Coarse-grained theory for motion of solitons and skyrmions in liquid crystals.
TL;DR: In this paper, a coarse-grained approach was developed to describe the dynamics of skyrmions in chiral nematic liquid crystals, where a localized excitation was represented by a few macroscopic degrees of freedom, including the position of the excitation and the orientation of the background director.
Abstract: 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.
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TL;DR: In this paper , the authors focus on chiral nematic liquid crystals to show how these experimentally highly accessible systems provide valuable insights into the structure and behavior of fractional, full and multi-integer two-dimensional skyrmions, dislocations and both abelian and non-abelian defect lines, as well as various three-dimensionalally localized, often knotted structures that include hopfions, heliknotons, torons and twistions.
Abstract: Widely known for their uses in displays and electro-optics, liquid crystals are more than just technological marvels. They vividly reveal the topology and structure of various solitonic and singular field configurations, often markedly resembling the ones arising in many field theories and in the areas ranging from particle physics to optics, hard condensed matter and cosmology. In this review, we focus on chiral nematic liquid crystals to show how these experimentally highly accessible systems provide valuable insights into the structure and behavior of fractional, full, and multi-integer two-dimensional skyrmions, dislocations and both abelian and non-abelian defect lines, as well as various three-dimensionally localized, often knotted structures that include hopfions, heliknotons, torons and twistions. We provide comparisons of some of these field configurations with their topological counterparts in chiral magnets, discussing close analogies between these two condensed matter systems.
10 citations
TL;DR: In this article , stable Hopf solitons in a liquid crystal material without the need of applied fields or confinement for stability were demonstrated. But the authors did not consider the effect of electric fields on the stability of the Hopf map.
Abstract: Arising in many branches of physics, Hopf solitons are three-dimensional particle-like field distortions with nontrivial topology described by the Hopf map. Despite their recent discovery in colloids and liquid crystals, the requirement of applied fields or confinement for stability impedes their utility in technological applications. Here we demonstrate stable Hopf solitons in a liquid crystal material without these requirements as a result of enhanced stability by tuning anisotropy of parameters that describe energetic costs of different gradient components in the molecular alignment field. Nevertheless, electric fields allow for inter-transformation of Hopf solitons between different geometric embodiments, as well as for their three-dimensional hopping-like dynamics in response to electric pulses. Numerical modelling reproduces both the equilibrium structure and topology-preserving out-of-equilibrium evolution of the soliton during switching and motions. Our findings may enable myriads of solitonic condensed matter phases and active matter systems, as well as their technological applications.
4 citations
TL;DR: In this paper , a nonpolar chiral liquid crystal system is used to show how twist domain walls can co-assemble with vortices to form spatially localized topological objects with spontaneous folding.
Abstract: Abstract Topological solitons commonly appear as energy-minimizing field configurations, but examples of stable, spatially localized objects with coexisting solitonic structures and singular defects are rare. Here we use a nonpolar chiral liquid crystal system to show how twist domain walls can co-self-assemble with vortices to form spatially localized topological objects with spontaneous folding. These soliton–vortex assemblies, which we call ‘möbiusons’, have a topology of the molecular alignment field resembling that of the Möbius strip’s surface and package localized field excitations into folded structures within a confinement-frustrated uniform far-field background. Upon supplying energy in the form of electric pulses, möbiusons with different overall symmetries of structure exhibit folding-dependent rotational and translational motions, as well as topological cargo-carrying abilities that can be controlled by tuning the amplitude and frequency of the applied fields. We demonstrate on-demand transformations between various möbiusons and show examples of encoding information by manipulating folds in such structures. A model based on the energetics of solitons and vortices provides insights into the origins of the folding instability, whereas minimization of the Landau–de Gennes free energy closely reproduces details of their internal structure. Our findings may provide a route towards topology-enabled light-steering designs.
