Ordering of two-dimensional crystals confined in strips of finite width

Ricci, Andrea; Nielaba, Peter; Sengupta, Surajit; Binder, Kurt

doi:10.1103/physreve.75.011405

Cited by 32 publications

(63 citation statements)

References 66 publications

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“…We return to the WC in the quasi-1D geometry. At sufficiently low temperatures, the positional correlation is disturbed by thermal phonons, similarly to the quasi-1D XY magnet, giving rise to the positional correlation decaying as r − at r Ͻ W and e −r/ at r Ͼ W. 10 Even though the positional correlation decays exponentially at large distances, our observation of the BC scattering indicates that the correlation length is sufficiently long below T 0 . In addition, our observation strongly indicates that the electrons within the correlation length maintain their relative positions for longer than the period of the vertical surface oscillation caused by the moving dimple lattice ͑G 1 ͒ −1 ϳ 10 −8 s, otherwise the BC scattering should not occur.…”

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confidence: 87%

“…Experimentally, the superfluid has, surprisingly, been observed for 4 He films formed on the surface of long cylinders, 2,3 which promoted many theoretical works. [4][5][6] In the case of the melting of a crystal in the quasi-1D geometry, a number of computer simulations have been carried out for particles interacting with the Coulomb repulsion 7,8 or other types of interactions, 9,10 and most simulations suggest an interesting anisotropic melting process. However, there have been few experiments on the melting process in the quasi-1D geometry because a very clean system must be used to obtain a clear result.…”

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confidence: 99%

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Melting of a quasi-one-dimensional Wigner crystal: Electrons on superfluidH4ein a narrow channel

2010

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We have investigated the melting process of electron crystals ͑or Wigner crystals͒ confined in quasi-onedimensional channels 10-60 electrons in width, formed on the surface of superfluid 4 He, paying special attention to the nonlinear behavior in resistivity unique to the crystal phase, the Bragg-Cherenkov ͑BC͒ scattering of surface waves. We observed that the BC scattering disappears at a higher temperature for fewer electrons in the confined direction, indicating that the crystal-like structure persists to a higher temperature. We show that this behavior is understood in terms of a naive model describing how the positional correlation is disordered by free dislocations in the quasi-one-dimensional geometry.The dimensionality of a system has a significant influence on the natures of phase transition and ordered states. It is generally accepted that in one-dimensional ͑1D͒ XY magnets, superfluids, and crystals, thermal fluctuations completely destroy the long-range order ͑LRO͒ at any finite temperature. In two-dimensional ͑2D͒ systems, the LRO is also destroyed but the weaker thermal effect allows the quasi-LRO to survive at low temperatures. The quasi-LRO is destroyed at a high temperature by the unbinding of pairs of topological defects, according to Kosterlitz and Thouless ͑KT͒. 1 In a quasi-1D geometry, such as in a strip or on the surface of a tube, the system shows 1D-like behavior when the coherence length is longer than the confining dimension whereas it is 2D-like in the opposite case. In such systems, fundamental questions arise as to whether the quasi-LRO develops at low temperatures and how the quasi-LRO is destroyed with increasing temperature. Experimentally, the superfluid has, surprisingly, been observed for 4 He films formed on the surface of long cylinders, 2,3 which promoted many theoretical works. [4][5][6] In the case of the melting of a crystal in the quasi-1D geometry, a number of computer simulations have been carried out for particles interacting with the Coulomb repulsion 7,8 or other types of interactions, 9,10 and most simulations suggest an interesting anisotropic melting process. However, there have been few experiments on the melting process in the quasi-1D geometry because a very clean system must be used to obtain a clear result.In this Rapid Communication, we experimentally address the melting mechanism of electron crystals in a quasi-1D geometry by employing a very clean electron system, i.e., electrons formed on the superfluid 4 He. 11,12 We carried out transport measurements of the electrons confined in micrometer-wide channels 10-60 electrons in width, paying special attention to the nonlinear transport unique to the electron crystal, the Bragg-Cherenkov ͑BC͒ scattering. [13][14][15][16] The understanding of the properties of confined electrons on a micrometer scale is also of particular importance in the context of quantum information processing. 17,18 In a 2D system, the melting of a crystal is considered to be the KT-type transition but with a slight difference. A 2D hexag...

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confidence: 87%

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confidence: 99%

Melting of a quasi-one-dimensional Wigner crystal: Electrons on superfluidH4ein a narrow channel

2010

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“…efficient r −12 potential with a cutoff (in order to make it strictly short ranged), a shift (in order to ensure that it ends with a value of zero), and a smoothing factor (to make it differentiable). A further motivation to use this model potential is that it is essentially the same potential used in the studies of confinement effects on colloidal crystals without shear [25][26][27][28][29][30] and of two-dimensional melting [44]. This potential is defined as [41,42] …”

Section: Details Of the Simulationmentioning

confidence: 99%

Langevin dynamics simulations of a two-dimensional colloidal crystal under confinement and shear

et al. 2012

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Langevin dynamics simulations are used to study the effect of shear on a two-dimensional colloidal crystal (with implicit solvent) confined by structured parallel walls. When walls are sheared very slowly, only two or three crystalline layers next to the walls move along with them, while the inner layers of the crystal are only slightly tilted. At higher shear velocities, this inner part of the crystal breaks into several pieces with different orientations. The velocity profile across the slit is reminiscent of shear banding in flowing soft materials, where liquid and solid regions coexist; the difference, however, is that in the latter case the solid regions are glassy while here they are crystalline. At even higher shear velocities, the effect of the shearing becomes smaller again. Also the effective temperature near the walls (deduced from the velocity distributions of the particles) decreases again when the wall velocity gets very large. When the walls are placed closer together, thereby introducing an incommensurability between the periodicity of the confined crystal and the walls, a structure containing a soliton staircase arises in simulations without shear. Introducing shear increases the disorder in these systems until no solitons are visible anymore. Instead, similar structures like in the case without mismatch result. At high shear rates, configurations where the incommensurability of the crystalline structure is compensated by the creation of holes become relevant.

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“…Therefore, we assume that the deformation energy decreases with the distance r from the crystal/melt interface. In line with the findings of Binder et al [10,11] we assume that the dependence of the stress energy on the distance from a flat surface is described by an exponential decay law: …”

Section: The Modelmentioning

confidence: 74%