Topological Point Defects Research Articles

Reactivity Enhancement and Fingerprints of Point Defects on a MoS2 Monolayer Assessed by ab Initio Atomic Force Microscopy

The effect of topological point defects, vacancies, and substitutional antisites, in a monolayer MoS2, has been analyzed by ab initio atomic force microscopy (AFM) simulations. Our calculations based on density functional theory (DFT) show how a careful combination of measurements at different distances enables the characterization of each defect on the monolayer in future noncontact AFM experiments. Taking into account the minimum in the forces, atomic displacements, and charge transfer, a great enhancement has been found on the reactivity of MoS2 when some defects are included in the monolayer. We demonstrate the strong influence of the chemical composition of the tip and the environment of the chosen site on the calculated force. Furthermore, we show that the results can be mostly understood considering a standard metal–semiconductor junction model. Finally, our study exhibits the possibility of local atomic doping using the AFM tip.

Topological solitons in optical oscillators

We present an overview of theoretical and experimental works on self-sustaining localized structures—spatial solitons—which can be formed in optical bistable oscillators with laser and/or parametric gain. The main attention is paid to the existence and dynamical properties of spatial solitons containing phase and polarization topological defects including vortices, points of circular polarizations and lines of linear polarization, domain walls and composed domain walls with Néel point topological defects.

Annihilation dynamics of topological monopoles on a fiber in nematic liquid crystals.

We use the laser tweezers to create isolated pairs of topological point defects in a form of radial and hyperbolic hedgehogs, located close and attracted to a thin fiber with perpendicular surface orientation of nematic liquid crystal molecules in a thin planar nematic cell. We study the time evolution of the interaction between the two monopoles by monitoring their movement and reconstructing their trajectories and velocities. We find that there is a crossover in the pair interaction force between the radial and hyperbolic hedgehog. At small separation d, the elastic force between the opposite monopoles results in an increase of the attractive force with respect to the far field, and their relative velocity v scales as a v(d)∝d^{-2±0.2} power law. At large separations, the two oppositely charged monopoles can either attract or repel with constant interaction force. We explain this strange far-field behavior by the experimental inaccuracy in setting the fiber exactly perpendicular to the cell director.

Reversal of helicoidal twist handedness near point defects of confined chiral liquid crystals

Handedness of the director twist in cholesteric liquid crystals is commonly assumed to be the same throughout the medium, determined solely by the chirality of constituent molecules or chiral additives, albeit distortions of the ground-state helicoidal configuration often arise due to the effects of confinement and external fields. We directly probe the twist directionality of liquid crystal director structures through experimental three-dimensional imaging and numerical minimization of the elastic free energy and show that spatially localized regions of handedness opposite to that of the chiral liquid crystal ground state can arise in the proximity of twisted-soliton-bound topological point defects. In chiral nematic liquid crystal confined to a film that has a thickness less than the cholesteric pitch and perpendicular surface boundary conditions, twisted solitonic structures embedded in a uniform unwound far-field background with chirality-matched handedness locally relieve confinement-imposed frustration and tend to be accompanied by point defects and smaller geometry-required, energetically costly regions of opposite twist handedness. We also describe a spatially localized structure, dubbed a "twistion," in which a twisted solitonic three-dimensional director configuration is accompanied by four point defects. We discuss how our findings may impinge on the stability of localized particlelike director field configurations in chiral and nonchiral liquid crystals.

Topological Point Defects in Relaxor Ferroelectrics.

First-principles-based effective Hamiltonian simulations are used to reveal the hidden connection between topological defects (hedgehogs and antihedgehogs) and relaxor behavior. Such defects are discovered to predominantly lie at the border of polar nanoregions in both Ba(Zr_{0.5}Ti_{0.5})O_{3} (BZT) and Pb(Sc_{0.5}Nb_{0.5})O_{3} (PSN) systems, and the temperature dependency of their density allows us to distinguish between noncanonical (PSN) and canonical (BZT) relaxor behaviors (via the presence or absence of a crossing of a percolation threshold). This density also possesses an inflection point at precisely the temperature for which the dielectric response peaks. Moreover, hedgehogs and antihedgehogs are found to be mobile excitations, and the dynamical nature of their annihilation is demonstrated (using simple hydrodynamical arguments) to follows laws, such as those of Vogel-Fulcher and Arrhenius, that are characteristic of dipolar relaxation kinetics of relaxor ferroelectrics.

Frustration and Self-Ordering of Topological Defects in Ferroelectrics.

A first-principles-based effective Hamiltonian technique is used to investigate the interplay between geometrical frustration and the ordering of topological defects in a ferroelectric nanocomposite consisting of a square array of BaTiO_{3} nanowires embedded in a Ba_{0.15}Sr_{0.85}TiO_{3} matrix. Different arrangements of the wires' chiralities geometrically frustrate the matrix, which in response exhibits point topological defects featuring self-assembled ordered structures spatially fluctuating down to the lowest temperatures. These fluctuations thereby endow the system with residual configurational entropy from which many properties characteristic of geometric frustration, such as the ground state degeneracy and the broadness of the dielectric response, are further found to originate.