3 citations
TL;DR: In this article , the authors harness the non-reciprocal nature of these facile electric responses to demonstrate colloidal locomotion, and observe the colloid-hedgehog dipole accompanied by an umbilical defect in the tilt directionality field (c-field), along with the texture of elastic distortions that evolves with a change in the applied voltage.
Abstract: Colloidal particles in liquid crystals tend to induce topological defects and distortions of the molecular alignment within the surrounding anisotropic host medium, which results in elasticity-mediated interactions not accessible to their counterparts within isotropic fluid hosts. Such particle-induced coronae of perturbed nematic order are highly responsive to external electric fields, even when the uniformly aligned host medium away from particles exhibits no response to fields below the realignment threshold. Here we harness the nonreciprocal nature of these facile electric responses to demonstrate colloidal locomotion. Oscillations of the electric field prompt repetitive deformations of the corona of dipolar elastic distortions around the colloidal inclusions, which upon appropriately designed electric driving synchronize the displacement directions. We observe the colloid-hedgehog dipole accompanied by an umbilical defect in the tilt directionality field (c-field), along with the texture of elastic distortions that evolves with a change in the applied voltage. The temporal out-of-equilibrium evolution of the director and c-field distortions around particles when the voltage is turned on and off is not invariant upon reversal of time, prompting lateral translations and interactions that markedly differ from those accessible to these colloids under equilibrium conditions. Our findings may lead to both technological and fundamental science applications of nematic colloids as both model reconfigurable colloidal systems and as mesostructured materials with predesigned temporal evolution of structure and composition.
3 citations
TL;DR: In this paper , the authors theoretically investigate the interaction between magnons and a Skyrmion-textured domain wall in a two-dimensional antiferromagnet and elucidate the resultant properties of magnon transport.
Abstract: We theoretically investigate the interaction between magnons and a Skyrmion-textured domain wall in a two-dimensional antiferromagnet and elucidate the resultant properties of magnon transport. Using supersymmetric quantum mechanics, we solve the scattering problem of magnons on top of the domain wall and obtain the exact solutions of propagating and bound magnon modes. Then, we find their properties of reflection and refraction in the Skyrmion-textured domain wall, where magnons experience an emergent magnetic field due to its non-trivial spin texture-induced effective gauge field. Based on the obtained scattering properties of magnons and the domain wall, we show that the thermal transport decreases as the domain wall's chirality increases. Our results suggest that the thermal transport of an antiferromagnet is tunable by modulating the Skyrmion charge density of the domain wall, which might be useful for realizing electrically tunable spin caloritronic devices.
1 citations
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TL;DR: Aspects of the theory of homotopy groups are described in a mathematical style closer to that of condensed matter physics than that of topology in this paper, where the focus is on mathematical pedagogy rather than on a systematic review of applications.
Abstract: Aspects of the theory of homotopy groups are described in a mathematical style closer to that of condensed matter physics than that of topology. The aim is to make more readily accessible to physicists the recent applications of homotopy theory to the study of defects in ordered media. Although many physical examples are woven into the development of the subject, the focus is on mathematical pedagogy rather than on a systematic review of applications.
1,612 citations
1,429 citations
TL;DR: In this article, a two-stage scheme is presented to study structural perturbations of the sine-Gordon equation, which is based upon the inverse scattering transform, detailed knowledge of this technical apparatus is not necessary in order to effect the calculations.
Abstract: A two-stage scheme is presented to study structural perturbations of the sine-Gordon equation. Although the method is based upon the inverse scattering transform, detailed knowledge of this technical apparatus is not necessary in order to effect the calculations. In the first stage, slow modulations of speeds and positions for the soliton components are computed. The radiation resulting from the acceleration of the solitons is then calculated as a first-order correction through an easily constructed radiative Green's function. The method is exemplified by using it to study several outstanding problems that arise in applications of the Josephson transmission line. In particular we consider: (i) the pinning of flux quanta by microshorts, (ii) the quantum flux shuttle, (iii) annihilation conditions for fluxon-antifluxon collisions, (iv) breather decay, and (v) radiation from a moving fluxon.
735 citations