Structure Of Topological Defects Research Articles

Nematic colloids entangled by topological defects

Assembly of colloidal particles in nematic liquid crystals is governed by the symmetry of building blocks and type of defects in the liquid crystalline orientation. Particles in a nematic act as nucleation sites for topological defect structures that are homotopic to point defects. The tendency for a minimal deformation free energy and topological constraints limit possible defect configurations to extended and localized defect loops. Here we report on a recently discovered colloidal binding, where particles are entangled by disclination loops. Nematic braids formed by such disclinations stabilize multi-particle objects and entrap particles in a complex manner. Observed binding potentials are highly anisotropic showing string-like behavior and can be of an order of magnitude stronger compared to non-entangled colloids. Controlling the assembly based on entangled disclination lines one can build multi-particle structures with potentially useful features (shapes, periodic structure, chirality, etc.) for photonic and plasmonic applications.

Boundary localized symmetry breaking and topological defects

We discuss the structure of topological defects in the context of extra dimensions where the symmetry breaking terms are localized. These defects develop structure in the extra dimension which differs from the case where symmetry breaking is not localized. This new structure can lead to corrections to the mass scale of the defects which is not captured by a simple effective theory obtained by integrating out the extra dimension. We also consider the Higgsless model of symmetry breaking and show that no finite energy defects appear in some situations where they might have been expected.

Three-dimensional parallel vortex rings in Bose-Einstein condensates

We construct three-dimensional structures of topological defects hosted in trapped wave fields, in the form of vortex stars, vortex cages, parallel vortex lines, perpendicular vortex rings, and parallel vortex rings, and we show that the latter exist as robust stationary, collective states of nonrotating Bose-Einstein condensates. We discuss the stability properties of excited states containing several parallel vortex rings hosted by the condensate, including their dynamical and structural stability.

Structural and electronic properties of the metal-metal intramoleular junctions of single-walled carbon nanotubes

Several intramolecular junctions (IMJs) connecting two metallic (11, 8) and (9, 6) carbon nanotubes along their common axis have been realized by using a layer-divided technique to the nanotubes and introducing the topological defects. Atomic structure of each IMJ configuration is optimized with a combination of density-functional theory (DFT) and the universal force field (UFF) method, based upon which a four-orbital tight-binding calculation is made on its electronic properties. Different topological defect structures and their distributions on the IMJ interfaces have been found, showing decisive effects on the localized density of states, while the sigma-pi coupling effect is negligible near Fermi energy (EF). Finally, a new IMJ model has been proposed, which probably reflects a real atomic structure of the M-M IMJ observed in the experiment [Science 291, 97 (2001)].

Optical properties of the semiconductor carbon nanotube intramolecular junctions

The π-orbital tight-binding model and sum-over-state method have been used to study the linear polarizability absorption spectra of several intramolecular junctions (IMJs) connecting two semiconductor single-wall carbon nanotubes (SWNTs), whose atomic structures are optimized with a combination of density-functional theory (DFT) and the universal force field (UFF) method. Our results indicate that IMJs optical properties are influenced by different topological defects and their distributions on the interfaces, making the absorption spectra exhibit some new characters, e.g., some new absorption peaks appear together with the original characteristic peaks of two SWNTs on either side. It is suggested that the optical absorption could be used for a supplemental experimental tool to distinguish the topological defect structures of IMJs.

Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement.

We investigate the orientation profile and the structure of topological defects of a nematic liquid crystal around a spherical particle using an adaptive mesh refinement scheme developed by us previously. The previous work [J. Fukuda et al., Phys. Rev. E 65, 041709 (2002)] was devoted to the investigation of the fine structure of a hyperbolic hedgehog defect that the particle accompanies and in this paper we present the equilibrium profile of the Saturn ring configuration. The radius of the Saturn ring r(d) in units of the particle radius R(0) increases weakly with the increase of Epsilon, the ratio of the nematic coherence length to R(0). Next we discuss the energetic stability of a hedgehog and a Saturn ring. The use of adaptive mesh refinement scheme together with a tensor orientational order parameter Q (alpha, beta) allows us to calculate the elastic energy of a nematic liquid crystal without any assumption of the structure and the energy of the defect core as in the previous similar studies. The reduced free energy of a nematic liquid crystal, F= F/L1RO, with L(1) being the elastic constant, is almost independent of Epsilon in the hedgehog configuration, while it shows a logarithmic dependence in the Saturn ring configuration. This result clearly indicates that the energetic stability of a hedgehog to a Saturn ring for a large particle is definitely attributed to the large defect energy of the Saturn ring with a large radius.