Two-dimensional hexagonal smectic structure formed by topological defects.

A two-dimensional hexagonal smectic structure formed by point topological defects and intersecting defect walls was discovered. This unique structure was predicted theoretically about 30 years ago but not observed. For a long time the hexagonal structure was a challenge for experimentalists. A different type of self-organization in smectic films was found and used to form the hexagonal structure. Methods applied for building the hexagonal phase can be used for the formation of complicated liquid-crystal structures.

Stick-slip motion of surface point defects prompted by magnetically controlled colloidal-particle dynamics in nematic liquid crystals

We explore the dynamics of topological point defects on surfaces of magnetically responsive colloidal microspheres in a uniformly aligned nematic liquid crystal host. We show that pinning of the liquid crystal director to a particle surface with random nanostructured morphology results in unexpected translational dynamics of both particles and topological point defects on their surfaces when subjected to rotating magnetic fields. We characterize and quantify the "stick-slip" motion of defects as a function of field rotation rates as well as temperature, demonstrating the roles played by the competition of elastic forces, surface anchoring, and magnetic torques on the sphere as well as random-surface-mediated pinning of the easy axis of the nematic director on colloidal microspheres. We analyze our findings through their comparison to similar dynamic processes in other branches of science.

Quantum gases. Observation of isolated monopoles in a quantum field.

Topological defects play important roles throughout nature, appearing in contexts as diverse as cosmology, particle physics, superfluidity, liquid crystals, and metallurgy. Point defects can arise naturally as magnetic monopoles resulting from symmetry breaking in grand unified theories. We devised an experiment to create and detect quantum mechanical analogs of such monopoles in a spin-1 Bose-Einstein condensate. The defects, which were stable on the time scale of our experiments, were identified from spin-resolved images of the condensate density profile that exhibit a characteristic dependence on the choice of quantization axis. Our observations lay the foundation for experimental studies of the dynamics and stability of topological point defects in quantum systems.

Instability of point defects in a two-dimensional nematic liquid crystal model

We study a class of symmetric critical points in a variational 2D Landau–de Gennes model where the state of nematic liquid crystals is described by symmetric traceless 3×3 matrices. These critical points play the role of topological point defects carrying a degree k2 for a nonzero integer k. We prove existence and study the qualitative behavior of these symmetric solutions. Our main result is the instability of critical points when |k|≥2.

Topological defects in smectic islands in freely suspended films

Textures created by point topological defects in defects in polar smectic films have been studied. Such defects have been created by the dynamic method (substance from a very thin film does not have time to approach its edges and thicker islands with a topological defect are controllably formed). Topological defects have been studied in smectic islands with a thickness of six to eight molecular layers in a film with a thickness of two molecular layers. Competition between two-dimensional orientational elasticity in islands and the orientation of the director at the boundary of smectic islands results in different configurations of the field of the c-director created by a topological defect. A transition between configurations occurs at a change in the dimension of islands and depends on the dipole polarization of a liquid crystal. The comparison of the numerical calculations of the structure of topological defects with experimental data has allowed determining the dependence of the anisotropy of the two-dimensional orientational elasticity on the polarization of smectic films.

Anyonic symmetries and topological defects in Abelian topological phases: An application to theADEclassification

We study symmetries and defects of a wide class of two dimensional Abelian topological phases characterized by Lie algebras. We formulate the symmetry group of all Abelian topological field theories. The symmetries relabel quasiparticles (or anyons) but leave exchange and braiding statistics unchanged. Within the class of $ADE$ phases in particular, these anyonic symmetries have a natural origin from the Lie algebra. We classify one dimensional gapped phases along the interface between identical topological states according to symmetries. This classification also applies to gapped edges of a wide range of fractional quantum spin Hall(QSH) states. We show that the edge states of the $ADE$ QSH systems can be gapped even in the presence of time reversal and charge conservation symmetry. We distinguish topological point defects according to anyonic symmetries and bound quasiparticles. Although in an Abelian system, they surprisingly exhibit non-Abelian fractional Majorana-like characteristics from their fusion behavior.

Geometrically unrestricted, topologically constrained control of liquid crystal defects using simultaneous holonomic magnetic and holographic optical manipulation.

Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.

The atomic scale structure of nanographene platelets studied by X-ray diffraction, high-resolution transmission electron microscopy and molecular dynamics

The atomic structure of commercially available nanographene platelets has been studied by high energy X-ray diffraction, high-resolution transmission electron microscopy, X-ray photoelectron spectroscopy and molecular dynamics simulations using the reactive empirical bond order potential. Atomic models of the structure have been constructed and then relaxed using the molecular dynamics method and the model based simulations are compared with the experimental data both in reciprocal and real space. All model relaxations and the X-ray diffraction experiments have been carried out at 300K. The proposed models consisting of about 2500 carbon atoms arranged within four graphitic layers with a diameter of 46Å, reproduced correctly all features of the experimental data. The atomic arrangement within an individual layer can be described in terms of the paracrystalline ordering, in which lattice distortions propagate proportionally to the square root of interatomic distances. The paracrystalline structure was simulated by introducing the topological point defects such as the Stone–Thrower–Wales defects, single- and double-vacancies, randomly distributed in the network. Such defects lead to curvature of individual layers and this effect was also analyzed. The generated models are related to the observations by high-resolution transmission electron microscopy.

