Geometrical defects in two-dimensional melting of many-particle Yukawa systems

Melting, freezing, and dynamics of two-dimensional dipole systems in screening bulk media

This paper reports on the molecular dynamics simulations of classical two-dimensional (2D) electric dipole systems. The properties of 2D systems with bare (nonscreened) and screened dipole-dipole interactions have been investigated. Based on the polygon construction method, we present simulation results on the phase transition, and we locate the melting and freezing points of 2D dipole systems in terms of a polygon disorder parameter, with the polygon disorder parameter being the sum of nontriangular polygon order parameters. It was found that the phase transition of the system occurs when the polygon disorder parameter has a value 0.165. This result was cross-checked by using both local and overall orientational order parameters. We also identified that the value of the average local orientational order parameter at the phase transition point is 0.67. These results are valid for the ordinary (bare) dipole-dipole interaction as well as the screened dipole-dipole interaction, and they are expected to be general for other 2D systems with repulsive pair interaction. We observed that both melting and freezing points shift to lower values of temperature due to screening. In the liquid state, the radial distribution function and polygon construction method show the loss of order in a structure as screening becomes more severe. Furthermore, the impact of screening on the system's collective excitation spectra and diffusive characteristics at liquid and solid states has been studied. Results show the decrease in the values of both longitudinal and transverse sound speeds and the emergence of anomalous superdiffusive motion in the liquid state due to screening.

Topological vacancies in spherical crystals

Understanding geometric frustration of ordered phases in two-dimensional condensed matter on curved surfaces is closely related to a host of scientific problems in condensed matter physics and materials science. Here, we show how two-dimensional Lennard-Jones crystal clusters confined on a sphere resolve geometric frustration and form pentagonal vacancy structures. These vacancies, originating from the combination of curvature and physical interaction, are found to be topological defects and they can be further classified into dislocational and disclinational types. We analyze the dual role of these crystallographic defects as both vacancies and topological defects, illustrate their formation mechanism, and present the phase diagram. The revealed dual role of the topological vacancies may find applications in the fabrication of robust nanopores. This work also shows the promising potential of exploiting richness in both physical interactions and substrate geometries to create new types of crystallographic defects, which have strong connections with the design of crystalline materials.

Polydispersity-driven topological defects as order-restoring excitations

The engineering of defects in crystalline matter has been extensively exploited to modify the mechanical and electrical properties of many materials. Recent experiments on manipulating extended defects in graphene, for example, show that defects direct the flow of electric charges. The fascinating possibilities offered by defects in two dimensions, known as topological defects, to control material properties provide great motivation to perform fundamental investigations to uncover their role in various systems. Previous studies mostly focus on topological defects in 2D crystals on curved surfaces. On flat geometries, topological defects can be introduced via density inhomogeneities. We investigate here topological defects due to size polydispersity on flat surfaces. Size polydispersity is usually an inevitable feature of a large variety of systems. In this work, simulations show well-organized induced topological defects around an impurity particle of a wrong size. These patterns are not found in systems of identical particles. Our work demonstrates that in polydispersed systems topological defects play the role of restoring order. The simulations show a perfect hexagonal lattice beyond a small defective region around the impurity particle. Elasticity theory has demonstrated an analogy between the elementary topological defects named disclinations to electric charges by associating a charge to a disclination, whose sign depends on the number of its nearest neighbors. Size polydispersity is shown numerically here to be an essential ingredient to understand short-range attractions between like-charge disclinations. Our study suggests that size polydispersity has a promising potential to engineer defects in various systems including nanoparticles and colloidal crystals.

Topological defects in flat geometry: the role of density inhomogeneity

Topological defects are found in particles confined to planar disks interacting via the 1/r Coulomb potential. The total interior topological charge is found to monotonically converge to a negative value as the energy decreases during the relaxation process regardless of initial configurations; it is more negative in a larger cluster. The comparison with a uniform hyperbolic tessellation reveals an underlying hyperbolic structure in a low-energy configuration where the particle density increases from the center of the disk to its boundary. An elliptic structure is identified in an opposite particle distribution where the particle density decreases from the center to the edge of the disk. The novel mechanism of density inhomogeneity driven topological defects as well as the underlying geometric structure may shed light in understanding a wide variety of relevant systems.