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

TL;DR: In this article, 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 were presented analytically and independently through molecular dynamic simulations.

Abstract: 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.

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TL;DR: In this article, the statics and dynamics of vortices in the presence of a periodic quasi-one-dimensional substrate were examined, focusing on the limit where the vortex lattice constant is smaller than the substrate lattice period.

Abstract: 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.

27 citations

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TL;DR: In this article, the phonon spectra of two-dimensional liquid dusty plasmas on a one-dimensional periodic substrate using numerical simulations were investigated, and it was shown that increasing the width or decreasing the depth of the substrate minima allows the particles to buckle into a zigzag structure, and the resulting spectra developed two branches, one for sloshing motion and one for breathing motion.

Abstract: 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.

18 citations

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TL;DR: In this article, the diffusive behavior of active brownian particles under lateral parabolic confinement was studied, and it was shown that the behavior changes from sub-diffusion to ballistic motion as the angular noise strength and confinement intensity varies.

Abstract: 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).

14 citations

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TL;DR: The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations and it is found 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.

Abstract: 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.

13 citations

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TL;DR: In this article, the authors considered a system of two-dimensional (2D) charged particles, interacting through a repulsive Yukawa potential, and obtained the ground-state configurations and the normal-mode spectra of the system as a function of the periodicity and strength of the periodic potential.

Abstract: 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 ${V}_{0}$.

10 citations

##### References

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TL;DR: A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams, where decoherence is negligible, and the measurement can be carried out with a high efficiency.

Abstract: A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams. Quantum gates involving any pair, triplet, or subset of ions can be realized by coupling the ions through the collective quantized motion. In this system decoherence is negligible, and the measurement (readout of the quantum register) can be carried out with a high efficiency.

3,247 citations

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Lawrence Berkeley National Laboratory

^{1}, IBM^{2}, University of Michigan^{3}, Columbia University^{4}TL;DR: It is demonstrated that electrical charges on sterically stabilized nanoparticles determine B NSL stoichiometry; additional contributions from entropic, van der Waals, steric and dipolar forces stabilize the variety of BNSL structures.

Abstract: The assembly of nanoparticles of two different materials into a binary nanoparticle superlattice is a promising way of synthesizing a large variety of materials (metamaterials) with precisely controlled chemical composition and tight placement of the components. In theory only a few stable binary superlattice structures can assemble from hard spheres, potentially limiting this approach. But all is not lost because at the nanometre scale there are additional forces (electrostatic, van der Waals and dipolar) that can stabilize binary nanoparticulate structures. Shevchenko et al. now report the synthesis of a dozen novel structures from various combinations of metal, semiconductor, magnetic and dielectric nanoparticles. This demonstrates the potential of self-assembly in designing families of novel materials and metamaterials with programmable physical and chemical properties. Assembly of small building blocks such as atoms, molecules and nanoparticles into macroscopic structures—that is, ‘bottom up’ assembly—is a theme that runs through chemistry, biology and material science. Bacteria1, macromolecules2 and nanoparticles3 can self-assemble, generating ordered structures with a precision that challenges current lithographic techniques. The assembly of nanoparticles of two different materials into a binary nanoparticle superlattice (BNSL)3,4,5,6,7 can provide a general and inexpensive path to a large variety of materials (metamaterials) with precisely controlled chemical composition and tight placement of the components. Maximization of the nanoparticle packing density has been proposed as the driving force for BNSL formation3,8,9, and only a few BNSL structures have been predicted to be thermodynamically stable. Recently, colloidal crystals with micrometre-scale lattice spacings have been grown from oppositely charged polymethyl methacrylate spheres10,11. Here we demonstrate formation of more than 15 different BNSL structures, using combinations of semiconducting, metallic and magnetic nanoparticle building blocks. At least ten of these colloidal crystalline structures have not been reported previously. We demonstrate that electrical charges on sterically stabilized nanoparticles determine BNSL stoichiometry; additional contributions from entropic, van der Waals, steric and dipolar forces stabilize the variety of BNSL structures.

1,981 citations

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TL;DR: In this article, the energy of interaction between free electrons in an electron gas is considered and the correlation energy is calculated by an approximation method which is, essentially, a development of the energy by means of the Rayleigh-Schrodinger perturbation theory in a power series of e2.

Abstract: The energy of interaction between free electrons in an electron gas is considered. The interaction energy of electrons with parallel spin is known to be that of the space charges plus the exchange integrals, and these terms modify the shape of the wave functions but slightly. The interaction of the electrons with antiparallel spin, contains, in addition to the interaction of uniformly distributed space charges, another term. This term is due to the fact that the electrons repell each other and try to keep as far apart as possible. The total energy of the system will be decreased through the corresponding modification of the wave function. In the present paper it is attempted to calculate this “correlation energy” by an approximation method which is, essentially, a development of the energy by means of the Rayleigh-Schrodinger perturbation theory in a power series of e2.

1,815 citations

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TL;DR: In this article, the Coulomb crystals and liquids were directly observed for the first time using an optical microscope and the system parameters, hexagonal, fcc and bcc crystal structures and solids with coexisting different crystal structures can be formed.

Abstract: The strongly coupled dusty plasmas are formed by suspending negatively charged ${\mathrm{SiO}}_{2}$ fine particles with 10 \ensuremath{\mu}m diameter in weakly ionized rf Ar discharges. The Coulomb crystals and liquids are directly observed for the first time using an optical microscope. By properly controlling the system parameters, hexagonal, fcc and bcc crystal structures and solids with coexisting different crystal structures can be formed. Increasing the rf power causes the transition to the more disordered liquid state.

1,032 citations

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TL;DR: The electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with the approach to controlling opposite-charge interactions facilitating the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications.

Abstract: Colloidal suspensions are widely used to study processes such as melting, freezing1,2,3 and glass transitions4,5. This is because they display the same phase behaviour as atoms or molecules, with the nano- to micrometre size of the colloidal particles making it possible to observe them directly in real space3,4. Another attractive feature is that different types of colloidal interactions, such as long-range repulsive1,3, short-range attractive5, hard-sphere-like2,3,4 and dipolar3, can be realized and give rise to equilibrium phases. However, spherically symmetric, long-range attractions (that is, ionic interactions) have so far always resulted in irreversible colloidal aggregation6. Here we show that the electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with our theory and simulations confirming the stability of these structures. We find that in contrast to atomic systems, the stoichiometry of our colloidal crystals is not dictated by charge neutrality; this allows us to obtain a remarkable diversity of new binary structures. An external electric field melts the crystals, confirming that the constituent particles are indeed oppositely charged. Colloidal model systems can thus be used to study the phase behaviour of ionic species. We also expect that our approach to controlling opposite-charge interactions will facilitate the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications7.

915 citations