Results for “topological defects”

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 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 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↗

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)↗

DOE OSTI2025

Atomic-Scale Tracking of Topological Defect Motion and Incommensurate Charge Order Melting

Charge order pervades the phase diagrams of quantum materials where it competes with superconducting and magnetic phases, hosts electronic phase transitions and topological defects, and couples to the lattice generating intricate structural distortions. Incommensurate charge order is readily stabilized in manganese oxides, where it is associated with anomalous electronic and magnetic properties, but its nanoscale structural inhomogeneity complicates precise characterization and understanding of its relationship with competing phases. Leveraging atomic-resolution variable-temperature cryogenic scanning transmission electron microscopy, we characterize the thermal evolution of charge order as it transforms from its ground state in a model manganite system. We find that mobile networks of discommensurations and dislocations generate phase inhomogeneity and induce global incommensurability in an otherwise lattice-locked modulation. Driving the order to melt at high temperatures, the discommensuration density grows, and regions of order locally decouple from the lattice periodicity. Published by the American Physical Society 2025

Schnitzer, Noah (ORCID:0000000210421146)↗

DOE OSTI2025

Dynamical Scaling Reveals Topological Defects and Anomalous Evolution of a Photoinduced Phase Transition

Nonequilibrium states of quantum materials can exhibit exotic properties and enable unprecedented functionality and applications. These transient states are inherently inhomogeneous, characterized by the formation of topologically protected structures, requiring nanometer spatial resolution on femtosecond timescales to resolve their evolution. Using ultrafast total x-ray scattering at a free electron laser and a sophisticated scaling analysis, we gain unique access to the dynamics on the relevant mesoscopic length scales. Our results provide direct evidence that ultrafast excitation of LaTe 3 leads to formation of topological vortex strings of the charge density wave. These dislocations of the charge density wave exhibit anomalous, subdiffusive dynamics, slowing the equilibration process, providing rare insight into the nonequilibrium mesoscopic response in a quantum material. Our findings establish a general framework to investigate properties of topological defects, which are expected to be ubiquitous in nonequilibrium phase transitions and may arrest equilibration and enhance competing orders.

Orenstein, Gal [SLAC National Accelerator Laborato↗

DOE OSTI2024

X-ray linear dichroic tomography of crystallographic and topological defects

Abstract The functionality of materials is determined by their composition 1–4 and microstructure, that is, the distribution and orientation of crystalline grains, grain boundaries and the defects within them 5,6 . Until now, characterization techniques that map the distribution of grains, their orientation and the presence of defects have been limited to surface investigations, to spatial resolutions of a few hundred nanometres or to systems of thickness around 100 nm, thus requiring destructive sample preparation for measurements and preventing the study of system-representative volumes or the investigation of materials under operational conditions 7–15 . Here we present X-ray linear dichroic orientation tomography (XL-DOT), a quantitative, non-invasive technique that allows for an intragranular and intergranular characterization of extended polycrystalline and non-crystalline 16 materials in three dimensions. We present the detailed characterization of a polycrystalline sample of vanadium pentoxide (V 2 O 5 ), a key catalyst in the production of sulfuric acid 17 . We determine the nanoscale composition, microstructure and crystal orientation throughout the polycrystalline sample with 73 nm spatial resolution. We identify and characterize grains, as well as twist, tilt and twin grain boundaries. We further observe the creation and annihilation of topological defects promoted by the presence of volume crystallographic defects. The non-destructive and spectroscopic nature of our method opens the door to operando combined chemical and microstructural investigations 11,18 of functional materials, including energy, mechanical and quantum materials.

Science & Technology - Other Topics↗

DOE OSTI2024

Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking

In this article, we consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between classical long-range order of local order parameters and quantum order of long-range entanglement in the ground states, we study the topological point defects and textures of order parameters in such systems. We show that the universal properties of point defects and textures are determined by the remnant symmetry enriched topological order in the symmetry-breaking ground states with a nonfluctuating order parameter, and provide a classification for their properties based on the inflation-restriction exact sequence. We highlight a few phenomena revealed by our theory framework. First, in the absence of intrinsic topological orders, we show a connection between the symmetry properties of point defects and textures to deconfined quantum criticality. Second, when the symmetry-breaking ground state has intrinsic topological orders, we show that the point defects can permute different anyons when braided around. They can also obey projective fusion rules in the sense that multiple vortices can fuse into an Abelian anyon, a phenomenon for which we coin “defect fractionalization.” Finally, we provide a formula to compute the fractional statistics and fractional quantum numbers carried by textures (skyrmions) in Abelian topological orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Mechanochemical topological defects in an active nematic

We propose a reaction-diffusion system that converts topological information of an active nematic into chemical signals. We show that a curvature-activated reaction dipole is sufficient for creating a system that dynamically senses topology by producing a concentration field possessing local extrema coinciding with ±$\frac{1}{2}$ defects. The enabling term is analogous to polarization charge density seen in dielectric materials. We demonstrate the ability of this system to identify defects in both passive and active nematics. Our results illustrate that a relatively simple feedback scheme, expressed as a system of partial differential equations, is capable of producing chemical signals in response to inherently nonlocal structures in anisotropic media. Here, we posit that such coarse-grained systems can help generate testable hypotheses for regulated processes in biological systems, such as morphogenesis, and motivate the creation of bio-inspired materials that utilize dynamic coupling between nematic structure and biochemistry.

42 ENGINEERING↗

DOE OSTI2025

Topological Defect Mediated Helical Phase Reorientation by Uniaxial Stress

Strain engineering enables precise, energy-efficient control of nanoscale magnetism. However, unlike well-studied strain-dislocation interactions in mechanical deformation, the spatial evolution of strain-induced spin rearrangement remains poorly understood. Using Lorentz transmission electron microscopy, we manipulate and observe helical domain reorientation under quantitatively applied uniaxial tensile stress. Our findings reveal striking similarity to plastic deformation in metals, where the critical stress for propagation vector ( Q ) reorientation depends on its angle with the stress direction. Magnetic defects mediate reorientation via “break-and-reconnect” or “dislocation gliding–annihilation” processes. Simulations confirm that strain-induced anisotropic Dzyaloshinskii-Moriya interaction may play a key role. These insights advance strain-driven magnetism and offer a promising route for energy-efficient magnetic nanophase control in next-generation information technology. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