Disclination Core Research Articles

Trapping of isotropic droplets by disclinations in nematic liquid crystals controlled by surface anchoring and elastic constant disparity.

Linear defects such as dislocations and disclinations in ordered materials attract foreign particles since they replace strong elastic distortions at the defect cores. In this work, we explore the behavior of isotropic droplets nucleating at singular disclinations in a nematic liquid crystal, predesigned by surface photopatterning. Experiments show that in the biphasic nematic-isotropic region, although the droplets are attracted to the disclination cores, their centers of mass shift away from the core centers as the temperature increases. The shift is not random, being deterministically defined by the surrounding director field. The effect is explained by the balance of interfacial anchoring and bulk elasticity. An agreement with the experiment can be achieved only if the model accounts for the disparity of the nematic elastic constants; the so-called one-constant approximation, often used in the theoretical analysis of liquid crystals, produces qualitatively wrong predictions. In particular, the experimentally observed shift towards the bend region around a +1/2 disclination core can be explained only when the bend constant is larger than the splay constant. The described dependence of the precise location of a foreign inclusion at defect cores on the elastic and surface anchoring properties can be used in rational design of microscale architectures.

Vortex solitons in topological disclination lattices

Abstract The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in these systems, as the vortex state in the disclination lattice bifurcates from its linear topological counterpart, while the position of its propagation constant within the bandgap and localization can be controlled by its power. It is shown that vortex solitons are characterized by strong field confinement at the disclination core due to their topological nature, leading to enhanced stability. Simultaneously, the global discrete rotational symmetry of the disclination lattice imposes restrictions on the maximal possible topological charge of such vortex solitons. The results illustrate the strong stabilizing action that topologically nontrivial structures may exert on excited soliton states, opening new prospects for soliton-related applications.

A computational study of nematic core structure and disclination interactions in elastically anisotropic nematics.

A singular potential method in the Q tensor order parameter representation of a nematic liquid crystal is used to study the equilibrium configuration of a disclination dipole. Unlike the well studied isotropic limit (the so called one constant approximation), we focus on the case of anisotropic Frank elasticity (bend/splay elastic constant contrast). Prior research has established that the singular potential method provides an accurate description of the tensor order parameter profile in the vicinity of a disclination core of a highly anisotropic lyotropic chromonic liquid crystal. This research is extended here to two interacting disclinations forming a dipole configuration. The director angle is shown to decay in the far field inversely with distance to the dipole as is the case in the isotropic limit, but with a different angular dependence. Therefore elastic constant anisotropy modifies the elastic screening between disclinations, with implications for the study of ensembles of defects as seen, for example, in active matter in the extended system limit.

Observation of nonlinear disclination states

Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations. Appearance of these topological states is consistent with the bulk-disclination correspondence principle, and is due to the filling anomaly that results in fractional charges to the boundary unit cells. So far, topological disclination states were observed only in the linear regime, while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally. We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique. The transition between nontopological and topological phases in such structures is controlled by the Kekulé distortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I, corner-II, and extended edge states at the outer edge of the structure. We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and, hence, their spatial localization can be controlled by their power. Nonlinear disclination states can be efficiently excited by Gaussian input beams, but only if they are focused into the waveguides belonging to the disclination core, where such topological states reside. Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science, including Bose-Einstein and polariton condensates, where potentials with the disclinations can be created.

Kinematics and dynamics of disclination lines in three-dimensional nematics

An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameterQis derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues ofQcross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives ofQon the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation forQ, analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. The analytic results are shown to be in agreement with three-dimensional numerical calculations based on a singular Maier–Saupe free energy that allows for anisotropic elasticity.

Photonic topological pump between chiral disclination states

Topological pump describes the quantized transport of charges (or particles) in the absence of a net external electric or magnetic field. Here the authors show that topological pumps can happen between disclination states with different chiralities in a distorted lattice. By constructing structures with one and two disclination cores, they achieve topological pumping both within a single disclination core and between different disclination cores.