Γ-Convergence Analysis of Systems of Edge Dislocations: the Self Energy Regime

This paper deals with the elastic energy induced by systems of straight edge dislocations in the framework of linearized plane elasticity. The dislocations are introduced as point topological defects of the displacement-gradient fields. Following the core radius approach, we introduce a parameter \({\varepsilon > 0}\) representing the lattice spacing of the crystal, we remove a disc of radius \({\varepsilon}\) around each dislocation and compute the elastic energy stored outside the union of such discs, namely outside the core region. Then, we analyze the asymptotic behaviour of the elastic energy as \({\varepsilon \rightarrow 0}\) , in terms of Γ-convergence. We focus on the self energy regime of order \({\log\frac{1}{\varepsilon}}\) ; we show that configurations with logarithmic diverging energy converge, up to a subsequence, to a finite number of multiple dislocations and we compute the corresponding Γ-limit.

Optically generated reconfigurable photonic structures of elastic quasiparticles in frustrated cholesteric liquid crystals

We describe laser-induced two-dimensional periodic photonic structures formed by localized particle-like excitations in an untwisted confined cholesteric liquid crystal. The individual particle-like excitations (dubbed "Torons") contain three-dimensional twist of the liquid crystal director matched to the uniform background director field by topological point defects. Using both single-beam-steering and holographic pattern generation approaches, the periodic crystal lattices are tailored by tuning their periodicity, reorienting their crystallographic axes, and introducing defects. Moreover, these lattices can be dynamically reconfigurable: generated, modified, erased and then recreated, depending on the needs of a particular photonic application. This robust control is performed by tightly focused laser beams of power 10-100 mW and by low-frequency electric fields at voltages ~10 V applied to the transparent electrodes.

Quantum destruction of spiral order in two-dimensional frustrated magnets

We study the fate of spin-1/2 spiral-ordered two-dimensional quantum antiferromagnets that are disordered by quantum fluctuations. A crucial role is played by the topological point defects of the spiral phase, which are known to have a Z2 character. Previous works established that a nontrivial quantum spin-liquid phase results when the spiral is disordered without proliferating the Z2 vortices. Here, we show that when the spiral is disordered by proliferating and condensing these vortices, valence-bond solid ordering occurs due to quantum Berry phase effects. We develop a general theory for this latter phase transition and apply it to a lattice model. This transition potentially provides a new example of a Landau-forbidden deconfined quantum critical point.

Surface Alignment, Anchoring Transitions, Optical Properties and Topological Defects in Nematic Bent-Core Materials C7 and C12

We address the status of oxadiazole mesogens, C7 and C12, reported to show the biaxial nematic phase, by exploring material aspects (chemical stability, surface anchoring, optical and dielectric properties, topological defects) linked to the type of nematic order. We demonstrate that the isogyres splitting in conoscopic patterns of homeotropic state depends on sample thickness and is associated with variations of molecular tilt along the normal to substrates. We observe isolated topological point defects (boojums and hedgehogs), as well as nonsingular “escaped” disclinations pertinent only to the uniaxial nematic order. Our conclusion is that C7 and C12 feature only a uniaxial nematic phase and the apparent biaxiality is caused by surface effects.

Fractionally charged topological point defects on the kagome lattice

We study a two-dimensional system of spin-polarized fermions on the kagome lattice at filling fraction f=1/3 interacting through a nearest-neighbor interaction V. Above a critical interaction strength V_c a charge-density wave with a broken Z_3 symmetry is stabilized. Using the unrestricted mean-field approximation, we present several arguments showing that elementary topological point defects in the order parameter bind a fractional charge. Our analysis makes use of two appealing properties of the model: (i) For weak interaction, the low-energy degrees of freedom are described by Dirac fermions coupled to a complex-valued mass field (order parameter). (ii) The nearest-neighbor interaction is geometrically frustrated at filling f=1/3. Both properties offer a route to fractionalization and yield a consistent value 1/2 for the fractional charge as long as the symmetry between the up and the down triangles of the kagome lattice is preserved. If this symmetry is violated, the value of the bound charge varies continuously with the strength of the symmetry-breaking term in the model. In addition, we have numerically computed the confining potential between two fractionally charged defects. We find that it grows linearly at large distances but can show a minimum at a finite separation for intermediate interactions. This indicates that the polaron state, formed upon doping the charge-density wave, can be viewed as a bound state of two defects.

Counting Majorana zero modes in superconductors

A counting formula for computing the number of (Majorana) zero modes bound to topological point defects is evaluated in a gradient expansion for systems with charge-conjugation symmetry. This semi-classical counting of zero modes is applied to some examples that include graphene and a chiral $p$-wave superconductor in two-dimensional space. In all cases, we explicitly relate the counting of zero modes to Chern numbers.