What Phasons Look Like: Particle Trajectories in a Quasicrystalline Potential

Abstract

Among the distinctive features of quasicrystals-structures with long-range order but without periodicity-are phasons. Phasons are hydrodynamic modes that, like phonons, do not cost free energy in the long-wavelength limit. For light-induced colloidal quasicrystals, we analyze the collective rearrangements of the colloids that occur when the phasonic displacement of the light field is changed. The colloidal model system is employed to study the link between the continuous description of phasonic modes in quasicrystals and collective phasonic flips of atoms. We introduce characteristic areas of reduced phononic and phasonic displacements and use them to predict individual colloidal trajectories. In principle, our method can be employed with all quasicrystalline systems in order to derive collective rearrangements of particles from the continuous description of phasons.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

“…Experiments and computational studies have shown that in the absence of a drive, a variety of orderings can arise for colloidal particles interacting with one-dimensional (1D) periodic substrates [13,32,33], two-dimensional (2D) periodic substrates [15,20,21,[34][35][36][37][38], 2D quasiperiodic substrates [39][40][41][42][43], or 2D random substrates [44]. While these studies have provided a better understanding of several features of commensurateincommensurate behaviors, being able to dynamically control the particle ordering and dynamics could lead to a variety of applications, including self-assembled structures, particle separation, and photonic crystals.…”

Colloidal Trajectories in Two-Dimensional Light-Induced Quasicrystals with 14-Fold Symmetry due to Phasonic Drifts

“…2. The diagrams correspond to those obtained for the D = 4 quasicrystals in [16,20]. The procedure to derive a trajectory for the case v = 0 (see Fig.…”

“…In a quasicrystal, we can map all particle positions onto particles inside characteristic areas of small phononic and phasonic displacements [16,20]. To determine the characteristic areas, we rst calculate phononic and phasonic displacements ∆u, ∆v and ∆w that change the dierences between the phases φ j − φ k in Eq.…”

“…For example, quasicrystalline ordering can be established by employing an interference pattern with quasicrystalline symmetry [718], these colloidal systems connect to the growing subject of soft matter quasicrystals (see, e.g., [19]). By tuning the laser phases appropriately it is possible to change the phasonic displacement of the system in a controlled way [9,11,16]. Thus, we can study the trajectories of the colloids that follow the maxima in the light eld.…”

“…In recent works [16,20], a method was presented to predict the trajectories of colloidal particles in a quasicrystalline laser eld when a phasonic drift is applied, i.e., when the phasonic displacement changes at a constant rate in time. It was shown that every colloid can be mapped into characteristic areas of reduced phononic and phasonic displacement.…”