Observation of Degenerate Zero-Energy Topological States at Disclinations in an Acoustic Lattice.

Building upon the bulk-boundary correspondence in topological phases of matter, disclinations have recently been harnessed to trap fractionally quantized density of states (DOS) in classical wave systems. While these fractional DOS have associated states localized to the disclination's core, such states are not protected from deconfinement due to the breaking of chiral symmetry, generally leading to resonances which, even in principle, have finite lifetimes and suboptimal confinement. Here, we devise and experimentally validate in acoustic lattices a paradigm by which topological states bind to disclinations without a fractional DOS but which preserve chiral symmetry. The preservation of chiral symmetry pins the states at the midgap, resulting in their protected maximal confinement. The integer DOS at the defect results in twofold degenerate states that, due to symmetry constraints, do not gap out. Our study provides a fresh perspective about the interplay between symmetry protection in topological phases and topological defects, with possible applications in classical and quantum systems alike.

All-dielectric photonic crystal with unconventional higher-order topology

Photonic crystals (PhCs) have been demonstrated as a versatile platform for the study of topological phenomena. The recent discovery of higher-order topological insulators introduces new aspects of topological PhCs that are yet to be explored. Here, we propose an all-dielectric PhC with an unconventional higher-order band topology. Besides the conventional spectral features of gapped edge states and in-gap corner states, topological band theory predicts that the corner boundary of the higher-order topological insulator hosts a 2/3 fractional charge. We demonstrate that in the PhC such a fractional charge can be verified from the local density-of-states of photons, through the concept of local spectral charge as an analog of the local electric charge due to the band filling anomaly in electronic systems. Furthermore, we show that by introducing a disclination in the proposed PhC, localized states and a 2/3 fractional spectral charge emerge around the disclination core. The emergence of the fractional spectral charges and topological boundary modes here, however, is distinct from the known cases; particularly by the 2/3 fractional spectral charges and the unique topological indices. The predicted effects can be readily observed in the state-of-the-art experiments and may lead to potential applications in integrated and quantum photonics.

Atomistic simulation of interaction between wedge disclination and self-interstitial atom in bcc tungsten

Molecular dynamics method has been employed to investigate the interaction between wedge disclination and self-interstitial atom in bcc tungsten. Long-range tensile stress field is shown around the disclination. The interaction energy between self-interstitial atom and the disclination ranges from −1eVto −6.13eV, which decreases with self-interstitial atom closer to the disclination core. Self-interstitial atoms around the disclination can be absorbed by the edge dislocations of the disclination, leading to a negative climb and thus reduction of the strain energy. It can be concluded that absorption of self-interstitial atoms by the wedge disclination is an energy downhill process, and disclination can serve as an effective sink for eliminating the radiation-induced self-interstitial atoms in bcc tungsten.

A revisit of the elastic fields of straight disclinations with new solutions for a rigid core

The classical solutions for straight disclinations in an infinite elastic solid have been obtained by integrating the results for disclination densities. In this paper, the equilibrium equations are solved directly for straight twist and wedge disclinations, subject to the boundary conditions of the defects and rigid body translations/rotations. For a twist or wedge disclination in an infinite solid, the current solutions, based on a core fixed at a point to remove rigid body motion, differ from the classical ones by the constant $$-\hbox {log }r_{i}$$ , where $$r_{i }$$ is the radius of the disclination core. For a wedge disclination in an infinitely long cylinder, additional terms of the form 1 / r in the radial displacement and $$1/r^{2}$$ in the stresses appear in the solutions. The dependence of the current and classical results on the Lame constants highlights significant differences near the disclination line, which will impact studies of disclination relaxation such as crack nucleation and core amorphization. The energy of a singular wedge disclination in a cylinder without a core mostly underestimates that of a wedge disclination with a core.

