Results for “Topological defects”

DOE OSTI2022

Non-symmetric pinning of topological defects in living liquid crystals

Topological defects, such as vortices and disclinations, play a crucial role in spatiotemporal organization of equilibrium and non-equilibrium systems. The defect immobilization or pinning is a formidable challenge in the context of the out-of-equilibrium system, like a living liquid crystal, a suspension of swimming bacteria in lyotropic liquid crystal. Here we control the emerged topological defects in a living liquid crystal by arrays of 3D-printed microscopic obstacles (pillars). Our studies show that while –1/2 defects may be easily immobilized by the pillars, +1/2 defects remain motile. Due to attraction between oppositely charged defects, positive defects remain in the vicinity of pinned negative defects, and the diffusivity of positive defects is significantly reduced. Experimental findings are rationalized by computational modeling of living liquid crystals. Our results provide insight into the engineering of active systems via targeted immobilization of topological defects.

42 ENGINEERING↗

DOE OSTI2024

Approach and rotation of reconnecting topological defect lines in liquid crystal

Topological defects are a universal concept across many disciplines, such as crystallography, liquid-crystalline physics, low-temperature physics, cosmology, and even biology. In nematic liquid crystals, topological defects called disclinations have been widely studied. For their three-dimensional (3D) dynamics, however, only recently have theoretical approaches dealing with fully 3D configurations been reported. Further, recent experiments have observed 3D disclination line reconnections, a phenomenon characteristic of defect line dynamics, but detailed discussions were limited to the case of approximately parallel defects. In this paper, we focus on the case of two disclination lines that approach at finite angles and lie in separate planes, a more fundamentally 3D reconnection configuration. Observing and analyzing such reconnection events, we find the square-root law of the distance between disclinations and the decrease of the interdisclination angle over time. We compare the experimental results with theory and find qualitative agreement on the scaling of distance and angle with time, but quantitative disagreement on distance and angle relative mobilities. To probe this disagreement, we derive the equations of motion for systems with reduced twist constant and also carry out simulations for this case. These, together with the experimental results, suggest that deformations of disclinations may be responsible for the disagreement. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

DOE OSTI2024

Approach and rotation of reconnecting topological defect lines in liquid crystal

Topological defects are a universal concept across many disciplines, such as crystallography, liquid-crystalline physics, low-temperature physics, cosmology, and even biology. In nematic liquid crystals, topological defects called disclinations have been widely studied. For their three-dimensional (3D) dynamics, however, only recently have theoretical approaches dealing with fully 3D configurations been reported. Further, recent experiments have observed 3D disclination line reconnections, a phenomenon characteristic of defect line dynamics, but detailed discussions were limited to the case of approximately parallel defects. In this paper, we focus on the case of two disclination lines that approach at finite angles and lie in separate planes, a more fundamentally 3D reconnection configuration. Observing and analyzing such reconnection events, we find the square-root law of the distance between disclinations and the decrease of the interdisclination angle over time. We compare the experimental results with theory and find qualitative agreement on the scaling of distance and angle with time, but quantitative disagreement on distance and angle relative mobilities. To probe this disagreement, we derive the equations of motion for systems with reduced twist constant and also carry out simulations for this case. These, together with the experimental results, suggest that deformations of disclinations may be responsible for the disagreement.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Ultrafast formation of topological defects in a two-dimensional charge density wave

Topological defects play a central role in dynamical systems undergoing a non-adiabatic transition. In solids, topological defects as a result of femtosecond laser excitation have attracted increasing interest not only because they are key to understanding phase transitions but also because they can generate a variety of hidden orders that are not accessible in thermal equilibrium. Despite the common occurrence of these defects in a non-equilibrium system, the fundamental limit on how fast they can emerge in solids and the generic pathway for defect creation at such fast timescales have remained open questions. Here we apply ultrafast electron diffraction to study the reciprocal-space signatures of transient defects in a two-dimensional charge density wave, where simultaneous measurements of both defect and phonon dynamics yield a microscopic view of defect formation in the femtosecond regime. We find that one-dimensional domain walls are generated well within 1 ps following photoexcitation, during which the defect growth is not dictated by the amplitude of the order parameter but is mediated by a non-thermal population of longitudinal optical phonons. In conclusion, our work provides a framework for the ultrafast engineering of topological defects that are coupled to specific collective modes, which will prove useful for the dynamical control of non-equilibrium phases in correlated materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

