Quasiperiodic Substrates Research Articles

Evaporation of liquid droplets on solid substrates. II. Periodic substrates with moving contact lines

The model in Part I is adapted for curved substrates. For periodic substrates, apparent contact angle is periodic and ``apparent stick-slip'' motion is observed. For quasiperiodic substrates, apparent contact angle is no longer periodic and contact line dynamics is not limited to apparent stick-slip.

Experimental Observation of Directional Locking and Dynamical Ordering of Colloidal Monolayers Driven across Quasiperiodic Substrates

We experimentally investigate the structural behavior of an interacting colloidal monolayer being driven across a decagonal quasiperiodic potential landscape created by an optical interference pattern. When the direction of the driving force is varied, we observe the monolayer to be directionally locked on angles corresponding to the symmetry axes of the underlying potential. At such locking steps, we observe a dynamically ordered smectic phase in agreement with recent simulations. We demonstrate that such dynamical ordering is due to the interaction of particle lanes formed by interstitial and noninterstitial particles.

Phase ordering of hard needles on a quasicrystalline substrate

Quasicrystals possess long-range positional and orientational order. However, they cannot be periodic in space due to their non-crystallographic symmetries such as a 10-fold rotational axis. We perform Monte Carlo simulations of two-dimensional hard-needle systems subject to a quasiperiodic substrate potential. We determine phase diagrams as a function of density and potential strength for two needle lengths. With increasing potential strength short needles tend to form isolated clusters that display directional order along the decagonal directions. Long needles create interacting clusters that stabilize the nematic phase. At large potential strengths the clusters position themselves on two interwoven Fibonacci sequences perpendicular to the cluster orientation. Alternatively, one obtains extended domains of needle clusters which are aligned along all decagonal symmetry directions.

Vortex dynamics and symmetry locking on quasiperiodic and periodic substrates

We examine the dynamics of vortices driven over quasicrystalline and periodic pinning arrays where the direction of the external drive is varied with respect to the substrate orientation. For periodic arrays there is a strong directional locking and the vortex motion can lock to symmetry directions of the pinning lattice even when the drive is not applied along the same symmetry direction. This locking can be detected as a series of steps in the velocity vs driving angle curves and is also associated with dynamical ordering of the vortices along these steps into anisotropic square and triangular lattices. Even though quasicrystalline arrays lack translational order, we show that quasicrystalline substrates also exhibit symmetry locking due to their orientational ordering. The vortex configurations in the nonlocking regimes are much more disordered for the quasiperiodic substrates than for the periodic substrates.

Dynamical Ordering and Directional Locking for Particles Moving over Quasicrystalline Substrates

We use molecular dynamics simulations to study the driven phases of particles such as vortices or colloids moving over a decagonal quasiperiodic substrate. In the regime where the pinned states have quasicrystalline ordering, the driven phases can order into moving square or smectic states, or into states with aligned rows of both square and triangular tiling which we term dynamically induced Archimedean-like tiling. We show that when the angle of the drive is varied with respect to the substrate, directional locking effects occur where the particle motion locks to certain angles. It is at these locking angles that the dynamically induced Archimedean tiling appears. We also demonstrate that the different dynamical orderings and locking phases show pronounced changes as a function of filling fraction.

Self-assembly, structure, and electronic properties of a quasiperiodic lead monolayer

A quasiperiodic Pb monolayer has been formed on the fivefold surface of the Al-Pd-Mn quasicrystal. Growth of the monolayer proceeds via self-assembly of an interconnected network of pentagonal Pb stars, which are shown to be $\ensuremath{\tau}$ inflated compared to similar structural elements of the quasiperiodic substrate. Measurements of the electronic structure of the system using scanning tunneling spectroscopy and ultraviolet photoemission spectroscopy reveal that the Pb monolayer displays a pseudogap at the Fermi level which is directly related to its quasiperiodic structure.

