We examine the statics and dynamics of vortices in the presence of a periodic quasi-one-dimensional substrate, focusing on the limit where the vortex lattice constant is smaller than the substrate lattice period. As a function of the substrate strength and filling factor, within the pinned state, we observe a series of order-disorder transitions associated with buckling phenomena in which the number of vortex rows that fit between neighboring substrate maxima increases. These transitions coincide with steps in the depinning threshold, jumps in the density of topological defects, and changes in the structure factor. At the buckling transition, the vortices are disordered, while between the buckling transitions the vortices form a variety of crystalline and partially ordered states. In the weak substrate limit, the buckling transitions are absent and the vortices form an ordered hexagonal lattice that undergoes changes in its orientation with respect to the substrate as a function of vortex density. At intermediate substrate strength, certain ordered states appear that are correlated with peaks in the depinning force. Under an applied drive, the system exhibits a rich variety of distinct dynamical phases, including plastic flow, a density-modulated moving crystal, and moving floating solid phases. We also find a dynamic smectic-to-smectic transition in which the smectic ordering changes from being aligned with the substrate to being aligned with the external drive. The different dynamical phases can be characterized using velocity histograms and the structure factor. We discuss how these results are related to recent experiments on vortex ordering in thin films with periodic thickness modulations. Our results should also be relevant for other types of systems such as ions, colloids, or Wigner crystals interacting with periodic quasi-one-dimensional substrates.

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Orientational Ordering, Buckling, and Dynamic Transitions for Vortices Interacting with a Periodic Quasi-One Dimensional Substrate

We investigate the phonon spectra of two-dimensional liquid dusty plasmas on a one-dimensional periodic substrate using numerical simulations. The propagation of the waves across the potential wells of the substrate is inhibited due to the confinement of the dust particles by the substrate minima. If the substrate wells are narrow or deep, one-dimensional chains of particles are formed in each minimum, and the longitudinal motion of an individual chain dominates the propagation of waves along the potential wells of the substrate. Increasing the width or decreasing the depth of the substrate minima allows the particles to buckle into a zigzag structure, and the resulting spectra develop two branches, one for sloshing motion and one for breathing motion. The repulsion between neighboring dust particles produces backward propagation of the sloshing wave for small wave numbers.

Phonon spectra of two-dimensional liquid dusty plasmas on a one-dimensional periodic substrate

In this work we studied the diffusive behavior of active brownian particles under lateral parabolic confinement. The results showed that we go from subdiffusion to ballistic motion as we vary the angular noise strength and confinement intensity. We argued that the subdiffusion regimes appear as consequence of the restricted space available for diffusion (achieved either through large confinement and/or large noise); we saw that when there are large confinement and noise intensity, a similar configuration to single file diffusion appears; on the other hand, normal and superdiffusive regimes may occur due to low noise (longer persistent motion), either through exploring a wider region around the potential minimum in the transverse direction (low confinement), or by forming independent clusters (high confinement).

Active matter in lateral parabolic confinement: From subdiffusion to superdiffusion

The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous magnetic field. For a strong applied magnetic field, we find that the mobility of the system, the exponent of diffusion, and the crossover time among different diffusion regimes can be tuned by the orientation of the magnetic field. For weak magnetic fields, the exponent of diffusion in the subdiffusive regime is independent of the orientation of the external field.

Tunable diffusion of magnetic particles in a quasi-one-dimensional channel

We consider a classical system of two-dimensional (2D) charged particles, interacting through a repulsive Yukawa potential $\text{exp}(\ensuremath{-}r/\ensuremath{\lambda})/r$, and confined in a parabolic channel that limits the motion of the particles in the $y$ direction. Along the $x$ direction, the particles are subject to a periodic potential. The ground-state configurations and the normal-mode spectra of the system are obtained as a function of the periodicity and strength of the periodic potential (${V}_{0}$) and density. An interesting set of tunable ground-state configurations are found, with first- or second-order structural transitions between them. A configuration with particles aligned, perpendicular to the $x$ direction, in each minimum of the periodic potential is obtained for ${V}_{0}$ larger than some critical value that has a power-law dependence on the density. The phonon spectrum of different configurations was also calculated. A localization of the modes into a small frequency interval is observed for sufficiently large strength of the periodic potential, and a tunable gap in the phonon spectrum is found as a function of ${V}_{0}$.

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Yukawa particles confined in a channel and subject to a periodic potential : ground state and normal modes

The ground state configurations and the ``normal'' mode spectra of a quasi-one-dimensional binary system of charged particles interacting through a screened Coulomb potential are presented. The minimum energy configurations were obtained analytically and independently through molecular dynamic simulations. A rich variety of ordered structures was found as a function of the screening parameter, the particle density, and the ratio between the charges of the distinct types of particles. Continuous and discontinuous structural transitions as well as an unexpected symmetry breaking in the charge distribution are observed when the density of the system is changed. For nearly equal charges, we found a disordered phase where a mixing of the two types of particles occurs. The phonon dispersion curves were calculated within the harmonic approximation for the one- and two-chain structures.

P. W. S. Oliveira

Papers

Structural and dynamical properties of a quasi-one-dimensional classical binary system