A Monte Carlo simulation study of a Janus discotic liquid crystal droplet.

The study of discotic liquid crystals (DLCs) under spherical confinement has gained considerable significance due to its relevance in the design and optimization of advanced materials with tailored properties. The unique characteristics of DLC fluids, coupled with confinement within a spherical Janus surface, offer a compelling avenue for exploring novel behaviors and emergent phenomena. In this study, Monte Carlo simulations within the NpT ensemble are employed to investigate the behavior of a DLC fluid confined by a spherical Janus surface. The Janus surface is characterized by distinct hemispheres, with one promoting homeotropic (face-on) anchoring and the other planar (edge-on) anchoring. Our analysis reveals the emergence of two topological defects: one exclusively on the edge-anchoring hemisphere and the other at the boundary of both anchorings. Each topological defect possessing a topological charge ofk= +1/2. We observe that as the temperature transitions the central region of the droplet into a nematic phase, a disclination line forms, linking the two surface defects. By investigating droplets of three different sizes, we confirm that the isotropic-nematic transition is first-order for the larger droplet studied. However, this transition becomes continuous under strong confinement conditions. In contrast, the nematic-columnar transition remains first order even for smaller systems.

Growth-induced collective bending and kinetic trapping of cytoskeletal filaments.

Growth and turnover of actin filaments play a crucial role in the construction and maintenance of actin networks within cells. Actin filament growth occurs within limited space and finite subunit resources in the actin cortex. To understand how filament growth shapes the emergent architecture of actin networks, we developed a minimal agent-based model coupling filament mechanics and growth in a limiting subunit pool. We find that rapid filament growth induces kinetic trapping of highly bent actin filaments. Such collective bending patterns are long-lived, organized around nematic defects, and arise from competition between filament polymerization and bending elasticity. The stability of nematic defects and the extent of kinetic trapping are amplified by an increase in the abundance of the actin pool and by crosslinking the network. These findings suggest that kinetic trapping is a robust consequence of growth in crowded environments, providing a route to program shape memory in actin networks.

Design rules for controlling active topological defects.

Topological defects play a central role in the physics of many materials, including magnets, superconductors, and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here, we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move, and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory, and logic.

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 22.5 mA cm-2 at 0.8 V 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 0.74 V), 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.

Correlated order at the tipping point in the kagome metal CsV3Sb5.

Spontaneously broken symmetries are at the heart of many phenomena of quantum matter and physics more generally. However, determining the exact symmetries that are broken can be challenging due to imperfections such as strain, in particular when multiple electronic orders are competing. This is exemplified by charge order in some kagome systems, where evidence of nematicity and flux order from orbital currents remains inconclusive due to contradictory measurements. Here we clarify this controversy by fabricating highly symmetric samples of a member of this family, CsV3Sb5, and measuring their transport properties. We find that a measurable anisotropy is absent at any temperature in the unperturbed material. However, a pronounced in-plane transport anisotropy appears when either weak magnetic fields or strains are present. A symmetry analysis indicates that a perpendicular magnetic field can indeed lead to in-plane anisotropy by inducing a flux order coexisting with more conventional bond order. Our results provide a unifying picture for the controversial charge order in kagome metals and highlight the need for materials control at the microscopic scale in the identification of broken symmetries.

Topological Defect-Regulated Porous Carbon Anodes with Fast Interfacial and Bulk Kinetics for High-Rate and High-Energy-Density Potassium-Ion Batteries.

Carbonaceous materials are regarded as one of the most promising anodes for potassium-ion batteries (PIBs), but their rate capabilities are largely limited by the slow solid-state potassium diffusion kinetics inside anode and sluggish interfacial potassium ion transfer process. Herein, high-rate and high-capacity PIBs are demonstrated by facile topological defect-regulation of the microstructure of carbon anodes. The carbon lattice of the as-obtained porous carbon nanosheets (CNSs) with abundant topological defects (TDPCNSs) holds relatively high potassium adsorption energy yet low potassium migration barrier, thereby enabling efficient storage and diffusion of potassium inside graphitic layers. Moreover, the topological defects can induce preferential decomposition of anions, leading to the formation of high potassium ion conductive solid electrolyte interphase (SEI) film with decreased potassium ion de-solvation and transfer barrier. Additionally, the dominant sp2-hybridized carbon conjugated skeleton of TDPCNSs enables high electrical conductivity (39.4 S cm-1) and relatively low potassium storage potential. As a result, the as-constructed TDPCNSs anode demonstrates high potassium storage capacity (504 mA h g-1 at 0.1 A g-1), remarkable rate capability (118 mA h g-1 at 40 A g-1), as well as long-term cycling stability.

