-range order, from two seeds at various distances and with different orientations by using dynamical phase-field crystal calculations. We compare the results to the growth of periodic crystals from two seeds. There, a domain border consisting of dislocations is observed in case of large distances between the seed and large angles between their orientation. Furthermore, a domain border is found if the seeds are placed at a distance that does not fit to the periodic lattice. In the case of the growth of quasicrystals, we only observe domain borders for large distances and different orientations. Note that all distances do inherently not match to a perfect domain wall-free quasicrystalline structure. Nevertheless, we find dislocation-free growth for all seeds at a small enough distance and for all seeds that approximately have the same orientation. In periodic structures, the stress that occurs due to incommensurate distances between the seeds results in phononic strain fields or, in the case of too large stresses, in dislocations. In contrast, in quasicrystals an additional phasonic strain field can occur and suppress dislocations. Phasons are additional degrees of freedom that are unique to quasicrystals. As a consequence, the additional phasonic strain field helps to distribute the stress and facilitates the growth of dislocation-free quasicrystals from multiple seeds. In contrast, in the periodic case the growth from multiple seeds most likely leads to a structure with multiple domains. Our work lays the theoretical foundations for growing perfect quasicrystals from different seeds and is therefore relevant for many applications.

Properties of quasiperiodic functions

Today, quasiperiodic tilings are well known and have been studied in great detail since they are very useful to describe the properties of metallic and soft matter quasicrystals. A closely related topic are quasiperiodic functions which have also gained large interest recently. Different types of such functions and there interrelation will be presented here. The main topic will be quasiperiodic potentials generated by laser beams and their variability. The distribution of extremal points and local isomorphisms of quasiperiodic functions will also be addressed.

Detection of phonon and phason modes in intrinsic colloidal quasicrystals by reconstructing their structure in hyperspace

Phasons are additional degrees of freedom which occur in quasicrystals alongside the phonons known from conventional periodic crystals. The rearrangements of particles that are associated with a phason mode are hard to interpret in physical space. We reconstruct the quasicrystal structure by an embedding into extended higher-dimensional space, where phasons correspond to displacements perpendicular to the physical space. In dislocation-free decagonal colloidal quasicrystals annealed with Brownian dynamics simulations, we identify thermal phonon and phason modes. Finite phononic strain is pinned by phasonic excitations even after cooling down to zero temperature. For the phasonic displacements underlying the flip pattern, the reconstruction method gives an approximation within the limits of a multi-mode harmonic ansatz, and points to fundamental limitations of a harmonic picture for phasonic excitations in intrinsic colloidal quasicrystals.

Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review

We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves, electron crystals, colloids, stripe and pattern forming systems, and skyrmions, and could also have connections to jamming, glassy behaviors, and active matter. These systems are also ideal for exploring the broader issues of characterizing transient and steady state nonequilibrium flow phases as well as nonequilibrium phase transitions between distinct dynamical phases, analogous to phase transitions between different equilibrium states. We discuss the differences between elastic and plastic depinning on random substrates and the different types of nonequilibrium phases which are associated with specific features in the velocity-force curves, fluctuation spectra, scaling relations, and local or global particle ordering. We describe how these quantities can change depending on the dimension, anisotropy, disorder strength, and the presence of hysteresis. Within the moving phase we discuss how there can be a transition from a liquid-like state to dynamically ordered moving crystal, smectic, or nematic states. Systems with periodic or quasiperiodic substrates can have multiple nonequilibrium second or first order transitions in the moving state between chaotic and coherent phases, and can exhibit hysteresis. We also discuss systems with competing repulsive and attractive interactions, which undergo dynamical transitions into stripes and other complex morphologies when driven over random substrates. Throughout this work we highlight open issues and future directions such as absorbing phase transitions, nonequilibrium work relations, inertia, the role of non-dissipative dynamics such as Magnus effects, and how these results could be extended to the broader issues of plasticity in crystals, amorphous solids, and jamming phenomena.

Comment on "quantum quasicrystals of spin-orbit-coupled dipolar bosons"

A Comment on the Letter by S. Gopalakrishnan, I. Martin, and E. A. Demler, Phys. Rev. Lett. 111, 185304 (2013).. The authors of the Letter offer a Reply.

Growth modes of quasicrystals

The growth of quasicrystals, i.e., aperiodic structures with long-range order, seeded from the melt is investigated using a dynamical phase field crystal model. Depending on the thermodynamic conditions, two different growth modes are detected, namely defect-free growth of the stable quasicrystal and a mode dominated by phasonic flips which are incorporated as local defects into the grown structure such that random tilinglike ordering emerges. The latter growth mode is unique to quasicrystals and can be verified in experiments on one-component mesoscopic systems.

Phason-induced dynamics of colloidal particles on quasicrystalline substrates

Phasons are special hydrodynamic modes that occur in quasicrystals. The trajectories of particles due to a phasonic drift were recently studied by Kromer et al. (Phys. Rev. Lett. 108, 218301 (2012)) for the case where the particles stay in the minima of a quasicrystalline potential. Here, we study the mean motion of colloidal particles in quasicrystalline laser fields when a phasonic drift or displacement is applied and also consider the cases where the colloids cannot follow the potential minima. While the mean square displacement is similar to the one of particles in a random potential with randomly changing potential wells, there also is a net drift of the colloids that reverses its direction when the phasonic drift velocity is increased. Furthermore, we explore the dynamics of the structural changes in a laser-induced quasicrystal during the rearrangement process that is caused by a steady phasonic drift or an instantaneous phasonic displacement.