The fate of liquid crystal topological defects on chemically patterned surfaces during phase transitions

Controlling topological defects in liquid crystals (LCs) is an essential element in the development of areas such as directed self-assembly and micropatterning materials. However, during the phase transition on confined patterned surfaces, how the morphologies in one liquid crystalline phase change from deformations or defects into another phase is much less known. Here, we examine the fate of defects in a LC confined on a patterned surface during smectic-A–nematic and nematic–isotropic phase transitions, using experiments and simulation analyses. Upon heating from smectic-A to nematic, a Toric focal conical domain (TFCD) melts into a +1 converging boojum defect, which then transitioned into a concentric configuration as temperature increases, attributed to a steeper decrease of the bend and twist modulus compared to splay modulus. During cooling, TFCDs are developed from two distinct pathways depending on the cooling rates. Our continuum simulation recapitulates these transformations and provides elastic constant-based explanations for the two pathways. Although the phase transition pathways of defects are independent of the geometry of the confined patterns, the arrangement of FCDs is highly dependent on the size and shape of the patterns. Finally, taken together, this simple approach offers promising opportunities for tuning the micro- or nano-patterning of topological defects in liquid crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

GUTs, hybrid topological defects, and gravitational waves

The symmetry breaking of grand unified gauge groups in the early Universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable, with one defect "eating" the other via the conversion of its rest mass into the other's kinetic energy and, subsequently, decaying via gravitational waves. In this work, we determine the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and "eat" the strings, 2) the collapse and decay of a monopole-string network by strings that eat the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and eat the wall, and 4) the collapse and decay of a string-bounded wall network by walls that eat the strings. We call the gravitational wave signals produced from the eating of one topological defect by another "gravitational wave gastronomy." We find that the four gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the SO (10) symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects. Moreover, the systems we consider are unlikely to have a residual monopole or domain wall problem.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g-function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Behavior of thermally quenched topological defects in quasicrystal artificial spin ices

We report that understanding the formation of topological defects in connected magnetic nanowires such as in artificial spin ices (ASIs) is critical to controlling their behavior. Moreover, emergent frustration behavior of these defects can be expected due to complex underlying lattice geometry of the ASIs. We have explored in situ thermalization and quenching of quasicrystalline ASIs, which exhibit additional frustration due to aperiodicity from near the Curie temperature, and we observe the formation of two sets of topological vortex defects: within the magnetic bars and within the vertices at which the bars meet. By varying the laser fluence, we show that the number of defects in the vertices varies as the quenching rate changes following a power law relation, which we interpret as being related to the ferromagnetic-to-paramagnetic phase transition. Conversely, the defects formed within the bars are metastable states related to the spontaneous magnetization reversal of the magnetic bars and are therefore strongly dependent on underlying lattice geometry. These results provide insight into the emergence and control of topological defects in confined frustrated magnetic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Dynamic Motions of Topological Defects in Nematic Liquid Crystals under Spatial Confinement

Abstract Topological defects (TDs) have become a sensational topic due to their significant influence on the unusual optical and physiochemical characteristics of the material. To facilitate their application across a wide range of disciplines it is desirable to analyze and gain fundamental understanding of TDs in both equilibrium and nonequilibrium systems. Liquid crystals (LCs) are considered an ideal system for study given the direct visualization of TDs and a straightforward analyzation process. In addition to the equilibrium morphology of LC TDs, it is also of great interest to track and control the formation and annihilation of defects during thermodynamic processes. However, controlling the dynamic behavior of formed defects remains a challenge. Here, nematic LCs confined in a cell exhibiting surfaces with periodic anchoring conditions containing surface topography are relied on. The effects of patterned surface characteristics such as width, periodicity, and degree of curvature on defects dynamic motion, stabilization, and annihilation are explored. The computational experiments recapitulate the TDs transition path and provide free energy‐based predictions of critical distances for defect annihilation. Taken together, this simple approach offers a promising opportunity to control the dynamics of TDs in LCs through chemical patterned surfaces with topography.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Describing Point Defect Topology in 2D Energy Materials Through Computer Vision

