Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals

Convolutional neural network analysis of optical texture patterns in liquid-crystal skyrmions

Liquid crystals are known for their optical birefringence, a property that gives rise to intricate patterns and colors when viewed in a microscope between crossed polarisers. Resulting images are rich in geometric patterns and serve as valuable fingerprints of the liquid crystal's intrinsic properties. By using machine learning techniques, it is possible to extract from the images information about, e.g., liquid crystal elastic constants, the scalar order parameter, local orientation of the director, etc. Machine learning can also be employed to identify phase transitions and classify different liquid crystalline phases and topological defects. In addition to well studied singular defects such as point or line disclinations, liquid crystals can also host non-singular solitonic defects such as skyrmions, hopfions, and torons. The solitons, with their localised and stable configurations, offer an alternative view into material properties and behaviour of liquid crystals. In this study, we demonstrate that the optical signatures of skyrmions can be utilised effectively in machine learning to predict important system parameters. Our method focuses specifically on the skyrmion-localised regions, reducing significantly the computational cost. By training convolutional neural networks on simulated polarised optical microscopy images of liquid crystal skyrmions, we showcase the ability of trained networks to accurately predict several selected parameters such as the free energy, cholesteric pitch, and strength of applied electric fields. This study highlights the importance of localised topologically arrested order parameter configurations for materials characterisation research empowered by state-of-the-art data science methods, and may pave the way for the development of advanced skyrmion-based applications.

Liquid crystal torons in Poiseuille-like flows

Three-dimensional (3D) simulations of the structure of liquid crystal (LC) torons, topologically protected distortions of the LC director field, under material flows are rare but essential in microfluidic applications. Here, we show that torons adopt a steady-state configuration at low flow velocity before disintegrating at higher velocities, in line with experimental results. Furthermore, we show that under partial slip conditions at the boundaries, the flow induces a reversible elongation of the torons, also consistent with the experimental observations. These results are in contrast with previous simulation results for 2D skyrmions under similar flow conditions, highlighting the need for a 3D description of this LC soliton in relation to its coupling to the material flow. These findings pave the way for future studies of other topological solitons, like hopfions and heliknotons, in flowing soft matter systems.

Flowing Liquid Crystal Torons Around Obstacles

Liquid crystal torons, localized topological structures, are known for their stability and dynamic behaviour in response to external stimuli, making them attractive for advanced material applications. In this study, we investigate the flow of torons in chiral nematic liquid crystals around obstacles. We simulate the fluid flow and director field interactions using a hybrid numerical method combining lattice Boltzmann and finite difference techniques. Our results reveal that the toron dynamical behaviour depends strongly on the impact parameter from the obstacle. At impact parameters smaller than half cholesteric pitch, the flowing toron is destabilized by the interaction with the obstacle; otherwise, the flowing toron follows a trajectory with a deflection which decays exponentially with the impact parameter. Additionally, we explore the scattering of torons by multiple obstacles, providing insights into how the dynamics of these structures respond to complex environments.

Out-of-equilibrium interactions and collective locomotion of colloidal spheres with squirming of nematoelastic multipoles

Many living and artificial systems show similar emergent behavior and collective motions on different scales, starting from swarms of bacteria to synthetic active particles, herds of mammals, and crowds of people. What all these systems often have in common is that new collective properties like flocking emerge from interactions between individual self-propelled or driven units. Such systems are naturally out-of-equilibrium and propel at the expense of consumed energy. Mimicking nature by making self-propelled or externally driven particles and studying their individual and collective motility may allow for deeper understanding of physical underpinnings behind collective motion of large groups of interacting objects or beings. Here, using a soft matter system of colloids immersed into a liquid crystal, we show that resulting so-called nematoelastic multipoles can be set into a bidirectional locomotion by external oscillating electric fields. Out-of-equilibrium elastic interactions between such colloidal objects lead to collective flock-like behaviors emerging from time-varying elasticity-mediated interactions between externally driven propelling particles. Repulsive elastic interactions in the equilibrium state can be turned into attractive interactions in the out-of-equilibrium state under applied external electric fields. We probe this behavior at different number densities of colloidal particles and show that particles in dense dispersions collectively select the same direction of a coherent motion due to elastic interactions between near neighbors. In our experimentally implemented design, their motion is highly ordered and without clustering or jamming often present in other colloidal transport systems, which is promising for technological and fundamental-science applications, like nano-cargo transport, out-of-equilibrium assembly, and microrobotics.

