Generic properties of a quasi-one-dimensional classical Wigner crystal

Abstract

We studied the structural, dynamical properties and melting of a quasi-one-dimensional system of charged particles, interacting through a screened Coulomb potential. The ground state energy was calculated and, depending on the density and the screening length, the system crystallizes in a number of chains. As a function of the density (or the confining potential), the ground state configurations and the structural transitions between them were analyzed both by analytical and Monte Carlo calculations. The system exhibits a rich phase diagram at zero temperature with continuous and discontinuous structural transitions. We calculated the normal modes of the Wigner crystal and the magneto-phonons when an external constant magnetic field B is applied. At finite temperature the melting of the system was studied via Monte Carlo simulations using the modif ied Lindemann criterion (MLC). The melting temperature as a function of the density was obtained for different screening parameters. Reentrant melting as a function of the density was found as well as evidence of directional dependent melting. The single chain regime exhibits anomalous melting temperatures according to the MLC and as a check we study the pair correlation function at different densities and different temperatures, which allowed us to formulate a different criterion. Possible connection with recent theoretical and experimental results are discussed and experiments are proposed.

Formation of defects in multirow Wigner crystals

“…Assuming staggering in the x-direction between neighboring rows and inversion symmetry of the y-positions of the rows with respect to the wire axis, the number of minimization parameters is M/2 ((M − 1)/2) for even (odd) number of rows M , and the minimization is straightforward. Within these constraints, the minimization of the energy with respect to the electron configuration reveals 7,8,25 that a one-dimensional crystal is stable for densities ν < 0.78, whereas a zigzag chain forms at intermediate densities 0.78 < ν < 1.71. More rows appear as the density further increases.…”

“…Upon increasing density (and, thus, the interaction energy), or weakening the confining potential, the crystal deviates from its strictly one-dimensional structure. It has been shown that at a critical density, a transition to a zigzag crystal takes place 7,11,23,25,26 . Though not for electrons, this zigzag transition has indeed been observed using 24 Mg + ions in a quadrupole storage ring 27 .…”

“…The three-dimensional Wigner crystal and its two-dimensional counterpart have been extensively studied, and there exist beautiful experimental realizations of the latter using electrons trapped on the surface of liquid Helium [2][3][4][5] . More recently, Wigner crystallization in one dimension has received renewed interest [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] ; for recent reviews see Refs. 23 and 24.…”

Dusty plasma (Yukawa) rings

“…To overcome these drawbacks it may be possible to create a one-dimensional Coulomb ring [13] or dusty plasma ring [14] using a two-dimensional (2D) annular potential well. A dusty plasma ring will provide the most direct test of the theory for lattice waves in unbounded Yukawa chains [15], as well as a system with which to explore phenomena such as single-file diffusion [16] and the properties of quasi-one-dimensional systems [17].…”

Tunneling of hybridized pairs of electrons through a one-dimensional channel

“…The long-range Coulomb interaction between electrons becomes relatively important at low electron densities resulting in the formation of a 1D Wigner crystal [2,6,7]. But, the role played by the Coulomb repulsion between electrons is also made greater until it overcomes the confinement potential, as the density is increased, at which point the ground state and one of the excited states are interchanged [8] which may result in hybridization and anticrossing. In Refs.…”