Point defects such as vacancies and impurity atoms strongly impact the performance of 2D materials. Traditional efforts often rely on manual detection, a process that is time-intensive, prone to human error, and challenging to scale. Here we leverage machine learning (ML) methods to identify and quantify vacancies within 2D transition metal carbides (Ti3C2, MXenes), aiming to expedite detection while improving accuracy. MXenes exhibit valuable defect-defined electrochemical properties, but we currently lack statistical understanding of defect topology needed to fully harness these materials. We employ a convolutional neural network for semantic segmentation of experimental MXene images, opening an opportunity to conduct a rigorous statistical study on defect hierarchy while investigating local relaxation in the lattice. We show how the integration of ML can yield fundamental insight into point defects, providing a powerful tool that will play an increasingly crucial role in the future of materials science.

2D materials↗

NASA NTRS1990

Topological defects in extended inflation

The production of topological defects, especially cosmic strings, in extended inflation models was considered. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large scale structure via cosmic strings.

Copeland, Edmund J.↗

DOE OSTI2025

Real-space chirality from crystalline topological defects in the Kitaev spin liquid

We show that certain crystalline topological defects in the gapless Kitaev honeycomb spin liquid model generate a chirality and Majorana fermion orbital magnetization that depends in a universal manner on their emergent flux. Focusing on 5–7 dislocations as building blocks, consisting of pentagon and heptagon disclinations, we identify the Kitaev bond label configurations that preserve solvability. By computing two formulations of local markers M(r) we find that the 5 and 7 lattice defects generate a real-space contribution to Chern number and an associated Majorana fermion orbital magnetization proportional to M(r). The sign of the M(r) contribution from each 5/7 defect, i.e. its q M = ± 1 chirality, is determined by the defect Frank angle sign F and emergent gauge field flux W = ± i through the expression q M = − iFW. Remarkably, though lattice curvature and torsion can interplay with the surrounding gapless background to modify the profile of M(r), its sign q M is determined locally, implying that crystalline defects in the Kitaev spin liquid can generate a robust and observable chirality.

Magnetic properties and materials↗

DOE OSTI2024

Identifying Topological Defects in Lamellar Phases through Contour Analysis of Complex Wave Fields

Lamellar phases frequently contain structural imperfections that significantly affect their behaviors and properties. Our previous research successfully reconstructed real-space configurations of defective lamellar phases from diffuse scattering patterns, indicating the presence of phase vortices as a potential method for identifying topological defects disrupting the smectic ordering. Here, this report presents a mathematical framework using regularized wave fields to represent defective lamellar structures in real space. Phase singularities, resulting from the interference of random waves and indicating lamellar order disruption, are identified through a contour integral. These wave fields, derived from coherent scattering in reciprocal space, were validated via computational benchmarks analyzing small-angle neutron scattering data from AOT surfactant solutions, facilitating further statistical analysis of the defects. Our study highlights the potential to extract meaningful information about topological defects in lyotropic phases by inversely analyzing experimentally measured two-point static correlations. Our method allows for detailed structural analysis of various lyotropic phases, both particulate and nonparticulate, in their quiescent states and facilitates quantitative investigation of defects’ role in phase transitions. By integrating small-angle scattering, deep learning, and vortex tangle analysis, our comprehensive approach shows promise in addressing complex challenges in the structural analysis of soft matter systems.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Static and dynamic topological defects in the domain textures in the helical antiferromagnet Ni 2 ⁢CoTeO 6

Real-space Bragg coherent x-ray-diffractive imaging unveils the formation of bubble and stripe antiferromagnetic (AFM) phase domains on the surface of Ni 2 ⁢CoTeO 6 single crystal. The stripe domains exhibit dislocation-type topological defects. The defects typically form as defect-antidefect pairs and can be created or annihilated by temperature changes and local heating. Thermal fluctuations of the AFM domain walls are observed near the Néel temperature. Topological defect pairs dynamically form and disappear in the fluctuating state. These observations provide a real-space perspective on the dynamics of the AFM phase transition in a helical antiferromagnet. Finally, the remarkable tunability of AFM domain walls in a helical antiferromagnet underscores their potential for AFM spintronics applications.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Describing Point Defect Topology in 2D Energy Materials through Computer Vision

