Trajectories of Colloidal Particles in Laser Fields with Eight-, Ten-, or Twelve-Fold Symmetry and Phasonic Drift

Sandbrink, Matthias; Schmiedeberg, Michael

doi:10.1007/978-94-007-6431-6_35

Cited by 8 publications

(14 citation statements)

References 18 publications

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“…On the basis of the 14-fold rotational symmetry, we have extended previous studies [16,20] to quasicrystals with rank D = 6. We showed how one can still predict colloidal trajectories that are caused by phasonic drifts in spite of the increased complexity in the phasonic space.…”

Section: Discussionmentioning

confidence: 94%

“…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.…”

Section: Analyzing Colloidal Trajectories 41 Methodsmentioning

confidence: 97%

“…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.…”

Section: Characteristic Displacements and Characteristic Areasmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

2014

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Quasicrystals are structures that are not periodic but possess a long range positional order. They can have any rotational symmetry including those that are forbidden in periodic crystals. The symmetry is classied by the point group and the rank D. In quasicrystals, phasons as additional hydrodynamic modes cause correlated rearrangements of the particles. The number of phasonic degrees of freedom depends on the rank. For colloidal quasicrystals that are induced by laser elds, specic phasonic displacements can be realized by changing the phases of the laser beams in a well-determined way. The arising trajectories of colloids in two-dimensional light-induced colloidal quasicrystals with rank D = 4 have already been analyzed in detail. Here, we analyze the colloidal trajectories in two-dimensional quasicrystals with 14-fold symmetry having rank D = 6. We observe complex paths of the colloids consisting of straight and winding lines as well as jumps.

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Section: Discussionmentioning

confidence: 94%

“…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.…”

Section: Analyzing Colloidal Trajectories 41 Methodsmentioning

confidence: 97%

Section: Characteristic Displacements and Characteristic Areasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2014

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“…Phonons and phasons both preserve the LI class in the limit of long wavelengths [25]. The behavior of colloids in laser fields with changing phasonic displacements have already been studied for decagonal quasicrystals in [22,32] and for other two-dimensional quasicrystals in [31,33]. For a recent discussion how the phasonic degrees of freedom differ from modes that change the LI class, see also [34][35][36].…”

Section: Substrates With Quasicrystalline Symmetrymentioning

confidence: 99%

Effective substrate potentials with quasicrystalline symmetry depend on the size of the adsorbed particles

et al. 2015

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Abstract. We explore the effective potential landscapes that extended particles experience when adsorbed on the surface of quasicrystals. Commonly, these are solids with long-ranged order but no translational symmetry. The effective potentials significantly depend on the size of the adsorbed particles. We show how changing the particle radius changes the so-called local isomorphism class of the effective quasicrystalline pattern. This means effective potentials for different particle sizes cannot directly be mapped onto each other. Our theoretical predictions are confirmed by Monte Carlo simulations. The results are important for colloidal particles with different sizes that are subjected to laser fields with quasicrystalline symmetry as well as for systems where extended molecules are deposited onto the surface of metallic quasicrystals.

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

Hielscher

Martinsons²,

Schmiedeberg³

et al. 2017

J. Phys.: Condens. Matter

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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.

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Trajectories of Colloidal Particles in Laser Fields with Eight-, Ten-, or Twelve-Fold Symmetry and Phasonic Drift

Cited by 8 publications

References 18 publications

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

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

Effective substrate potentials with quasicrystalline symmetry depend on the size of the adsorbed particles

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

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