Particle-based model of liquid crystal skyrmion dynamics

Motivated by recent experimental results that reveal rich collective dynamics of thousands-to-millions of active liquid crystal skyrmions, we have developed a coarse-grained, particle-based model of the dynamics of skyrmions in a dilute regime. The basic physical mechanism of skyrmion motion is related to squirming undulations of domains with high director twist within the skyrmion cores when the electric field is turned on and off. The motion is not related to mass flow and is caused only by the reorientation dynamics of the director field. Based on the results of the "fine-grained" Frank-Oseen continuum model, we have mapped these squirming director distortions onto an effective force that acts asymmetrically upon switching the electrical field on or off. The resulting model correctly reproduces the skyrmion dynamics, including velocity reversal as a function of the frequency of a pulse width modulated driving voltage. We have also obtained approximate analytical expressions for the phenomenological model parameters encoding their dependence upon the cholesteric pitch and the strength of the electric field. This has been achieved by fitting coarse-grained skyrmion trajectories to those determined in the framework of the Frank-Oseen model.

Field-controlled dynamics of skyrmions and monopoles

Magnetic monopoles, despite their ongoing experimental search as elementary particles, have inspired the discovery of analogous excitations in condensed matter systems. In chiral condensed matter systems, emergent monopoles are responsible for the onset of transitions between topologically distinct states and phases, such as in the case of transitions from helical and conical phase to A-phase comprising periodic arrays of skyrmions. By combining numerical modeling and optical characterizations, we describe how different geometrical configurations of skyrmions terminating at monopoles can be realized in liquid crystals and liquid crystal ferromagnets. We demonstrate how these complex structures can be effectively manipulated by external magnetic and electric fields. Furthermore, we discuss how our findings may hint at similar dynamics in other physical systems and their potential applications.

Temperature reconfigurable skyrmionic solitons in cholesteric liquid crystals

In this work, a reversible transformation between torons and cholesteric fingers is realized by continuously changing the pitch through temperature variation of the chiral nematic liquid crystal twist inversion system. By decreasing the pitch, the torons act as seeds from which cholesteric fingers gradually grow. By increasing the pitch, the cholesteric fingers gradually shorten and transform back to the initial state. We find that although the morphology of the torons is severely deformed and cannot be distinguished during the heating-cooling loops, the torons are very well topologically protected and can hardly be destroyed.

Active nematic liquid crystals simulated by particle-based mesoscopic methods

Two Multi-particle collision dynamics algorithms that simulate nematic liquid crystals are generalised to reproduce active behaviour. One of the algorithms is due to Shendruk and Yeomans and is based on particles that carry an orientation vector ordered by a mean-field energy [T. N. Shendruk and J. M. Yeomans, Soft Matter, 2015, 11, 5101]. In the other algorithm, due to Mandal and Mazza, particles possess an order parameter tensor which evolves according to the Qian-Sheng model of nematohydrodynamics [S. Mandal and M. G. Mazza, Phys. Rev. E, 2019, 99, 063319]. For both methods activity is incorporated through a force proportional to the divergence of the local average order parameter tensor. Both implementations produce disclination curves in the nematic fluid that undergo nucleation and self-annihilation dynamics. Topological defects are found to be consistent with those observed in recent experiments of three-dimensional active nematics. Results permit to compare the length-scales over which the different nematic Multi-particle collision dynamics methods operate. The structure and dynamics of the orientation and flow fields agree with those obtained recently in numerical studies of continuum three-dimensional active nematics. Overall, our results open the opportunity to use mesoscopic particle-based approaches to study active liquid crystals in situations such as nonequilibrium states driven by flow or colloidal particles in active anisotropic solvents.

