Crystallization of a classical two-dimensional electron system: Positional and orientational orders

Crystallization of a classical two-dimensional one-component plasma (electrons interacting with the Coulomb repulsion in a uniform neutralizing positive background) is investigated with a molecular dynamics simulation. The positional and the orientational correlation functions are calculated for the first time. We have found an indication that the solid phase has a quasi-long-range (power-law) positional order along with a long-range orientational order. This indicates that, although the long-range Coulomb interaction is outside the scope of Mermin's theorem, the absence of ordinary crystalline order at finite temperatures applies to the electron system as well. The `hexatic' phase, which is predicted between the liquid and the solid phases by the Kosterlitz-Thouless-Halperin-Nelson-Young theory, is also discussed.Comment: 3 pages, 4 figures; Corrected typos; Double columne

Topological Defects, Orientational Order, and Depinning of the Electron Solid in a Random Potential

We report on the results of molecular dynamics simulation (MD) studies of the classical two-dimensional electron crystal in the presence disorder. Our study is motivated by recent experiments on this system in modulation doped semiconductor systems in very strong magnetic fields, where the magnetic length is much smaller than the average interelectron spacing $a_0$, as well as by recent studies of electrons on the surface of helium. We investigate the low temperature state of this system using a simulated annealing method. We find that the low temperature state of the system always has isolated dislocations, even at the weakest disorder levels investigated. We also find evidence for a transition from a hexatic glass to an isotropic glass as the disorder is increased. The former is characterized by quasi-long range orientational order, and the absence of disclination defects in the low temperature state, and the latter by short range orientational order and the presence of these defects. The threshold electric field is also studied as a function of the disorder strength, and is shown to have a characteristic signature of the transition. Finally, the qualitative behavior of the electron flow in the depinned state is shown to change continuously from an elastic flow to a channel-like, plastic flow as the disorder strength is increased.Comment: 31 pages, RevTex 3.0, 15 figures upon request, accepted for publication in Phys. Rev. B., HAF94MD

Generic properties of a quasi-one dimensional classical Wigner crystal

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 $modified$ $Lindemann$ $criterion$ (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, formulating a different criterion. Possible connection with recent theoretical and experimental results are discussed and experiments are proposed.Comment: 13 pages text, 21 picture

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

The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the Monte-Carlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and 1/r^{12} repulsive inter-particle interactions. The melting temperature for the five different lattice structures of the bilayer Wigner crystal is obtained, and a phase diagram is constructed as a function of the interlayer distance. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures. This is a consequence of the specific topology of the defects which are created with increasing temperature and which have a larger energy as compared to the defects in e.g. a hexagonal lattice.Comment: Accepted for publication in Physical Review