Pinning and depinning of a classic quasi-one-dimensional Wigner crystal in the presence of a constriction

Piacente, G.; Peeters, F. M.

doi:10.1103/physrevb.72.205208

Cited by 59 publications

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“…For such a system, the formation of layers has been reported as well [10]. The change of the number of such layers in the vicinity of a constriction has been predicted from Langevin dynamics simulations of Yukawa particles [11]. The main advantage of the use of superparamagnetic colloids instead of electrons is given by the size of the colloids, which can be easily monitored in a standard video microscopy setup.…”

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Layer Reduction in Driven 2D-Colloidal Systems through Microchannels

et al. 2006

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The transport behavior of a system of gravitationally driven superparamagnetic colloidal particles is investigated. The motion of the particles through a narrow channel is governed by magnetic dipole interactions, and a layered structure forms parallel to the walls. The arrangement of the particles is perturbed by diffusion and the motion induced by gravity leading to a density gradient along the channel. Our main result is the reduction of the number of layers. Experiments and Brownian dynamics simulations show that this occurs due to the density gradient along the channel. DOI: 10.1103/PhysRevLett.97.208302 PACS numbers: 82.70.Dd, 61.72.ÿy, 64.60.Cn, 75.40.Mg Lattice defects can be introduced in perfectly ordered crystals by deformations due to external forces. Despite their importance, the dynamical behavior of single dislocations is still rather poorly understood, because they are difficult to generate and observe on the atomic scale. Therefore, the observation of this behavior in a model system will lead to insights that can be transferred to a broad range of systems. Studies of isolated lattice defects have recently become possible in static systems of colloidal crystals [1]. Experiments on the behavior of such defects in a nonequilibrium system can lead to a better understanding of the transport behavior of a wide range of systems.In biological systems, the transport of interacting particles through narrow constrictions is of high importance for many processes, for example, for the size selectivity of transport in ion channels [2]. The complexity of such systems allows one to only make hypotheses on the underlying physics governing such phenomena. Model systems that can be easily accessed experimentally can reveal many of the underlying processes [3]. This requires studies of particle transport through channels with variously shaped walls. In order to perform these studies, transport through channels with straight walls has to be well understood in experiments shown in this Letter.In this work, we report on studies of the transport behavior of colloids in a quasi-two-dimensional (2D) setup. The colloids are superparamagnetic; therefore, the interaction energy can be continuously tuned by the application of an external magnetic field [4]. The particles are driven by gravity through a narrow constriction (channel). Such driven diffusive systems serve as model systems for theoretical studies of nonequilibrium behavior [5]. In addition, such a system resembles the classical case of a quantum point contact in mesoscopic electronics [6,7] or in metallic single atom contacts [8,9]. These contacts exhibit transport in electronic channels due to quantization effects. These quantum channels can be seen as analogous to the layers in the macroscopic transport, since both occur due to the interaction of the particles with the confining potential. A classical version of a similar scenario can be built on a liquid helium surface, which is loaded with charges. For such a system, the formation of layers has been repor...

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Layer Reduction in Driven 2D-Colloidal Systems through Microchannels

et al. 2006

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“…If instead the vortices are only partially coupled between layers, the response is reduced in the undriven layer compared to the driven layer. A similar coupling-decoupling transition is also predicted for coupled wires containing 1D Wigner crystals [8], and certain drag effects in 1D wires have been interpreted as resulting from the formation of 1D Wigner crystal states [9].Many of these systems can contain some form of quenched disorder which could produce pinning effects [11]; however, very little is known about how pinning alters the drag or transport properties in layered geometries. The quenched disorder could be strong in one channel and weak in another, or it could be of equal strength in both channels, resulting in different types of dynamic phases.…”

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“…The specific system we consider could be realized experimentally using colloidal particles in channel geometries [16] where a driving force is applied to one channel via optical means or an electric field. The effects we observe could also be studied with coupled 1D Wigner crystals [9,11,17,18] or in superconductors with nanofabricated channel geometries [19] when the current is applied to only one channel and the response is measured in both channels. In our system, we find that without pinning there is a finite drive transition from a locked regime to a partially decoupled regime in which the response of the drag channel decreases with increasing drive.…”

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confidence: 99%

“…Many of these systems can contain some form of quenched disorder which could produce pinning effects [11]; however, very little is known about how pinning alters the drag or transport properties in layered geometries. The quenched disorder could be strong in one channel and weak in another, or it could be of equal strength in both channels, resulting in different types of dynamic phases.…”

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The effect of pinning on drag in coupled one-dimensional channels of particles