Programming Solitons in Liquid Crystals Using Surface Chemistry

AC electric fields cause three-dimensional orientational fluctuations (solitons) to form and rapidly propagate in confined films of liquid crystals (LCs), offering the basis of a new class of active soft matter (e.g., for accelerating mixing and transport processes in microscale chemical systems). How surface chemistry impacts the formation and trajectories of solitons, however, is not understood. Here, we show that self-assembled monolayers (SAMs) formed from alkanethiols on gold, which permit precise control over surface chemistry, are electrochemically stable over voltage and frequency windows (<100 V; 1 kHz) that lead to soliton formation in achiral nematic films of 4'-butyl-4-heptyl-bicyclohexyl-4-carbonitrile (CCN-47). By comparing soliton formation in LC films confined by SAMs formed from hexadecanethiol (C₁₆SH) or pentadecanethiol (C₁₅SH), we reveal that the electric field required for soliton formation increases with the LC anchoring energy: surfaces patterned with regions of C₁₆SH and C₁₅SH SAMs thus permit spatially controlled creation and annihilation of solitons necessary to generate a net flux of solitons. We also show that solitons propagate in orthogonal directions when confined by obliquely deposited gold films decorated with SAMs formed from C₁₆SH or C₁₅SH and that the azimuthal direction of propagation of solitons within achiral LC films possessing surface-induced twists is not unique but reflects variation in the spatial location of the solitons across the thickness of the twisted LC film. Finally, discontinuous changes in LC orientation induced by patterned surface anchoring lead to a range of new soliton behaviors including refraction, reflection, and splitting of solitons at the domain boundaries. Overall, our results provide new approaches for the controlled generation and programming of solitons with complex and precise trajectories, principles that inform new designs of chemical soft matter.

Recent Progresses on Experimental Investigations of Topological and Dissipative Solitons in Liquid Crystals

Solitons in liquid crystals have received increasing attention due to their importance in fundamental physical science and potential applications in various fields. The study of solitons in liquid crystals has been carried out for over five decades with various kinds of solitons being reported. Recently, a number of new types of solitons have been observed, among which, many of them exhibit intriguing dynamic behaviors. In this paper, we briefly review the recent progresses on experimental investigations of solitons in liquid crystals.

Coarse-grained theory for motion of solitons and skyrmions in liquid crystals

Recent experiments have found that applied electric fields can induce motion of skyrmions in chiral nematic liquid crystals. To understand the magnitude and direction of the induced motion, we develop a coarse-grained approach to describe dynamics of skyrmions, similar to our group's previous work on the dynamics of disclinations. In this approach, we represent a localized excitation in terms of a few macroscopic degrees of freedom, including the position of the excitation and the orientation of the background director. We then derive the Rayleigh dissipation function, and hence the equations of motion, in terms of these macroscopic variables. We demonstrate this theoretical approach for 1D motion of a sine-Gordon soliton, and then extend it to 2D motion of a skyrmion. Our results show that skyrmions move in a direction perpendicular to the induced tilt of the background director. When the applied field is removed, skyrmions move in the opposite direction but not with equal magnitude, and hence the overall motion may be rectified.

Surface anchoring as a control parameter for shaping skyrmion or toron properties in thin layers of chiral nematic liquid crystals and noncentrosymmetric magnets

Existence of topological localized states (skyrmions and torons) and the mechanism of their condensation into modulated states are the ruling principles of condensed matter systems, such as chiral nematic liquid crystals (CLCs) and chiral magnets (ChM). In bulk helimagnets, skyrmions are rendered into thermodynamically stable hexagonal skyrmion lattice due to the combined effect of a magnetic field and, e.g., small anisotropic contributions. In thin glass cells of CLCs, skyrmions are formed in response to the geometrical frustration and field coupling effects. By numerical modeling, I undertake a systematic study of skyrmion or toron properties in thin layers of CLCs and ChMs with competing surface-induced and bulk anisotropies. The conical phase with a variable polar angle serves as a suitable background, which shapes skyrmion internal structure, guides the nucleation processes, and substantializes the skyrmion-skyrmion interaction. I show that the hexagonal lattice of torons can be stabilized in a vast region of the constructed phase diagram for both easy-axis bulk and surface anisotropies. A topologically trivial droplet is shown to form as a domain boundary between two cone states with different rotational fashion, which underpins its stability. The findings provide a recipe for controllably creating skyrmions and torons, possessing the features on demand for potential applications.

