Topological Defects Research Articles

Topological defects in multi-layered swarming bacteria.

Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid dynamics of swarming bacteria. The results are compared to the predictions of two-dimensional active nematics. We show that, even though some of the assumptions underlying the theory do not hold, the swarm dynamics is in agreement with two-dimensional nematic theory. In particular, we look into the multi-layered structure of the swarm, which is an important feature of real, natural colonies, and find a strong coupling between layers. Our results suggest that the defect-charge density is hyperuniform, i.e., that long range density-fluctuations are suppressed.

Design rules for controlling active topological defects

Design rules for controlling active topological defects

Quantum duality in electromagnetism and the fine structure constant

We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine structure constant is rational, the theory admits noninvertible symmetries which can be realized as composites of electric-magnetic duality and gauging a discrete subgroup of the one-form global symmetry. These noninvertible symmetries are approximate quantum invariances of the natural world which emerge in the infrared below the mass scale of charged particles. We construct these symmetries explicitly as topological defects and illustrate their action on local and extended operators. We also describe their action on boundary conditions and illustrate some consequences of the symmetry for Hilbert spaces of the theory defined in finite volume. Published by the American Physical Society 2024

Cell deformability drives fluid-to-fluid phase transition in active cell monolayers.

Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for tissue homeostasis and stable developmental processes. However, large-scale simulations of deformable cells have been restricted to those of polygonal-shaped cells, limiting our understanding of populations of arbitrarily deformable cells, such as mesenchymal, amoeboid cells, and nonconfluent epithelial cells. Here, we present an efficient approach for simulating large populations of nonpolygonally deformable cells with considerably higher computational efficiency than existing methods. Using the method, we demonstrate that the densely packed active cell population interacting via excluded volume interactions exhibits a fluid-to-fluid transition. An experimentally measurable index of topological defects, defined using the number of neighboring cells, is also proposed to characterize this transition. This study provides a flexible approach to tissue-scale cell population and a broader perspective on the biological fluid phases.

Spacetime magnetic hopfions from internal excitations and braiding of skyrmions

Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime magnetic hopfions: magnetic textures in two spatial dimensions that when excited by a time-periodic drive develop spacetime topology. We uncover two complementary construction routes using skyrmions by braiding their center of mass position and by controlling their internal low-energy excitations. Spacetime magnetic hopfions can be realized in nanopatterned grids to braid skyrmions and in frustrated magnets under an applied AC electric field. Their topological invariant, the spacetime Hopf index, can be tuned by the applied electric field as demonstrated by our collective coordinate modeling and micromagnetic simulations. The principles we have introduced to actively control spacetime topology are not limited to magnetic solitons, opening avenues to explore spacetime topology of general order parameters and fields.

Electrical engineering of topological magnetism in two-dimensional heterobilayers

The emergence of topological magnetism in two-dimensional (2D) van der Waals (vdW) magnetic materials and their heterostructures is an essential ingredient for next-generation information technology devices. Here, we demonstrate the all-electric switching of the topological nature of individual magnetic objects emerging in 2D vdW heterobilayers. We show from the first principles that an external electric field modifies the vdW gap between CrTe2 and (Rh, Ti)Te2 layers and alters the underlying magnetic interactions. This enables switching between ferromagnetic skyrmions and meron pairs in the CrTe2/RhTe2 heterobilayer while it enhances the stability of frustrated antiferromagnetic merons in the CrTe2/TiTe2 heterobilayer. We envision that the electrical engineering of distinct topological magnetic solitons in a single device could pave the way for novel energy-efficient mechanisms to store and transmit information with applications in spintronics.

Effects of Intrinsic Defects in Pt-Based Carbon Supports on Alkaline Hydrogen Evolution Reaction.

