Crystal-like State Research Articles

Phase transitions of a few-electron system in a spherical quantum dot

The spin configurations of a spherical quantum dot, defined by a three-dimensional (3D) harmonic confinement potential, containing a few Coulomb Fermi particles (electrons or holes) are studied. Quantum transitions involving a spin transformation and a ``cold melting'' (from a Wigner crystal-like state, i.e., from regime of strongly correlated electrons, to a Fermi-liquid-like phase) is driven by the dimensionless quantum control parameter q (which is connected with steepness of the confinement potential) is demonstrated. The pair correlation and radial distribution functions which characterize electronic quantum delocalization are analyzed. The calculations using the unrestricted variational Hartree-Fock method (for the ground state at $T=0 \mathrm{K})$ and the more computer intensive quantum path integral Monte Carlo method (for $T\ensuremath{\ne}0 \mathrm{K})$ are performed and compared. For small q, the ground state of the three electron system is crystal-like and has ${C}_{3}$ symmetry, i.e., the maxima of electron density are located at the nodes of an equilateral triangle. The preferable spin configuration for small q is ``ferromagnetic,'' with total spin $S=3/2.$ As q rises, the widths of the one-electron wave functions grow and become overlapping. At a critical value ${q}_{1}$ the ground state changes from $S=3/2$ to $S=1/2$ and at the same time, asymmetry appears in the triangle (i.e., spontaneous breaking of the ${C}_{3}$ symmetry to ${C}_{2}$ symmetry). At a second critical value ${q}_{2}$ the electron distribution undergoes a symmetry phase transition, from trianglelike (with ${C}_{2}$ symmetry) to axial symmetric (with ${C}_{\ensuremath{\infty}}$ symmetry). As q grows further, we obtain a Fermi-liquid-like (non-interacting) electron configuration in the ground state $(S=1/2).$ In addition, the $S=3/2$ state, at a critical q value (which is slightly larger than ${q}_{1})$ undergoes a dramatic charge redistribution.

Trapped nonneutral plasmas, liquids, and crystals (the thermal equilibrium states)

Plasmas consisting exclusively of particles with a single sign of charge (e.g., pure electron plasmas and pure ion plasmas) can be confined by static electric and magnetic fields (in a Penning trap) and also be in a state of global thermal equilibrium. This important property distinguishes these totally unneutralized plasmas from neutral and quasineutral plasmas. This paper reviews the conditions for, and the structure of, the thermal equilibrium states. Both theory and experiment are discussed, but the emphasis is decidedly on theory. It is a huge advantage to be able to use thermal equilibrium statistical mechanics to describe the plasma state. Such a description is easily obtained and complete, including for example the details of the plasma shape and microscopic order. Pure electron and pure ion plasmas are routinely confined for hours and even days, and thermal equilibrium states are observed. These plasmas can be cooled to the cryogenic temperature range, where liquid and crystal-like states are realized. The authors discuss the structure of the correlated states separately for three plasma sizes: large plasmas, in which the free energy is dominated by the bulk plasma; mesoscale plasmas, in which the free energy is strongly influenced by the surface; and Coulomb clusters, in which the number of particles is so small that the canonical ensemble is not a good approximation for the microcanonical ensemble. All three cases have been studied through numerical simulations, analytic theory, and experiment. In addition to describing the structure of the thermal equilibrium states, the authors develop a thermodynamic theory of the trapped plasma system. Thermodynamic inequalities and Maxwell relations provide useful bounds on and general relationships between partial derivatives of the various thermodynamic variables.

Plasmas with a single sign of charge (an overview)

This paper presents a brief overview of recent theory and experiment for plasmas with a single sign of charge. In principle these plasmas can be confined forever in a state of thermal equilibrium that is guaranteed to be stable and quiescent. In practice confinement times of hours are routinely obtained. The plasmas can be cooled to the cryogenic temperature range where liquid and crystal-like states are predicted and observed. The plasmas provide experimental access to the parameter regime of strong magnetization where a many particle adiabatic invariant constrains the collisional dynamics. Also, the plasmas can be used to model the 2D vortex dynamics and turbulence of an ideal (incompressible and inviscid) fluid

Laser cooling of 171Yb+ ions in a linear paul trap

We report laser cooling of trapped 171Yb+ ions. The ions are confined in a linear Paul trap. Temperatures below 1 K have been achieved, and evidence of a phase transition to a crystal-like state has been observed. The metastable 2 D 3/2 level is drained using a transition at 609.1 nm not previously used for this purpose. Laser cooling of 171Yb+ may be of importance to the development of new microwave frequency standards.

Crystallization and characterization of crystallites in charge stabilized suspensions

Abstract For three different types of polymer latex particles with widely different particle charges the structure of suspensions before and after crystallization is investigated. A liquid-like ordered state was achieved by shear melting crystal-like ordered samples. The structure factors S(Q) of the liquid-like suspensions are analyzed in terms of the resealed mean spherical approximation (RMSA) of Hansen and Hayter. The Bragg diffraction pattern of the crystallized samples shows that the structure is b.c.c. It is found that the particle number concentration n and the distance of nearest neighbours in corresponding liquid- and crystal-like states differ by less than 4 %. In the second part of the paper, Bragg diffraction was used to determine the crystallite size distribution in samples of different particle concentration.

Theory of the intermediate rippled phase of phospholipid bilayers.

A mathematical model of the periodic, rippled P beta' phase of phosphatidylcholine is described. In this model the P beta' phase shows a periodic variation in membrane properties corresponding to a lateral periodic variation between fluid-like and crystal-like states. The model is based on a curvature-dependent Landau-de Gennes free-energy functional. Our proposed form of the curvature-dependent free energy remedies a subtle mathematical flaw in an earlier model having similar physical content [Falkovitz, M. F., Seul, M., Frisch, H. L. & McConnell, H. M. (1982) Proc. Natl. Acad. Sci. USA 79, 3918-3921].

Ultrasonic Study of High Pressure Phase in Polyethylene

Behaviors of transitions and the nature of high pressure phase in polyethylene are studied using methods of longitudinal and transverse ultrasonic waves, differential thermal analysis (DTA) and X-ray diffraction by PSPC X-ray system. Two anomalous absorption peaks of longitudinal wave agree with the normal phase to high pressure phase transition temperature and the high pressure phase to fused phase transition temperature as observed by DTA and X-ray diffraction, respectively. For the folded-chain crystal sample, the recrystallization phenomena by lamella thickening during the heating process has been discovered by the anomaly in longitudinal sound velocity. The result of transverse wave shows that the modulus of rigidity of high pressure phase is of the same order in magnitude as that of the fused state. Therefore, the high pressure phase should be a nematic liquid crystal-like state.