Dynamics of flowing 2D skyrmions

We investigate, numerically, the effects of externally imposed material flows on the structure and temporal evolution of liquid crystal (LC) skyrmions. The dynamics of a 2D system of skyrmions is modeled using the Ericksen-Leslie theory, which is based on two coupled equations, one for material flow and the other for the director field. As the time scales of the velocity and director fields differ by several orders of magnitude for realistic values of the system parameters, we have simplified the calculations by assuming that the velocity relaxes instantaneously when compared to the relaxation of the director field. Thus, we have used a finite-differences method known as artificial compressibility with adaptive time step to solve the velocity field and a fourth-order Runge-Kutta method for the director field. We characterized the skyrmion shape or configuration as a function of the time and the average velocity of the flow field. We found that for velocities above a certain threshold, the skyrmions stretch in the direction perpendicular to the flow, by contrast to the regime of weak flows where the skyrmions stretch along the streamlines of the flow field. These two regimes are separated by an abrupt (first-order) dynamical transition, which is robust with respect to e.g., the LC elastic anisotropy. Additionally, we have found how the presence of a second skyrmion affects the evolution of the shape of the skyrmions, by comparing the evolution of pairs of skyrmions to the evolution of a single-skyrmion.

Photo-reconfigurable twisting structure in chiral liquid crystals triggered by photoresponsive surface

Shape-transformable molecular additives with photoresponsivity, such as azobenzene or spiropyran, in matter are known to decrease the local order parameter and lead to drastic state variations under light irradiation. For example, a liquid crystalline state can be transformed to an isotropic liquid state by photo-exciting a tiny amount of azobenzene additives from trans- to cis-conformers. On the other hand, structural or shape transformation without changing the phase state is also intriguing since it offers an opportunity for manipulating specific structures. Here, we demonstrate an active control of the topology of chiral particle-like twisting structures, dubbed toron, by light. Interestingly, the individual twisting structure is fully reconfigurable between spherical and unique branched topological states. We reveal that the shape transformation is driven by the free-energy competition between the variation of surface anchoring strength and the elastic energy stored in the twisting structure. The mean-field simulation based on the Landau-de Gennes framework shows that the elastic anisotropy plays the dominant role in modifying the toron topology upon weak anchoring. The results offer a new path for understanding the process of topology-involved shape transformation and fabrication of novel functional materials.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Skyrmion Spin Ice in Liquid Crystals

We propose the first skyrmion spin ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasiparticles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasiparticles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of liquid crystal skyrmions as elementary degrees of freedom in the design of collective complex behaviors.

Differential rotation in cholesteric pillars under a temperature gradient

Steady rotation is induced in cholesteric droplets dispersed in a specific liquid solvent under a temperature gradient. In this phenomenon, two rotational modes have been considered: (1) collective rotation of the local director field and (2) rigid-body rotation of the whole droplet structure. However, here we present another rotational mode induced in a pillar-shaped cholesteric droplet confined between substrates under a temperature gradient, that is, a differential rotation where the angular velocity varies as a function of the radial coordinate in the pillar. A detailed flow field analysis revealed that every pillar under a temperature gradient involves a double convection roll. These results suggested that the differential rotation in the cholesteric pillars was driven by the inhomogeneous material flow induced by a temperature gradient. The present experimental study indicates that the coupling between the flow and the director motion plays a key role in the rotation of the cholesteric droplets under the temperature gradient.

Review: knots and other new topological effects in liquid crystals and colloids

Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.

Kinetics of motile solitons in nematic liquid crystals

The generation of spatially localized, soliton-like hydrodynamic disturbances in microscale fluidic systems is an intriguing challenge. Herein, we introduce nonequilibrium solitons in nematic liquid crystals stimulated by an electric field. These dynamic solitons are robust as long as the electric field is maintained. Interestingly, their kinetic behaviours depend on the field condition-Tuning of the amplitude and frequency of the applied electric field alters the solitons to self-assemble into lattice ordering like physical particles or to command them to various dynamic states. Our key property to the realisation is the electrohydrodynamic instability due to the coupling between the fluid elasticity and the background convection. This paper describes a new mechanism for realising dynamic solitons in fluid systems on the basis of the electrohydrodynamic phenomena.

