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 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↗

NASA NTRS1991

Grand unified theories, topological defects and ultrahigh-energy cosmic rays

The ultrahigh-energy (UHE) proton and neutrino spectra resulting from collapse or annihilations of topological defects surviving from the GUT era are calculated. Irrespective of the specific process under consideration (which determines the overall normalization of the spectrum), the UHE proton spectrum always 'recovers' at approximately 1.8 x 10 exp 11 GeV after a partial Greisen-Zatsepin-Kuz'min 'cutoff' at approximately 5 x 10 exp 10 GeV and continues to a GUT-scale energy with a universal shape determined by the physics of hadronic jet fragmentation. Implications of our results are discussed.

Bhattacharjee, Pijushpani↗

NASA NTRS1992

Grand unified theories, topological defects, and ultrahigh-energy cosmic rays

The ultrahigh-energy (UHE) proton and neutrino spectra resulting from collapse or annihilations of topological defects surviving from the GUT era are calculated. Irrespective of the specific process under consideration (which determines the overall normalization of the spectrum), the UHE proton spectrum always 'recovers' at approximately 1.8 x 10 exp 11 GeV after a partial Greisen-Zatsepin-Kuz'min 'cutoff' at approximately 5 x 10 exp 10 GeV and continues to a GUT-scale energy with a universal shape determined by the physics of hadronic jet fragmentation. Implications of the results are discussed.

Bhattacharjee, Pijushpani↗

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)↗

NASA NTRS1989

The formation of topological defects in phase transitions

It was argued, and fought through numerical work that the results of non-dynamical Monte Carlo computer simulations cannot be applied to describe the formation of topological defects when the correlation length at the Ginzburg temperature is significantly smaller than the horizon size. To test the current hypothesis that infinite strings at formation are essentially described by Brownian walks of size the correlation length at the Ginzburg temperature, fields at the Ginzburg temperature were equilibrated. Infinite structure do not exist in equilibrium for reasonable definitions of the Ginzburg temperature, and horizons must be included in a proper treatment. A phase transition, from small-scale to large-scale string or domain wall structure, is found to occur very close to the Ginzburg temperature, in agreement with recent work. The formation process of domain walls and global strings were investigated through the breaking of initially ordered states. To mimic conditions in the early Universe, cooling times are chosen so that horizons exist in the sample volume when topological structure formation occurs. The classical fields are evolved in real-time by the numerical solution of Langevin equations of motion on a three dimensional spatial lattice. The results indicate that it is possible for most of the string energy to be in small loops, rather than in long strings, at formation.

Hodges, Hardy M.↗

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↗