Wedge disclinations in the shell of a core–shell nanowire within the surface/interface elasticity

The elastic behaviors of a two-axes dipole of wedge disclinations and an individual wedge disclination located inside the shell of a free standing core–shell nanowire is studied within the surface/interface elasticity theory. The corresponding boundary value problem is solved using complex potential functions, defined through modeling the disclination dipole by two finite walls of infinitesimal edge dislocations. The stress field, disclination strain energies and image forces acting on the disclinations, are calculated and studied in detail. It is shown that the stresses are rather inhomogeneous across the nanowire cross section, change their signs and reach local maxima and minima far from the disclination lines in the bulk or on the surface of the nanowire. For negative values of the surface/interface modulus and relatively small values of the ratio of the shell and core shear moduli, the surface/interface effect manifests itself through non-classical stress oscillations along the shell free surface in the case of a disclination dipole and core–shell interface in both the cases of a disclination dipole and an individual disclination. The non-classical solution for the strain energy deviates from the classical solution with different effects caused by the surface/interface moduli on the wedge disclination dipole and an individual disclination. When the core is softer than the shell, the dipole with radial orientation of its arm has an unstable equilibrium position in the shell. In general, if the surface/interface modulus is positive, the surface/interface effects are rather weak; however, if it is negative, the effect can be very strong, especially near the shell surface.

Interaction between wedge disclination dipoles and core–shell nanowires with interface effects

Abstract In order to understand the influence of disclinations on mechanical properties of nanostructured composite materials, the interaction between a wedge disclination dipole and core–shell nanowires with interface effects is investigated. By using the complex variable method, the analytical solutions of complex potentials are derived for the interaction of a wedge disclination dipole and a core–shell nanowire considering interface effects. The stress fields, the elastic strain energy and the force acting on the wedge disclination dipole center are obtained. The influence of the feature of disclination dipole, the nanoscale coating thickness, the uniform eigenstrain and the material elastic dissimilarity on the equilibrium location and the stability of the dipole is studied when the size of the core–shell nanowire is reduced to nanometer scale. The results show that the impact of interface stresses on the equilibrium and the motion of the dipole near the core–shell nanowire is significant, namely, interface stresses have important effect on the strengthening and toughening of the nanostructured composite materials. The material properties of coating layer are dominant factors in the influence of the equilibrium location and the stability of disclination dipole for serious mismatch (i.e. very hard or very soft) and/or thick coating layer.

First-principles-based mesoscale modeling of the solute-induced stabilization of 〈1 0 0〉 tilt grain boundaries in an Al–Pb alloy

A first-principles disclination structural units (DSUM) model was used to calculate the energies of 12 〈0 0 1〉 symmetric tilt grain boundaries in Al for a pure system and a system in which Pb atoms substitute for Al at one-half of the lattices sites along the interfacial plane. The grain boundaries are modeled as disclination dipole walls with energies given as a weighted sum of individual disclination energies determined from special low-sigma structures, elastic terms and disclination core energies. Predictions of the DSUM using the bulk Al shear modulus and Poisson’s ratio in the elastic and core energy terms are found to be comparable to energies for fully atomistic simulations calculated using a modified embedded-atom method (MEAM) potential. No relation between grain boundary energies in pure Al and the degree of stabilization due to Pb doping was found. The DSUM parameterized to density functional theory calculations predicts a ∼50% reduction in the energy anisotropy with respect to angle due to doping compared to the pure system, while MEAM calculations yield no appreciable reduction in the energy anisotropy.

Point-Defect Haloing in Curved Nematic Films

We investigate the correlation between the point disclination energies and the surface curvature modulation of nematic liquid crystal membranes with a Gaussian bump geometry. Due to the correlation, disclinations feel an attractive force that confines them to an annulus region, resulting in a halo distribution around the top of the bump. The halo formation is a direct consequence of the nonzero Gaussian curvature of the bump that affects preferable configurations of liquid crystal molecules around the disclination core.