Probing active nematics with in situ microfabricated elastic inclusions.

In this work, we report a direct measurement of the forces exerted by a tubulin/kinesin active nematic gel as well as its complete rheological characterization, including the quantification of its shear viscosity, η, and its activity parameter, α. For this, we develop a method that allows us to rapidly photo-polymerize compliant elastic inclusions in the continuously remodeling active system. Moreover, we quantitatively settle long-standing theoretical predictions, such as a postulated relationship encoding the intrinsic time scale of the active nematic in terms of η and α. In parallel, we infer a value for the nematic elasticity constant, K, by combining our measurements with the theorized scaling of the active length scale. On top of the microrheology capabilities, we demonstrate strategies for defect encapsulation, quantification of defect mechanics, and defect interactions, enabled by the versatility of the microfabrication strategy that allows to combine elastic motifs of different shapes and stiffnesses that are fabricated in situ.

Biaxial Structures of Localized Deformations and Line-like Distortions in Effectively 2D Nematic Films.

We numerically studied localized elastic distortions in curved, effectively two-dimensional nematic shells. We used a mesoscopic Landau-de Gennes-type approach, in which the orientational order is theoretically considered by introducing the appropriate tensor nematic order parameter, while the three-dimensional shell shape is described by the curvature tensor. We limited our theoretical consideration to axially symmetric shapes of nematic shells. It was shown that in the surface regions of stomatocyte-class nematic shell shapes with large enough magnitudes of extrinsic (deviatoric) curvature, the direction of the in-plane orientational ordering can be mutually perpendicular above and below the narrow neck region. We demonstrate that such line-like nematic distortion configurations may run along the parallels (i.e., along the circular lines of constant latitude) located in the narrow neck regions of stomatocyte-like nematic shells. It was shown that nematic distortions are enabled by the order reconstruction mechanism. We propose that the regions of nematic shells that are strongly elastically deformed, i.e., topological defects and line-like distortions, may attract appropriately surface-decorated nanoparticles (NPs), which could potentially be useful for the controlled assembly of NPs.

Growth-induced collective bending and kinetic trapping of cytoskeletal filaments.

Growth and turnover of actin filaments play a crucial role in the construction and maintenance of actin networks within cells. Actin filament growth occurs within limited space and finite subunit resources in the actin cortex. To understand how filament growth shapes the emergent architecture of actin networks, we developed a minimal agent-based model coupling filament mechanics and growth in a limiting subunit pool. We find that rapid filament growth induces kinetic trapping of highly bent actin filaments. Such collective bending patterns are long-lived, organized around nematic defects, and arises from competition between filament polymerization and bending elasticity. The stability of nematic defects and the extent of kinetic trapping are amplified by an increase in the abundance of the actin pool and by crosslinking the network. These findings suggest that kinetic trapping is a robust consequence of growth in crowded environments, providing a route to program shape memory in actin networks.

Active smectics on a sphere.

The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.

Mechanical Actuation via Homeomorphic Transformations of Topological Solitons within Polymer Coatings.

Topological solitons are currently under investigation for their exotic properties, especially in nonlinear physics, optics, and material sciences. However, challenges of robust generation and limited stability over time have hindered their practical uses. To address this issue, an approach is developed to form structured arrays of solitons in films of polymerizable liquid crystals. Their complex molecular architecture is preserved by in situ photopolymerization forming a stable liquid crystal network. Most excitingly, their properties are advanced to include responsiveness functions. When thermally actuated, these topological solitons mediate the reconfiguration of surface topographies. Complex shape changes occur depending on the intrinsic complex spatial distribution of the director, which may even lead to full shape inversion and topographical changes as high as ≈40% of the initial thickness. Conversely, the shape changes provide information on the initial director profile, which is consistent with the mathematical model. The soliton-containing polymer coatings are applicable in multiple domains, ranging from tunable optics to haptics, and from shape-coupled sensing systems to temperature-coupled heat management.

Periodic Defect Engineering of Iron-Nitrogen-Carbon Catalysts for Nitrate Electroreduction to Ammonia.

Iron-nitrogen-carbon single atom catalyst (SAC) is regarded as one of the promising electrocatalysts for NO3 - reduction reaction (NO3 RR) to NH3 due to its high activity and selectivity. However, synergistic effects of topological defects and FeN4 active moiety in Fe-N-C SAC have rarely been investigated. By performing density functional theory (DFT) calculations, 13 defective graphene FeN4 with 585, 484, and 5775 topological line defects are constructed, yielding 585-68-FeN4 with optimal NO3 RR catalytic activity, high selectivity, as well as robust anti-dissolution stability. The high NO3 RR activity on 585-68-FeN4 is well explained by the high valence state of Fe center as well as asymmetric charge distribution on FeN4 moiety influenced by 5- and 8-member rings. This DFT work provides theoretical guidance for engineering NO3 RR performance of iron-nitrogen-carbon catalysts by modulating periodic topological defects.