Hopfions emerge in ferroelectrics

Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant, attract an intense attention in the diverse areas of physics ranging from high-energy physics, cosmology and astrophysics to biology, magneto- and hydrodynamics and condensed matter physics. Yet, while being of broad interest, they remain elusive and under-explored. Here we demonstrate that Hopfions emerge as a basic configuration of polarization field in confined ferroelectric nanoparticles. Our findings establish that Hopfions are of fundamental importance for the electromagnetic behavior of the nanocomposits and can result in advanced functionalities of these materials.

In spite of the growing recognition of the role of Hopfions in topological phases, their physical properties remain poorly understood. Here, the authors theoretically demonstrate that Hopfions are fundamental topological formations in confined ferroelectrics governing their electromagnetic response.

Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers, and their hybrids in chiral nematics

Chiral condensed matter systems, such as liquid crystals and magnets, exhibit a host of spatially localized topological structures that emerge from the medium's tendency to twist and its competition with confinement and field coupling effects. We show that the strength of perpendicular surface boundary conditions can be used to control the structure and topology of solitonic and other localized field configurations. By combining numerical modeling and three-dimensional imaging of the director field, we reveal structural stability diagrams and intertransformation of twisted walls and fingers, torons, and skyrmions and their crystalline organizations upon changing boundary conditions. Our findings provide a recipe for controllably realizing skyrmions, torons, and hybrid solitonic structures possessing features of both of them, which will aid in fundamental explorations and technological uses of such topological solitons. Moreover, we discuss how other material parameters can be used to determine soliton stability and how similar principles can be systematically applied to other liquid crystal solitons and solitons in other material systems.

Electrically powered motions of toron crystallites in chiral liquid crystals

Malleability of metals is an example of how the dynamics of defects like dislocations induced by external stresses alters material properties and enables technological applications. However, these defects move merely to comply with the mechanical forces applied on macroscopic scales, whereas the molecular and atomic building blocks behave like rigid particles. Here, we demonstrate how motions of crystallites and the defects between them can arise within the soft matter medium in an oscillating electric field applied to a chiral liquid crystal with polycrystalline quasi-hexagonal arrangements of self-assembled topological solitons called "torons." Periodic oscillations of electric field applied perpendicular to the plane of hexagonal lattices prompt repetitive shear-like deformations of the solitons, which synchronize the electrically powered self-shearing directions. The temporal evolution of deformations upon turning voltage on and off is not invariant upon reversal of time, prompting lateral translations of the crystallites of torons within quasi-hexagonal periodically deformed lattices. We probe how these motions depend on voltage and frequency of oscillating field applied in an experimental geometry resembling that of liquid crystal displays. We study the interrelations between synchronized deformations of the soft solitonic particles and their arrays, and the ensuing dynamics and giant number fluctuations mediated by motions of crystallites, five-seven defects pairs, and grain boundaries in the orderly organizations of solitons. We discuss how our findings may lead to technological and fundamental science applications of dynamic self-assemblies of topologically protected but highly deformable particle-like solitons.

Topological solitons, cholesteric fingers and singular defect lines in Janus liquid crystal shells

Topological solitons are non-singular but topologically nontrivial structures in fields, which have fundamental significance across various areas of physics, similar to singular defects. Production and observation of singular and solitonic topological structures remain a complex undertaking in most branches of science - but in soft matter physics, they can be realized within the director field of a liquid crystal. Additionally, it has been shown that confining liquid crystals to spherical shells using microfluidics resulted in a versatile experimental platform for the dynamical study of topological transformations between director configurations. In this work, we demonstrate the triggered formation of topological solitons, cholesteric fingers, singular defect lines and related structures in liquid crystal shells. We show that to accommodate these objects, shells must possess a Janus nature, featuring both twisted and untwisted domains. We report the formation of linear and axisymmetric objects, which we identify as cholesteric fingers and skyrmions or elementary torons, respectively. We then take advantage of the sensitivity of shells to numerous external stimuli to induce dynamical transitions between various types of structures, allowing for a richer phenomenology than traditional liquid crystal cells with solid flat walls. Using gradually more refined experimental techniques, we induce the targeted transformation of cholesteric twist walls and fingers into skyrmions and elementary torons. We capture the different stages of these director transformations using numerical simulations. Finally, we uncover an experimental mechanism to nucleate arrays of axisymmetric structures on shells, thereby creating a system of potential interest for tackling crystallography studies on curved spaces.