Self-winding of helices in plant tendrils and cellulose liquid crystal fibers

Passiflora edulis, like other climbing plants, possesses long, tender, soft, curly and flexible organs called tendrils whose circumnutation allows the plant to find support. Tendrils curl into spirals or twist into a helix, often of one handedness over half of its length and of the opposite handedness over the other half, the two halves being connected by a short straight section – a perversion, depending on whether they are supported at just one end or supported at both ends, respectively. This is a consequence of an intrinsic curvature of the tendrils. We report on liquid crystalline cellulosic fibers and jets, which mimic the shapes of helical tendril structures. Liquid crystalline and isotropic cellulosic precursor solutions of curved and straight fibers are examined using nuclear magnetic resonance imaging (MRI) and polarizing optical microscopy (POM) techniques to determine morphological and structural features contributing to fiber curvature. We study the subtle physical mechanisms responsible for self-winding behavior as a result of the intrinsic curvature due to the non-uniform deformation of filaments. In the case of liquid-crystalline cellulosic fibers, this is due to a core of disclination forming off-axis along the filament. We also highlight the critical dependence of the helical structures on temperature, which offers a potential for direct fabrication of biocompatible tunable high-surface area membranes with mechanical adaptability.

Surface disclination cores in the B2 phase of bent-shaped molecules described by the Peierls–Nabarro model

The Peierls–Nabarro model, originally proposed to describe dislocation core in solids, is used to model core structures of 2π- and π-surface disclinations in the B2 phase of bent-shaped molecules. Structures of disclination cores are determined by surface anchoring. Core parameters as core widths (and positions of two partial π-disclinations as parts comprising 2π-disclination) are estimated using surface anchoring energy. Disclination core widths are usually narrow for strong anchoring. In such a case they are barely observable; nevertheless, they can exist.

Atomistic simulations of the tensile strength of a disclinated bicrystalline nanofilm

The tensile strength of a metallic bicrystalline nanofilm containing a wedge disclination in the middle of a grain boundary (GB) terminating at the film surfaces was studied via atomistic simulations. The results show that an increase in the disclination power strengthens the film, which is contrary to intuition, if a crack initiates at one end of the terminated GB, whereas it weakens the film if a crack initiates at the disclination core. Both the strengthening and weakening demonstrate a size effect for film thickness in the range 10–20 nm, and are also significantly influenced by the GB misorientation. It is further shown that the strength can be increased to ∼80% of the theoretical strength of a defect-free film by introducing a disclination of moderate power in the GB.

Incoherent structural relaxation of fivefold twinned nanowires

Boron carbide nanowires with a fivefold twinned structure have been shown to have regular spaced microtwin lamellas localized in one of the crystalline segments. This defect structure is interpreted as incoherent structural relaxation to relieve the angular excess. A structural model, in terms of a disclination core surrounded by a small angle grain boundary with an intersecting microtwin lamella pair structure, has been proposed and strain analyses suggest it could be a common phenomena for nanowires with large angular mismatch and small twinning formation energy.

Computer simulation of crack formation in a nickel bicrystal nanowire containing a wedge disclination

Crack formation in a nickel bicrystal wire of radius 16 nm with a negative junction disclination lying along the axis has been studied by computer simulation. It has been revealed that at a disclination strength exceeding some critical value (approximately 17°), a crack is formed in the region of the disclination core; the crack represents an asymmetric two-sided wedge elongated along the grain boundary. The equilibrium length of the crack increases with increasing disclination strength. Disclinations with a strength that is less than critical can exist in nanocrystals obtained by compacting nanopowders and control their properties to a significant extent.

Continuum and all-atom description of the energetics of graphene nanocones

Energies of graphene nanocones with 1–5 pentagonal disclinations are studied on anatomically detailed level. The numerical results are interpreted in terms of three differentcontributions to the cone energy: the disclination core energy, the bending energy of thecone surface, and the ‘line tension’ energy of the cone edge that originates in reducedcoordination of carbon atoms situated at the edge. This continuum description allows for aconstruction of analytic expressions for the cone energetics and indicates different regimesof cone sizes in which cones with a particular number of disclinations are preferredenergywise. An important result of the study is that the energetics of various types of conesprofoundly depends upon whether the dangling carbon bonds at the cone basisare saturated by hydrogen atoms or not. This may be of use for explaining thedifferences in the yields of various cone types in different production processes.