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

Abstract

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.

Non-close-packed three-dimensional quasicrystals

“…Both approaches introduce local order that is incompatible with periodic lattices, like for example pentagonal rings of five particles. Phase diagrams of soft-core systems [28,[35][36][37] and the effect of quasiperiodicity on particle dynamics [38,39] and stabilization [40] have been studied in detail. Another direction are continuum simulations, such as phase field models [41][42][43][44].…”

Stability of particles in two-dimensional quasicrystals against phasonic perturbations

“…This obviously includes all structures induced by laser fields , but also quantum quasicrystals [36][37][38][39] have been shown to be similar [37]. Furthermore, even intrinsic quasicrystals and their thermally fluctuating phasonic displacements can be analyzed by comparing them to laser fields [35]. Note that phasonic flips due to thermal fluctuations are also important for the growth process of intrinsic quasicrystals [31,[40][41][42][43] and in future might be used to predict which parts of a quasicrystal grow without flips and which particles are more likely placed in a wrong position during the growth process.…”

“…1). Such tilings are found due to the similarity of selecting pronounced maxima in laser fields and selecting particles in superspace by an acceptance window [25,31,35].…”

Phasonic Diffusion and Self-confinement of Decagonal Quasicrystals in Hyperspace

“…1). Interactions are governed by the Lennard-Jones-Gauss pair potential V LJG (r ) that is designed to support the two length scales of quasicrystalline structures by its arXiv:1906.07045v1 [cond-mat.soft] 17 Jun 2019 two minima [1,9]. The hyperlattice model (absence of phonons) allows for a restriction of distances to discrete values that were extracted from Brownian dynamics simulations [9]:…”