Topological defects in spinor condensates

We investigate the structure of topological defects in the ground states of spinor Bose-Einstein condensates with spin F=1 or F=2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.

Topological defects in schlieren textures of biaxial and uniaxial nematics.

Monte Carlo and theoretical studies of thin 3D films of biaxial and uniaxial nematics with tangential boundary conditions show distinct differences in structure and evolution of topological defects. In the uniaxial films, defects of strength k=+/-1 are point defects that bear no bulk singularity and disappear by annihilation with each other. In the biaxial films, k=+/-1 defects are true singular bulk disclinations that split into pairs of k=+/-1/2 lines; the latter disappear by annihilation processes of the type +1/2-1/2=0. These observed differences are of relevance for the current debate on the existence of biaxial phases.

Amorphization mechanism and defect structures in ion-beam-amorphized Si, Ge, and GaAs

We are studying ion-irradiation-induced amorphization in Si, Ge, and GaAs using molecular-dynamics simulations. Although high-energy recoils produce defects and amorphous pockets, we show that low-energy recoils (about 5--10 eV) can lead to a significant component of the athermal recrystallization of preexisting damage. For typical experimental irradiation conditions this recrystallization is, however, not sufficient to fully recrystallize larger amorphous pockets, which grow and induce full amorphization. We also examine the coordination and topological defect structures in Si, Ge, and GaAs observed in the simulations, and find that these structures can explain some experimentally observed features found in amorphous semiconductors. For irradiated amorphous GaAs, we suggest that long (about 2.8 \AA{}) and weak Ga-Ga bonds, also present in pure Ga, are produced during irradiation.

Topological Structure in the O(n) Symmetric Time-Dependent-Ginzburg-Landau Model

A new topological current in the O(n) symmetrical time-dependent-Ginzburg-Landau model is discussed. Using ϕ-mapping theory, this topological current is studied. It is shown that the inner structure of topological defects can be classified by Brouwer degrees and Hopf indices of the ϕ-mapping.

Statistical mechanics of magnetic bubble arrays. I. Topology and thermalization.

Bubble domains in thin magnetic garnet films are an experimentally accessible two-dimensional system with well-characterized properties. Bubble arrays can be directly viewed with polarized light using optical microscopy, digital imaging, and computer-video techniques. The structure and dynamics of topological defects can be studied in detail. We present observations of the interactions and dynamics of defects in magnetic bubble arrays. Quasithermal Brownian motion of bubbles in an applied ac magnetic field arises from microscopic substrate roughness. Experimental measurements of diffusive bubble motion are used to estimate the effective temperature, and the effective pinning energy and length scales for microscopic roughness in the garnet film.

Defects in smectic C* liquid crystals

We consider the structure and properties of various topological defects that can occur in smectic C* liquid crystals. The polarization field associated with disclinations, the effect of incommensuration on the structure of dispirations, some interesting situations in the interaction between dispiration and disclination and between dispirations themselves have been discussed in detail. The properties of cholesteric type disclinations and a possible model for the core structure of a wedge disclination have also been dealt with.

Classification scheme for statistical theories with unusual symmetries

Abstract A large class of theories with unusual symmetries is constructed and discussed from a unified viewpoint. These are statistical models with symmetries which correspond to an interpolation between standard globally-invariant theories and theories with a local symmetry. The models describe the dynamics of U(1) (or Z(N)) variables, eiπ, located at the sited of a lattice of arbitrary dimension and geometry. We describe a classification of these theories based on what we call their symmetry index: the value of n for which the hamiltonian of a d-dimensional system is invariant under the transformation π(x1,…,xd) → π (x1,…,xd) + Λ (x1,…,xd), where Λ satisfies a set of n linearly-independent constraints. We discuss how the critical properties and the structure of topological defects of a model are determined by d and n.