Carbon material has widely been utilized in the synthesis of efficient carbon-supported Pt (Pt/C) catalysts, in which the structural properties greatly influence the electrocatalytic performances of Pt/C catalysts. However, the effects of intrinsic defects in carbon supports on the performance of the alkaline hydrogen evolution reaction (HER) have not been systematically investigated. Herein, porous carbon supports with different degrees of intrinsic defects were prepared by a simple template-assisted strategy, and the resulting samples were systematically studied by various analytical methods. The results suggested that the presence of abundant intrinsic defects (vacancy and topological defects) in the carbon support was advantageous in terms of favoring the dispersion and anchoring of Pt species, promoting electron transfer between Pt atoms and the carbon support, and tuning the electronic states of Pt species. These features improved the HER performance of Pt/C catalysts. Compared to the nontemplate-assisted carbon-supported Pt catalyst (Pt/NTC) with an overpotential of 178 mV, the optimized template-assisted carbon-supported Pt catalyst (Pt/TC) exhibited a lower overpotential of 58 mV at 10 mA cm-2. Besides, the Pt/TC catalyst displayed better HER durability than the Pt/NTC catalyst owing to its strong metal-support interaction. The DFT calculations confirmed the important role played by intrinsic defects (vacancy and topological defects) in stabilizing Pt atoms, with Pt-C3 coordination identified as the most favorable structure for improving the HER performance of Pt. Overall, novel insights on the significant contribution of intrinsic defects in porous carbon supports on the HER performances of Pt/C catalysts were provided, useful for future design and fabrication of advanced carbon-supported catalysts or other carbon-based electrode materials.

Irregular network of extended defects in graphene and a new criterion of the crystal lattice melting

Investigation of graphite defects has long and rich history. However, it turned out, that most point defects in graphene, such as vacancies or topological Stone-Wales defect, have high formation energies, preventing them from formation in large quantities. Recently, we have proposed a new type of extended defects in graphene, with formation energy per atom only slightly above the melting temperature. This means, that these planar defects may occur near the melting temperature in sufficient quantities to influence the thermodynamic properties of graphene. Still, there is discrepancy between thermodynamic properties of these defects and their topology, which can be successfully resolved by proposition of a new defects' type – irregular network of extended defects, which will be described in this paper. The study of network stability from these defects enables us to formulate a new criterion of crystal lattice melting, which supersedes the Lindemann/Born criteria.

Spin disorder control of topological spin texture

Stabilization of topological spin textures in layered magnets has the potential to drive the development of advanced low-dimensional spintronics devices. However, achieving reliable and flexible manipulation of the topological spin textures beyond skyrmion in a two-dimensional magnet system remains challenging. Here, we demonstrate the introduction of magnetic iron atoms between the van der Waals gap of a layered magnet, Fe3GaTe2, to modify local anisotropic magnetic interactions. Consequently, we present direct observations of the order-disorder skyrmion lattices transition. In addition, non-trivial topological solitons, such as skyrmioniums and skyrmion bags, are realized at room temperature. Our work highlights the influence of random spin control of non-trivial topological spin textures.

Electric-field-induced multiferroic topological solitons.

Topologically protected spin whirls in ferromagnets are foreseen as the cart-horse of solitonic information technologies. Nevertheless, the future of skyrmionics may rely on antiferromagnets due to their immunity to dipolar fields, straight motion along the driving force and ultrafast dynamics. While complex topological objects were recently discovered in intrinsic antiferromagnets, mastering their nucleation, stabilization and manipulation with energy-efficient means remains an outstanding challenge. Designing topological polar states in magnetoelectric antiferromagnetic multiferroics would allow one to electrically write, detect and erase topological antiferromagnetic entities. Here we stabilize ferroelectric centre states using a radial electric field in multiferroic BiFeO3 thin films. We show that such polar textures contain flux closures of antiferromagnetic spin cycloids, with distinct antiferromagnetic entities at their cores depending on the electric field polarity. By tuning the epitaxial strain, quadrants of canted antiferromagnetic domains can also be electrically designed. These results open the path to reconfigurable topological states in multiferroic antiferromagnets.