Optically enriched and guided dynamics of active skyrmions

Light provides a powerful means of controlling physical behavior of materials but is rarely used to power and guide active matter systems. We demonstrate optical control of liquid crystalline topological solitons dubbed "skyrmions", which recently emerged as highly reconfigurable inanimate active particles capable of exhibiting emergent collective behaviors like schooling. Because of a chiral nematic liquid crystal's natural tendency to twist and its facile response to electric fields and light, it serves as a testbed for dynamic control of skyrmions and other active particles. Using ambient-intensity unstructured light, we demonstrate large-scale multifaceted reconfigurations and unjamming of collective skyrmion motions powered by oscillating electric fields and guided by optically-induced obstacles and patterned illumination.

Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions

Current-induced motion of non-axisymmetric skyrmions within tilted ferromagnetic phases of polar helimagnets with the easy plane anisotropy is studied by micromagnetic simulations. Such non-axisymmetric skyrmions consist of a circular core and a crescent-shaped domain-wall region formed with respect to the tilted surrounding state. Current-driven motion of non-axisymmetric skyrmions exhibits two distinct time regimes: initially the skyrmions rotate towards the current flow direction and subsequently move along the current with the skyrmionic crescent first. According to the Thiele equation, the asymmetric distribution of the topological charge and the dissipative force tensor play an important role for giving the different velocities for the circular and the crescent-shaped constituent parts of the skyrmion what underlies such a shuttlecock-like movement. Moreover, the current-velocity relation depends on the angle of the tilted ferromagnetic phase what makes in particular the transverse velocity of skyrmions sensitive to their field-driven configurational transformation. We also argue the possibility of magnetic racetrack waveguides based on complex interplay of robust asymmetric skyrmions with multiple twisted edge states.

Schools of skyrmions with electrically tunable elastic interactions

Coexistence of order and fluidity in soft matter often mimics that in biology, allowing for complex dynamics and applications-like displays. In active soft matter, emergent order can arise because of such dynamics. Powered by local energy conversion, this behavior resembles motions in living systems, like schooling of fish. Similar dynamics at cellular levels drive biological processes and generate macroscopic work. Inanimate particles capable of such emergent behavior could power nanomachines, but most active systems have biological origins. Here we show that thousands-to-millions of topological solitons, dubbed “skyrmions”, while each converting macroscopically-supplied electric energy, exhibit collective motions along spontaneously-chosen directions uncorrelated with the direction of electric field. Within these “schools” of skyrmions, we uncover polar ordering, reconfigurable multi-skyrmion clustering and large-scale cohesion mediated by out-of-equilibrium elastic interactions. Remarkably, this behavior arises under conditions similar to those in liquid crystal displays and may enable dynamic materials with strong emergent electro-optic responses.

While flocking and schooling are more often associated with birds and fish, these types of behaviour can also be observed in inanimate systems. Here the authors demonstrate schooling of topological solitons in a liquid crystal system powered by oscillating electric fields.

Light-controlled skyrmions and torons as reconfigurable particles

Topological solitons, such as skyrmions, arise in field theories of systems ranging from Bose-Einstein condensates to optics, particle physics, and cosmology, but they are rarely accessible experimentally. Chiral nematic liquid crystals provide a platform to study skyrmions because of their natural tendency to form twisted structures arising from the lack of mirror symmetry at the molecular level. However, large-scale dynamic control and technological utility of skyrmions remain limited. Combining experiments and numerical modeling of chiral liquid crystals with optically controlled helical pitch, we demonstrate that low-intensity, unstructured light can control stability, dimensions, interactions, spatial patterning, self-assembly, and dynamics of these topological solitons.