Point defects such as vacancies and impurity atoms strongly impact the performance of 2D materials. Traditional efforts often rely on manual detection, a process that is time-intensive, prone to human error, and challenging to scale. Here we leverage machine learning (ML) methods to identify and quantify vacancies within 2D transition metal carbides (Ti3C2, MXenes), aiming to expedite detection while improving accuracy. MXenes exhibit valuable defect-defined electrochemical properties, but we currently lack statistical understanding of defect topology needed to fully harness these materials. Here we employ a convolutional neural network for semantic segmentation of experimental MXene images, opening an opportunity to conduct a rigorous statistical study on defect hierarchy while investigating local relaxation in the lattice. We show how the integration of ML can yield fundamental insight into point defects, providing a powerful tool that will play an increasingly crucial role in the future of materials science.

2d materials↗

DOE OSTI2026

Describing Point Defect Topology in 2D Energy Materials Through Computer Vision

Point defects such as vacancies and impurity atoms strongly impact the performance of 2D materials. Traditional efforts often rely on manual detection, a process that is time-intensive, prone to human error, and challenging to scale. Here we leverage machine learning (ML) methods to identify and quantify vacancies within 2D transition metal carbides (Ti3C2, MXenes), aiming to expedite detection while improving accuracy. MXenes exhibit valuable defect-defined electrochemical properties, but we currently lack statistical understanding of defect topology needed to fully harness these materials. Here we employ a convolutional neural network for semantic segmentation of experimental MXene images, opening an opportunity to conduct a rigorous statistical study on defect hierarchy while investigating local relaxation in the lattice. We show how the integration of ML can yield fundamental insight into point defects, providing a powerful tool that will play an increasingly crucial role in the future of materials science. ML is often not just a matter of straightforward application, and pretrained models proved ineffective in this case. Instead, we trained our own neural network (NN) and applied data augmentation techniques and fine-tuning to the training dataset. Since labeled microscopy data is often scarce, we developed training data from a previously published wide-frame MXene image, using customized Gaussian fitting to locate atomic positions. Our trained model was then applied to a large dataset of experimental images, enabling a statistical study of defect configurations across three samples prepared with different HF etchant concentrations (5%, 9.1%, and 12.5%), as shown in Fig. 1. This also allowed us to investigate local strain around vacancies, though we find that we are limited by the precision of measurements using high-angle annular dark field (HAADF) images, as shown in Fig. 2. This study demonstrates how ML enables large-scale, quantitative analysis of atomic defects - an otherwise infeasible task with traditional methods. While our NN was specialized for Ti3C2 MXenes, the pipeline we developed provides a foundation for future ML models tailored to other materials. Ultimately, we envision embedding the NN onto the microscope to give real-time feedback to the user. To make this a reality, continued work is necessary to fully understand the NN's capabilities and limitations. This study gets one step closer to our goals of automated experimentation moving away from traditional methods of manual labeling. As ML capabilities advance, we hope to continue adapting and applying these techniques in microscopy.

2D materials↗

DOE OSTI2025

Resolving electrochemically triggered topological defect dynamics and structural degradation in layered oxides

Understanding topological defects-controlled structural degradation of layered oxides—a key cathode material for high-performance lithium-ion batteries—plays a critical role in developing next-generation cathode materials. Here, by constructing a nanobattery in an electron microscope enabling atomic-scale monitoring of electrochemcial reactions, we captured the electrochemically driven atomistic dynamics and evolution of dislocations—a most important topological defect in material. We deciphered how dislocations nucleate, move, and annihilate within layered cathodes at the atomic scale. Specifically, we found two types of dislocation configurations, i.e., single dislocations and dislocation dipoles. Both pure dislocation glide/climb and mixed motions were captured, and the dislocation glide and climb velocities were first experimentally measured. Moreover, dislocation activity-mediated structural degradation such as crack nucleation, phase transformation, and lattice reorientation was unraveled. Our work provides deep insights into the atomistic dynamics of electrochemically driven dislocation activities in layered oxides.

Wang, Chunyang (ORCID:0000000184613952)↗

NASA NTRS1990

Effective actions for bosonic topological defects

A gauge field theory is considered which admits p-dimensional topological defects, expanding the equations of motion in powers of the defect thickness. In this way an effective action and effective equation of motion is derived for the defect in terms of the coordinates of the p-dimensional worldsurface defined by the history of the core of the defect.

Gregory, Ruth↗