Fracture behavior of graphene with intrinsic defects and externally introduced defects

Introducing and regulating defects to prepare functional graphene has become a research hotspot. However, most studies focus on the mechanical properties of functional graphene or the influence of a single defect, which cannot reflect the influence of multiple coupled defects on mechanical properties. In this study, molecular dynamics methods were used to investigate the fracture behavior of graphene under the coupled effects of intrinsic defects such as vacancies, cracks, and topological defects, as well as external introduced defects such as epoxy groups and hydroxyl groups. The results showed that the fracture behavior of graphene is strongly related to the defects' type, concentration, and functionality. Under the same conditions, the epoxy group has the strongest leading effect on fracture, followed by cracks, Stone-Wales topological defects, and hydroxyl groups. Based on the tensile simulation of defect-ordered graphene, the critical relative concentrations and functionalities of different defect types leading to fracture were further quantified and validated using an amorphous distribution model. In addition, the fracture mode dominated by epoxy groups is related to its functionality. Excessive or insufficient functionality will exhibit strong brittle fracture characteristics, and when the functionality is at a certain threshold, it will exhibit obvious ductile fracture characteristics; while hydroxyl-dominated fracture presents brittle mode. Finally, the coupled fracture mechanism was analyzed from the aspects of bonding characteristics and system energy. The research results can provide reference and reference for the theoretical research and technological development of graphene.

Mechanochemical dynamics of collective cells and hierarchical topological defects in multicellular lumens.

Collective cell dynamics is essential for tissue morphogenesis and various biological functions. However, it remains incompletely understood how mechanical forces and chemical signaling are integrated to direct collective cell behaviors underlying tissue morphogenesis. Here, we propose a three-dimensional (3D) mechanochemical theory accounting for biochemical reaction-diffusion and cellular mechanotransduction to investigate the dynamics of multicellular lumens. We show that the interplay between biochemical signaling and mechanics can trigger either pitchfork or Hopf bifurcation to induce diverse static mechanochemical patterns or generate oscillations with multiple modes both involving marked mechanical deformations in lumens. We uncover the crucial role of mechanochemical feedback in emerging morphodynamics and identify the evolution and morphogenetic functions of hierarchical topological defects including cell-level hexatic defects and tissue-level orientational defects. Our theory captures the common mechanochemical traits of collective dynamics observed in experiments and could provide a mechanistic context for understanding morphological symmetry breaking in 3D lumen-like tissues.

Highly Curved Defect Sites: How Curvature Effect Influences Metal-Free Defective Carbon Electrocatalysts.

Topological defects are widely recognized as effective active sites toward a variety of electrochemical reactions. However, the role of defect curvature is still not fully understood. Herein, carbon nanomaterials with rich topological defect sites of tunable curvature is reported. The curved defective surface is realized by controlling the high-temperature pyrolytic shrinkage process of precursors. Theoretical calculations demonstrate bending the defect sites can change the local electronic structure, promote the charge transfer to key intermediates, and lower the energy barrier for oxygen reduction reaction (ORR). Experimental results convince structural superiority of highly-curved defective sites, with a high kinetic current density of 22.5mAcm-2 at 0.8V versus RHE for high-curvature defective carbon (HCDC), ≈18 times that of low-curvature defective carbon (LCDC). Further raising the defect densities in HCDC leads to the dual-regulated products (HCHDC), which exhibit exceptionally outstanding ORR activity in both alkaline and acidic media (half-wave potentials: 0.88 and 0.74V), outperforming most of the reported metal-free carbon catalysts. This work uncovers the curvature-activity relationship in carbon defect for ORR and provides new guidance to design advanced catalysts via curvature-engineering.