Bairnsfather

Reichhardt

2011

EPL

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Abstract. -We consider a simple model for examining the effects of quenched disorder on drag consisting of particles interacting via a Yukawa potential that are placed in two coupled onedimensional channels. The particles in one channel are driven and experience a drag from the undriven particles in the second channel. In the absence of pinning, for a finite driving force there is no pinned phase; instead, there are two dynamical regimes of completely coupled or locked flow and partially coupled flow. When pinning is added to one or both channels, we find that a remarkably rich variety of dynamical phases and drag effects arise that can be clearly identified by features in the velocity force curves. The presence of quenched disorder in only the undriven channel can induce a pinned phase in both channels. Above the depinning transition, the drag on the driven particles decreases with increasing pinning strength, and for high enough pinning strength, the particles in the undriven channel reach a reentrant pinned phase which produces a complete decoupling of the channels. We map out the dynamic phase diagrams as a function of pinning strength and the density of pinning in each channel. Our results may be relevant for understanding drag coupling in 1D Wigner crystal phases, and the effects we observe could also be explored using colloids in coupled channels produced with optical arrays, vortices in nanostructured superconductors, or other layered systems where drag effects arise.There are many examples of one-and two-dimensional (1D and 2D) coupled bilayers or coupled channels of interacting particles, including vortices in superconducting bilayers [1,2], colloidal systems [3-6], dusty plasmas [7], and Wigner crystals [8][9][10]. In many of these systems it is possible to apply an external drive to one of the layers and measure the resulting response of the other layer as well as the drag effect produced by the particles in the undriven layer on those in the driven layer. For instance, this type of measurement has been performed for the transformer geometry in two-layer superconducting vortex systems [1,2]. If the vortices in each layer are completely coupled, the measured response is the same in both layers. If instead the vortices are only partially coupled between layers, the response is reduced in the undriven layer compared to the driven layer. A similar coupling-decoupling transition is also predicted for coupled wires containing 1D Wigner crystals [8], and certain drag effects in 1D wires have been interpreted as resulting from the formation of 1D Wigner crystal states [9].Many of these systems can contain some form of quenched disorder which could produce pinning effects [11]; however, very little is known about how pinning alters the drag or transport properties in layered geometries. The quenched disorder could be strong in one channel and weak in another, or it could be of equal strength in both channels, resulting in different types of dynamic phases. Particles driven over random quenched disorder in sin...

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“…Concernant la transition de dépiégeageélastique, les simulations numériques dans un espace de dimension d = 2 montrent des transitions du second ordre avec pour les interfaces β ≈ 1/3 [3], tandis que pour les structures périodiques des exposants très variés ontété trouvés. β ≈ 2/3 est mesuré pour les ondes de densité de charge [4], le cristal de Wigner [5] et pour les colloïdes [6], tandis que d'autres travaux ont trouvé β ≈ 0.5 [7] et β = 0.92 ± 0.01 [8] pour des colloïdes, et β = 0.35 [9] pour des systèmes de type stripes.…”

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Transition de dépiégeage élastique de vortex supraconducteurs

Olive¹,

Scala²,

Lansac³

et al. 2012

ESAIM: Proc.

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Résumé. Nous présentons des résultats de simulations numériquesà deux dimensions sur des réseaux de vortex dans les supraconducteurs que l'on met en mouvement dans un potentiel aléatoire. Onétudie la dynamique des vortex au seuil de dépiégeage Fc dans le cas d'un faible désordreà température nulle. Les régimesélastiques au seuil de dépiégeage sont analysés dans le cadre des transitions de phase continues (transitions du second ordre). La réponse en vitesse và la force d'entraînement F se comporte comme v ∼ (F − Fc) β au voisinage immédiat du seuil de dépiégeage. Dans la région critique obtenue pour différentes grandes tailles du système simulé, nous mesurons l'exposant critique β = 0.27 ± 0.04.Abstract. We present 2D numerical simulation results of superconductor vortex lattices driven over a random disorder. The vortex dynamics at the depinning threshold Fc is studied at zero temperature in the case of weak disorder. The dynamics is elastic and the depinning transition is analysed in the framework of a second order phase transition where the velocity response v to the driving force F behaves like v ∼ (F − Fc) β . The analysis of the critical region of several large lattice sizes leads to the result that β = 0.27 ± 0.04.

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Pinning and depinning of a classic quasi-one-dimensional Wigner crystal in the presence of a constriction

Cited by 59 publications

References 54 publications

Layer Reduction in Driven 2D-Colloidal Systems through Microchannels

Layer Reduction in Driven 2D-Colloidal Systems through Microchannels

The effect of pinning on drag in coupled one-dimensional channels of particles

Transition de dépiégeage élastique de vortex supraconducteurs

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