Nanoepitaxy: Size Selection in Self-Assembled and Oriented Al Nanocrystals Grown on a Quasicrystal Surface

The unusual interfacial lattice-mismatch properties of a periodic film and a quasiperiodic substrate are investigated in the Al films grown on an Al-Co-Ni decagonal substrate. The resulting mismatch causes the formation of well-oriented nanometric single crystals of Al, satisfying the epitaxial conditions on a local scale. Total-energy calculations based on a rigid-lattice atomic model for the interface between a cubic and the decagonal surface reproduce the low-energy electron diffraction results concerning the size of the clusters, their distribution, and the details of the orientational alignment of aluminum islands. Such systems can be used in self-size-selecting growth of nanocrystals.

Structural transitions and phonon localization in frenkel kontorova models with quasi-periodic potentials

We have studied the ground state and phonons of a generalized Frenkel Kontorova model with a quasiperiodic substrate potential. We have recently shown that, depending on the three mutually incommensurate, relevant lengths, a sliding mode below a critical coupling can either occur or be absent although a structural transition takes place in both cases. Besides, we observe a transition to localized phonon states. Here we investigate the structural and localization transitions in terms of a nonlinear discrete map.

Driven, underdamped Frenkel-Kontorova model on a quasiperiodic substrate.

We consider the underdamped dynamics of a chain of atoms subject to a dc driving force and a quasiperiodic substrate potential. The system has three inherent length scales which we take to be mutually incommensurate. We find that when the length scales are related by the spiral mean (a cubic irrational) there exists a value of the interparticle interaction strength above which the static friction is zero. When the length scales are related by the golden mean (a quadratic irrational) the static friction is always nonzero. From considerations based on the connection of this problem to standard map theory, we postulate that zero static friction is generally possible for incommensurate ratios of the length scales involved. However, when the length scales are quadratic irrationals, or have some commensurability with each other, the static friction will be nonzero for all choices of interaction parameters. We also comment on the nature of the depinning mechanisms and the steady states achieved by the moving chain.

Pinning and phonon localization in Frenkel-Kontorova models on quasiperiodic substrates

We show that the static and dynamic properties of the Frenkel-Kontorova (FK) model drastically change when an incommensurate harmonic is added to the periodic potential. Our model consists of a harmonic chain with spacing l on a quasiperiodic substrate potential of the form $V(x)=\ensuremath{\sigma}K/(2\ensuremath{\pi}{)}^{2}[1\ensuremath{-}\mathrm{cos}(2\ensuremath{\pi}x)]+(1\ensuremath{-}\ensuremath{\sigma})K/(2\ensuremath{\pi}\ensuremath{\tau}{)}^{2}[1\ensuremath{-}\mathrm{cos}(2\ensuremath{\pi}\ensuremath{\tau}x)],$ where the three relevant lengths l, 1, and ${\ensuremath{\tau}}^{\ensuremath{-}1}$ are chosen to be mutually incommensurate. Within this model we identify two classes of behavior. One presents a sliding mode up to an analyticity breaking, as in the FK model, and another is pinned for any strength of the additional harmonic. Besides, we show that in all cases if $\ensuremath{\sigma}\ensuremath{\ne}0$ or 1, localization of phonons exists beyond a critical value of the potential strength.

Study of the diffusion in disordered ionic conductors by Langevin molecular dynamics

Langevin molecular dynamics were used to directly simulate the diffusion, D( t), of charged particles in structurally disordered lattices, as a first step to study the non-Debye behaviour in this type of system. This method is an alternative to Monte Carlo (MC) simulation, but without the artificial time step inherent in this scheme. A 3D many-particle system is simulated in the canonical ensemble via a Langevin approach. Long-range Coulomb interaction between particles is considered as well as a quasi-periodic substrate potential to mimic the disordered lattice. The results show that a dispersive regime, D( t) ∼ β−1 , appears at length scales of the particle jumps. Thermal variations of β values have been performed and indicate a similar behaviour to MC simulations.

Third sound in superfluid helium film on a quasiperiodic substrate

Third sound in superfluid helium film on a quasiperiodic substrate