Formation Of Topological Defects Research Articles

Two-dimensional liquid crystalline growth within a phase-field-crystal model

By using a two-dimensional phase-field-crystal (PFC) model, the liquid crystalline growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from an isotropic phase is compared with that grown from a columnar or smectic-A (CSA) phase. While the shape of a PTC nucleus in the isotropic phase is almost identical to that of the classical PFC model, the shape of a PTC nucleus in CSA is affected by the orientation of stripes in the CSA phase, and irregular hexagonal, elliptical, octagonal, and rectangular shapes are obtained. Concerning the dynamics of the growth process, we analyze the topological structure of the nematic order, which starts from nucleation of +1/2 and -1/2 disclination pairs at the PTC growth front and evolves into hexagonal cells consisting of +1 vortices surrounded by six satellite -1/2 disclinations. It is found that the orientational and the positional order do not evolve simultaneously; the orientational order evolves behind the positional order, leading to a large transition zone, which can span over several lattice spacings.

Characterization of radiation-induced effects in amorphous arsenic sulfides by positron annihilation lifetime spectroscopy

Abstract

Controlling the Self‐Assembly of Periodic Defect Patterns in Smectic Liquid Crystal Films with Electric Fields

Large‐area periodic defect patterns are produced in smectic A liquid crystals confined between rigid plate electrodes that impose conflicting parallel and normal anchoring conditions, inducing the formation of topological defects. Highly oriented stripe patterns are created in samples thinner than 2 μm due to self‐assembly of linear defect domains with period smaller than 4 μm, whereas hexagonal lattices of focal conic domains appear for thicker samples. The pattern type (1d/2d) and period can be controlled at the nematic–smectic phase transition by applying an electric field, which confines the defect domains to a thin surface layer with thickness comparable to the nematic coherence length. The pattern morphology persists in the smectic phase even after varying the field or switching it off. Bistable, non‐equilibrium patterns are stabilized by topological constraints of the smectic phase that hinder the rearrangement of defects in response to field variations.

Transformation of membrane nanosurface of red blood cells under hemin action.

Hemin is the product of hemoglobin oxidation. Some diseases may lead to a formation of hemin. The accumulation of hemin causes destruction of red blood cells (RBC) membranes. In this study the process of development of topological defects of RBC membranes within the size range from nanoscale to microscale levels is shown. The formation of the grain-like structures in the membrane (“grains”) with typical sizes of 120–200 nm was experimentally shown. The process of formation of “grains” was dependent on the hemin concentration and incubation time. The possible mechanism of membrane nanostructure alterations is proposed. The kinetic equations of formation and transformation of small and medium topological defects were analyzed. This research can be used to study the cell intoxication and analyze the action of various agents on RBC membranes.

Universality of phase transition dynamics: Topological defects from symmetry breaking

In the course of a nonequilibrium continuous phase transition, the dynamics ceases to be adiabatic in the vicinity of the critical point as a result of the critical slowing down (the divergence of the relaxation time in the neighborhood of the critical point). This enforces a local choice of the broken symmetry and can lead to the formation of topological defects. The Kibble–Zurek mechanism (KZM) was developed to describe the associated nonequilibrium dynamics and to estimate the density of defects as a function of the quench rate through the transition. During recent years, several new experiments investigated the formation of defects in phase transitions induced by a quench both in classical and quantum mechanical systems. At the same time, some established results were called into question. We review and analyze the Kibble–Zurek mechanism focusing in particular on this surge of activity, and suggest possible directions for further progress.

Quantum simulation of the Kibble-Zurek mechanism using a semiconductor electron charge qubit

The Kibble-Zurek mechanism provides a description of the topological structure occurring in the symmetry breaking phase transitions, which may manifest as the cosmological strings in the early universe or vortex lines in the superfulid. A particularly intriguing analogy between Kibble-Zurek mechanism and a text book quantum phenomenon, Landau-Zener transition has been discovered, but is difficult to observe up to now. In recent years, there has been broad interest in quantum simulations using different well-controlled physical setups, in which full tunability allows access to unexplored parameter regimes. Here we demonstrate a proof-of-principle quantum simulation of Kibble-Zurek mechanism using a single electron charge qubit in double quantum dot, set to behave as Landau-Zener dynamics. We measure the qubit states as a function of driven pulse velocity and successfully reproduce Kibble-Zurek like dependence of topological defect density on the quench rate. The high-level controllability of semiconductor two-level system make it a platform to test the key elements of topological defect formation process and shed a new insight on the aspect of non-equilibrium phase transitions.

