Melting of the Classical Bilayer Wigner Crystal: Influence of Lattice Symmetry

Abstract

The melting transition of the five different lattices of a bilayer crystal is studied using the Monte-Carlo technique. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures, which is a consequence of the specific topology of the temperature induced defects. A new melting criterion is formulated which we show to be universal for bilayers as well as for single layer crystals.PACS numbers: 64.60. Cn, 64.70.Dv, 73.20.Dx Wigner crystallization of electrons on the surface of liquid helium was first observed experimentally by Grimes and Adams [1]. In the same year, Nelson, Halperin [2], and Young [3] developed a theory for a two stage continuous melting of a two dimensional (2D) crystal which was based on the ideas of Berenzinskii [4], Kosterlitz and Thouless [5]. Whether melting of a 2D crystal is a first order transition and proceeds discontinuously as described by the theories of Kleinert [6] and Chui [7], or is a second order transition in which the crystal first transits into a hexatic phase retaining quasi-long-range orientational order and then melts into an isotropic fluid, is still an open question and a controversial issue. These studies of the melting transition of a 2D systems were directed to single layer crystals, which have the hexagonal symmetry. This is the most energetically favored structure for potentials of the form 1/r n [8]. Disorder will influence Wigner crystallization as was demonstrated recently in Refs. [9].In recent experiments on dusty plasmas [10] and on ion plasmas [11] few layer and bilayer crystals were observed. Bilayer systems exhibit a much richer crystal structure (five different lattice types) as function of the inter-layer distance. This allows us to study the influence of the lattice symmetry on melting. Previously, the different types of lattices and structural transitions in a multilayer crystal at T = 0 with parabolic confinement was analysed in [12,13]. Different classes of lattices of the double-layer crystal were specified in [14] and in [15] the stability of the classical bilayer crystal was analysed in the harmonic approximation.In this letter we study the melting of a classical bilayer crystal, using the Monte Carlo (MC) simulation technique. In the crystal phase the particles are arranged into two parallel layers in the (x, y)-plane which are a distance d apart in the z-direction. The layers contain equal density of particles n/2 and have close packed symmetry. A single layer crystal is a limiting case of a bilayer crystal with d = 0 and particle density n.We assume that the particles interact through an isotropic Coulomb (κ = 0) or screened repulsive potentialwhere q is the particle charge, ǫ the dielectric constant, r = (x, y,(z=0, d)) the position of the particle, and 1/κ is the screening length. The type of lattice symmetry at T = 0 depends on the dimensionless parameter ν = d/a 0 , where d is the interlayer distance and a 0 = 1/ πn/2 is the mean interparticle distance. Fo...

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

“…5(b) of Ref. [39]). Pairs of disclinations can be found in an energy range of (0.216 ÷ 0.285)k B T 0 (group 2 in Fig.…”

“…5(e) of Ref. [39]) are formed which causes a substantial decrease of the translational order. These isomers refer to the next energy range up to E ≃ 1.4k B T 0 (group 2).…”

“…5(a) of Ref. [39]) and has an energy E = 0.285k B T 0 . The point defects and disclinations bound into a quartet have only negligible effect on G θ and G tr (see Fig.…”

“…The equilibrium states of a bilayer crystal at different temperatures (T ) will be investigated using the Monte Carlo (MC) simulation technique. Preliminary resuls of this study were published in [39].…”

Electrostatics in soft matter

“…Crystalline bilayers made up of charged particles have been intensively studied these last years in the soft matter colloid community [158,159] as well as in the solid state physics (classical [160,161,162,163,164] and non-classical electrons [165,166,167] ) and dusty plasma communities [168,169]. The effective interaction between these constitutive mesoscopic macroions is neither hard-sphere like nor purely Coulombic, but it is rather described by an intermediate screened Coulomb [also called Yukawa or DLVO (Derjaguin-Landau-Verwey-Overbeek) [170,171]] due to the screening mediated by the additional microions present in the system.…”