Melting of Unidirectional Charge Density Waves across Twin Domain Boundaries in GdTe3.

Solids undergoing a transition from order to disorder experience a proliferation of topological defects. The melting process generates transient quantum states. However, their dynamic nature with a femtosecond lifetime hinders exploration with atomic precision. Here, we suggest an alternative approach to the dynamic melting process by focusing on the interface created by competing degenerate quantum states. We use a scanning tunneling microscope (STM) to visualize the unidirectional charge density wave (CDW) and its spatial progression ("static melting") across a twin domain boundary (TDB) in the layered material GdTe3. Combining the STM with a spatial lock-in technique, we reveal that the order parameter amplitude attenuates with the formation of dislocations and thus two different unidirectional CDWs coexist near the TDB, reducing the CDW anisotropy. Notably, we discovered a correlation between this anisotropy and the CDW gap. Our study provides valuable insight into the behavior of topological defects and transient quantum states.

Migration and division in cell monolayers on substrates with topological defects.

Collective movement and organization of cell monolayers are important for wound healing and tissue development. Recent experiments highlighted the importance of liquid crystal order within these layers, suggesting that +1 topological defects have a role in organizing tissue morphogenesis. We study fibroblast organization, motion, and proliferation on a substrate with micron-sized ridges that induce +1 and -1 topological defects using simulation and experiment. We model cells as self-propelled deformable ellipses that interact via a Gay-Berne potential. Unlike earlier work on other cell types, we see that density variation near defects is not explained by collective migration. We propose instead that fibroblasts have different division rates depending on their area and aspect ratio. This model captures key features of our previous experiments: the alignment quality worsens at high cell density and, at the center of the +1 defects, cells can adopt either highly anisotropic or primarily isotropic morphologies. Experiments performed with different ridge heights confirm a prediction of this model: Suppressing migration across ridges promotes higher cell density at the +1 defect. Our work enables a mechanism for tissue patterning using topological defects without relying on cell migration.

Electronic Structure Modulation of Nanographenes for Second Order Nonlinear Optical Molecular Materials.

Nanographenes (NGs) have drawn extensive attention as promising candidates for next-generation optoelectronic and nonlinear optical (NLO) materials, owing to its unique optoelectronic properties and high thermal stability. However, the weak polarity or even non-polarity of NGs (resulting in weak even order NLO properties) and the high chemical reactivity of zigzag edged NGs hinder their further applications in nonlinear optics, thus stabilization (lowering the chemical reactivity) and polarizing the charge distribution in NGs are necessary for such applications of NGs. The fusion of heptagon and pentagon endows the azulene with the character of donor-acceptor, and the B=N unit is isoelectronic to C=C unit. The introduction of polar azulene and BN are idea to polarize and stabilize the electronic structure of NGs for NLO applications. In the present review, a survey on the functionalization and applications of NGs in nonlinear optics is conducted. The engineering of the electronic structure of NGs by topological defects, doping and edge modulation is summarized. Finally, a summary of challenges and perspectives for carbon-based NLO nanomaterials is presented.

Pseudocapacitive Potassium-Ion Intercalation Enabled by Topologically Defective Soft Carbon toward High-Rate, Large-Areal-Capacity, and Low-Temperature Potassium-Ion Batteries.

Carbonaceous materials are widely investigated as anodes for potassium-ion batteries (PIBs). However, the inferior rate capability, low areal capacity, and limited working temperature caused by sluggish K-ions diffusion kinetics are still primary challenges for carbon-based anodes. Herein, a simple temperature-programmed co-pyrolysis strategy is proposed for the efficient synthesis of topologically defective soft carbon (TDSC) based on inexpensive pitch and melamine. The skeletons of TDSC are optimized with shortened graphite-like microcrystals, enlarged interlayer spacing, and abundant topological defects (e.g., pentagons, heptagons, and octagons), which endow TDSC with fast pseudocapacitive K-ion intercalation behavior. Meanwhile, micrometer-sized structure can reduce the electrolyte degradation over particle surface and avoid unnecessary voids, ensuring a high initial Coulombic efficiency as well as high energy density. These synergistic structural advantages contribute to excellent rate capability (116 mA h g-1 at 20 C), impressive areal capacity (1.83 mA h cm-2 with a mass loading of 8.32 mg cm-2 ), long-term cycling stability (capacity retention of 91.8% after 1200 h cycling), and low working temperature (-10 °C) of TDSC anodes, demonstrating great potential for the practical application of PIBs.