Dynamics of Topological Defects in Single-Walled Carbon Nanotubes during Catalytic Growth

Nucleation and healing of structural defects in single-walled carbon nanotubes (SWCNTs) studied through reactive molecular dynamics simulations (RMD) and RMD trajectories reveal formation and healing mechanisms of various topological defects on the catalyst surface. A quality percentage of nanotubes is measured by calculating the amount of hexagons per carbon atom relative to the same quantity for a perfect nanotube of the same length. Following this approach, the concentration of defects is estimated for nanotubes grown on catalysts with different sizes and morphologies and for various temperatures and gas-phase densities. From this analysis, we identify specific catalyst morphologies that favor the growth of SWCNTs with low defect concentration. Vacancies, 5–7, and Stone–Wales defects are observed to nucleate distinctly in the tubes depending on the catalyst morphology. We find that a strong interaction between the catalyst surface and the graphitic lattice of the nanotube is absolutely necessary for he...

Orientational order and topological defects in two-dimensional Yukawa systems

Abstract New numerical results concerned with formation of orientational order and topological defects in non-ideal systems of particles, interacted via screened Coulomb potential, are presented. Calculations have been performed in a wide range of parameters, corresponding to the experimental conditions in the laboratory dusty plasmas. Relations between a number of topological defects and shape of a bond-angular correlation function are obtained for the first time.

Disclination lines at homogeneous and heterogeneous colloids immersed in a chiral liquid crystal.

In the present work we perform Monte Carlo simulations in the isothermal-isobaric ensemble to study defect topologies formed in a cholesteric liquid crystal due to the presence of a spherical colloidal particle. Topological defects arise because of the competition between anchoring at the colloidal surface and the local director. We consider homogeneous colloids with either local homeotropic or planar anchoring to validate our model by comparison with earlier lattice Boltzmann studies. Furthermore, we perform simulations of a colloid in a twisted nematic cell and discuss the difference between induced and intrinsic chirality on the formation of topological defects. We present a simple geometrical argument capable of describing the complex three-dimensional topology of disclination lines evolving near the surface of the colloid. The presence of a Janus colloid in a cholesteric host fluid reveals a rich variety of defect structures. Using the Frank free energy we analyze these defects quantitatively indicating a preferred orientation of the Janus colloid relative to the cholesteric helix.

Numerical Study of Membrane Configurations

We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit in-plane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells). The topological defects are always present on the surfaces with the topology of a sphere. The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy.

Elastic properties and large deformation of two-dimensional silicene nanosheets using molecular dynamics

This paper aims to compute the elastic properties and large deformation of two-dimensional silicene, a low buckled honeycomb structure of silicon, under uniaxial and biaxial tension by implementing molecular dynamics simulations in canonical ensemble (NVT). The results demonstrate that Young’s and bulk moduli and ultimate stress of silicene nanosheet are lower than those of graphene. Ultimate strain is found to be higher than that of graphene for armchair silicene, unlike the zigzag one. Moreover, Poisson’s ratio of silicene is found to be greater than that of its carbon counterpart due to longer Si–Si bond length and its low buckled honeycomb structure. Further, it is observed that bulk modulus is strongly size-dependent and it decreases by increasing the length of nanosheet. Finally, the silicene behavior under large deformation and fracture pattern are investigated and the formation of topological defects and silicon chains are observed. It is further revealed that the silicene is noticeably weaker than graphene in zigzag direction.

Stacking Order Dependent Second Harmonic Generation and Topological Defects in h-BN Bilayers

The ability to control the stacking structure in layered materials could provide an exciting approach to tuning their optical and electronic properties. Because of the lower symmetry of each constituent monolayer, hexagonal boron nitride (h-BN) allows more structural variations in multiple layers than graphene; however, the structure-property relationships in this system remain largely unexplored. Here, we report a strong correlation between the interlayer stacking structures and optical and topological properties in chemically grown h-BN bilayers, measured mainly by using dark-field transmission electron microscopy (DF-TEM) and optical second harmonic generation (SHG) mapping. Our data show that there exist two distinct h-BN bilayer structures with different interlayer symmetries that give rise to a distinct difference in their SHG intensities. In particular, the SHG signal in h-BN bilayers is observed only for structures with broken inversion symmetry, with an intensity much larger than that of single layer h-BN. In addition, our DF-TEM data identify the formation of interlayer topological defects in h-BN bilayers, likely induced by local strain, whose properties are determined by the interlayer symmetry and the different interlayer potential landscapes.

Condensed matter analogues of cosmology

Condensed matter analogues of cosmology

Causality and non-equilibrium second-order phase transitions in inhomogeneous systems

When a second-order phase transition is crossed at a finite rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: it obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental testing of defect formation theories.

Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals

Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, topological defects can form. The Kibble-Zurek mechanism predicts the defect densities to follow a power law that scales with the rate of the transition. Owing to its ubiquitous nature, this theory finds application in a wide field of systems ranging from cosmology to condensed matter. Here we present the successful creation of defects in ion Coulomb crystals by a controlled quench of the confining potential, and observe an enhanced power law scaling in accordance with numerical simulations and recent predictions. This simple system with well-defined critical exponents opens up ways to investigate the physics of non-equilibrium dynamics from the classical to the quantum regime.

Orientational order and formation of topological defects in two-dimensional systems

The formation dynamics of topological defects and the orientational order in nonideal systems of particles interacting with a screened Coulomb potential is numerically simulated. Calculations are performed in a broad range of parameters corresponding to experimental conditions in a laboratory dusty plasma. A relation is obtained between the number of defects, the shape of the orientational correlation function, and the coupling parameter of the system. New approximations are proposed for the orientational correlation function in the liquid and hexatic phases of structures analyzed.

On Defects in Biaxial Nematic Films with Random Planar Surface Alignment: A Monte Carlo Study

We present a detailed computer simulation study of the formation and evolution of topological defects in thin biaxial nematic films. We have used the Straley generalized Hamiltonian and a wide range of biaxial parameters to generate and explore a variety of mesophases. The differences obtained for the various cases are analyzed for thin biaxial nematic films with random planar (Schlieren) surface alignment.

Scaling Behavior and Beyond Equilibrium in the Hexagonal Manganites

We show that the improper ferroelectric phase transition in the multiferroic hexagonal manganites displays the same symmetry-breaking characteristics as those proposed in early-universe theories. We present an analysis of the Kibble-Zurek theory of topological defect formation applied to the hexagonal manganites, discuss the conditions determining the range of cooling rates in which Kibble-Zurek behavior is expected, and show that recent literature data are consistent with our predictions. We explore experimentally for the first time to our knowledge the cross-over out of the Kibble-Zurek regime and find a surprising "anti-Kibble-Zurek" behavior.

Tachyon Condensation and Brane Annihilation in Bose-Einstein Condensates: Spontaneous Symmetry Breaking in Restricted Lower-Dimensional Subspace

In brane cosmology, the Big Bang is hypothesized to occur by the annihilation of the brane–anti-brane pair in a collision, where the branes are three-dimensional objects in a higher-dimensional Universe. Spontaneous symmetry breaking accompanied by the formation of lower-dimensional topological defects, e.g. cosmic strings, is triggered by the so-called ‘tachyon condensation’, where the existence of tachyons is attributable to the instability of the brane–anti-brane system. Here, we discuss the closest analogue of the tachyon condensation in atomic Bose–Einstein condensates. We consider annihilation of domain walls, namely branes, in strongly segregated two-component condensates, where one component is sandwiched by two domains of the other component. In this system, the process of the brane annihilation can be projected effectively as ferromagnetic ordering dynamics onto a two-dimensional space. Based on this correspondence, three-dimensional formation of vortices from a domain-wall annihilation is considered to be a kink formation due to spontaneous symmetry breaking in the two-dimensional space. We also discuss a mechanism to create a ‘vorton’ when the sandwiched component has a vortex string bridged between the branes. We hope that this study motivates experimental researches to realize this exotic phenomenon of spontaneous symmetry breaking in superfluid systems.

Causality and defect formation in the dynamics of an engineered quantum phase transition in a coupled binary Bose–Einstein condensate

Continuous phase transitions occur in a wide range of physical systems, and provide a context for the study of non-equilibrium dynamics and the formation of topological defects. The Kibble–Zurek (KZ) mechanism predicts the scaling of the resulting density of defects as a function of the quench rate through a critical point, and this can provide an estimate of the critical exponents of a phase transition. In this work, we extend our previous study of the miscible–immiscible phase transition of a binary Bose–Einstein condensate (BEC) composed of two hyperfine states in which the spin dynamics are confined to one dimension (Sabbatini et al 2011 Phys. Rev. Lett.107 230402). The transition is engineered by controlling a Hamiltonian quench of the coupling amplitude of the two hyperfine states and results in the formation of a random pattern of spatial domains. Using the numerical truncated Wigner phase-space method, we show that in a ring BEC the number of domains formed in the phase transitions scales as predicted by the KZ theory. We also consider the same experiment performed with a harmonically trapped BEC, and investigate how the density inhomogeneity modifies the dynamics of the phase transition and the KZ scaling law for the number of domains. We then make use of the symmetry between inhomogeneous phase transitions in anisotropic systems, and an inhomogeneous quench in a homogeneous system, to engineer coupling quenches that allow us to quantify several aspects of inhomogeneous phase transitions. In particular, we quantify the effect of causality in the propagation of the phase transition front on the resulting formation of domain walls and find indications that the density of defects is determined during the impulse to adiabatic transition after the crossing of the critical point.