Topological defects and boundary states in four-dimensional topological insulator

We show the connection between the second Chern number and topological defects, in a (4+1)-dimensional time-reversal invariant Dirac lattice model. It is discovered that two types of topological defects, the five-dimensional (5D) and four-dimensional (4D) point defects arise from the singular points of wave functions together with the geometric meaning of the second Chern number. We demonstrated that the 5D point defects appear at the band crossing positions with a topological transition, leading to a jump of the second Chern number. The 4D point defects exist in an insulating bulk, whose topological charges can give the evaluations of the second Chern number of energy bands. Finally, we discussed the possible structures of the boundary states in the light of the realization way of the 4D model. Our theory provides not only a new perspective to grasp the second Chern number, but also a simple approach to derive its values without calculating any integrals.

Geometry-induced Bloch point domain wall in Permalloy conical frustum nanowires for advanced spintronics applications

In this study, we investigate the pseudo-static magnetic properties of Permalloy conical frustum nanowires using micromagnetic simulations. We thoroughly examine how both the major and minor radii influence the magnetic reversal mechanism when an external magnetic field is applied parallel to the nanowire axis. The obtained results show that under specific geometrical conditions, magnetization reverts though a Bloch point-type domain wall. In these cases, hysteresis curves exhibit two Barkhausen jumps during magnetization reversal, forming a plateau field range in which a Bloch point domain wall nucleates and propagates until its annihilation after the second Barkhausen jump. The nucleation of a Bloch point domain wall in a frustum conical nanowire geometry is reported. These findings highlight the significance of this geometry in nucleating these attractive topological defects for promising applications.

Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

The role of aspect ratio and activity on how active nematic defects distribute on toroidal surfaces

Active topological defects are one of the most exciting non-equilibrium systems of recent times. In our experiments, we confine an active nematic populated by positive and negative topological defects to a toroidal surface, and explore how the local geometry, parameterised by the Gaussian curvature, influences the distribution of defects. We find curvature-induced defect unbinding, for relatively thick tori and low activities. In contrast, for high activity and thin tori, which serve to locally approach the cylindrical limit, the relevance of the defect-curvature coupling is lost. Overall, our results illustrate how curvature and activity can both be used to affect how defects distribute on surfaces with varying curvature.

Real space iterative reconstruction for vector tomography (RESIRE-V)

Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method. To make the algorithm accessible to a broad user community, we have made our RESIRE-V MATLAB source codes and the data freely available at https://github.com/minhpham0309/RESIRE-V.

Fusion category symmetry. Part I. Anomaly in-flow and gapped phases

We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we describe ’t Hooft anomalies and classify gapped phases stabilized by these symmetries, including new 1+1D topological phases. The algebra of these operators is not a group but rather is described by their fusion ring and crossing relations, captured algebraically as a fusion category. Such data defines a Turaev-Viro/Levin-Wen model in 2+1D, while a 1+1D system with this fusion category acting as a global symmetry defines a boundary condition. This is akin to gauging a discrete global symmetry at the boundary of Dijkgraaf-Witten theory. We describe how to “ungauge” the fusion category symmetry in these boundary conditions and separate the symmetry-preserving phases from the symmetry-breaking ones. For Tambara-Yamagami categories and their generalizations, which are associated with Kramers-Wannier-like self-dualities under orbifolding, we develop gauge theoretic techniques which simplify the analysis. We include some examples of CFTs with fusion category symmetry derived from Kramers-Wannier-like dualities as an appetizer for the Part II companion paper.

Intrinsic conformal order revealed in geometrically confined long-range repulsive particles

Abstract Elucidating long-range interaction guided organization of matter is a fundamental question in physical systems covering multiple length scales. Here, based on the hexagonal disk model, we analyze the characteristic inhomogeneity created by long-range repulsions, and reveal the intrinsic conformal order in particle packings in equilibrium. Specifically, we highlight the delicate angle-preserved bending of the lattice to match the inhomogeneity condition. The revealed conformal order is found to be protected by the surrounding topological defects. These results advance our understanding on long-range interacting systems, and open the promising possibilities of using long-range forces to create particle packings not accessible by short-range forces, which may have practical consequences.