Evolution of Emergent Monopoles into Magnetic Skyrmion Strings.

Topological defects are fundamental concepts in physics, but little is known about the transition between distinct types across different dimensionalities. In topological magnetism, as in field theory, the transition between 1D strings and 0D monopoles is a key process whose observation has remained elusive. Here, we introduce a novel mechanism that allows for the controlled stabilization of emergent monopoles and show that magnetic skyrmion strings can be folded into monopoles. Conversely, they act as seeds out of which the entire string structure can unfold, containing its complete information. In chiral magnets, this process can be observed by resonant elastic X-ray scattering when the objects are in proximity to a polarized ferromagnet, whereby a pure monopole lattice is emerging on the surface. Our experimental proof of the reversible evolution from monopole to string sheds new light on topological defects and establishes the emergent monopole lattice as a new 3D topological phase.

Tunable three-dimensional architecture of nematic disclination lines.

Disclination lines play a key role in many physical processes, from the fracture of materials to the formation of the early universe. Achieving versatile control over disclinations is key to developing novel electro-optical devices, programmable origami, directed colloidal assembly, and controlling active matter. Here, we introduce a theoretical framework to tailor three-dimensional disclination architecture in nematic liquid crystals experimentally. We produce quantitative predictions for the connectivity and shape of disclination lines found in nematics confined between two thinly spaced glass substrates with strong patterned planar anchoring. By drawing an analogy between nematic liquid crystals and magnetostatics, we find that i) disclination lines connect defects with the same topological charge on opposite surfaces and ii) disclination lines are attracted to regions of the highest twist. Using polarized light to pattern the in-plane alignment of liquid crystal molecules, we test these predictions experimentally and identify critical parameters that tune the disclination lines' curvature. We verify our predictions with computer simulations and find nondimensional parameters enabling us to match experiments and simulations at different length scales. Our work provides a powerful method to understand and practically control defect lines in nematic liquid crystals.

Controlling liquid crystal boojum defects on fixed microparticle arrays via capillarity-assisted particles assembly.

HYPOTHESIS: Colloidal particles in nematic liquid crystals (LCs) are of high interest for self-assembly of soft matter systems. When two free particles approach within a uniaxially-oriented nematic LC, an elastic force is generated due to the distorted nematic director configuration around them, allowing particles to self-assemble by an attractive force. We hypothesize that if particles are immobilized, repulsive forces emerge instead, causing the deflection of the interacting defects to compensate for the energy increase. EXPERIMENTS: We fabricated tailored arrays of spherical silica microparticles via capillarity-assisted particle assembly (CAPA) to investigate the interactions of defects as a function of particle separation. By transferring the particle arrays from the CAPA templates to a glass substrate, we studied interacting boojum defect textures within thin LC films sandwiched between two substrates using polarized optical microscopy (POM). FINDINGS: We observed deflected boojum defects on arrays of fixed silica particles, confirming our hypothesis that the elastic repulsive force between the particles affects the defect orientation. The nematic director configuration is reconstructed by Landau-de Gennes q-tensor modeling, and simulated POM images are obtained by the Jones-Matrix method. Our results provide a new platform for controlling defect interactions and pave the way for future work to study topology and implement new defect based applications in LC films.

Edge-Site-Free and Topological-Defect-Rich Carbon Cathode for High-Performance Lithium-Oxygen Batteries.

The rational design of a stable and catalytic carbon cathode is crucial for the development of rechargeable lithium-oxygen (LiO2 ) batteries. An edge-site-free and topological-defect-rich graphene-based material is proposed as a pure carbon cathode that drastically improves LiO2 battery performance, even in the absence of extra catalysts and mediators. The proposed graphene-based material is synthesized using the advanced template technique coupled with high-temperature annealing at 1800 °C. The material possesses an edge-site-free framework and mesoporosity, which is crucial to achieve excellent electrochemical stability and an ultra-large capacity (>6700 mAh g-1 ). Moreover, both experimental and theoretical structural characterization demonstrates the presence of a significant number of topological defects, which are non-hexagonal carbon rings in the graphene framework. In situ isotopic electrochemical mass spectrometry and theoretical calculations reveal the unique catalysis of topological defects in the formation of amorphous Li2 O2 , which may be decomposed at low potential (∼ 3.6 V versus Li/Li+ ) and leads to improved cycle performance. Furthermore, a flexible electrode sheet that excludes organic binders exhibits an extremely long lifetime of up to 307 cycles (>1535 h), in the absence of solid or soluble catalysts. These findings may be used to design robust carbon cathodes for LiO2 batteries.