Paul J. Ackerman

Shape-dependent oriented trapping and scaffolding of plasmonic nanoparticles by topological defects for self-assembly of colloidal dimers in liquid crystals.

We demonstrate scaffolding of plasmonic nanoparticles by topological defects induced by colloidal microspheres to match their surface boundary conditions with a uniform far-field alignment in a liquid crystal host. Displacing energetically costly liquid crystal regions of reduced order, anisotropic nanoparticles with concave or convex shapes not only stably localize in defects but also self-orient with respect to the microsphere surface. Using laser tweezers, we manipulate the ensuing nanoparticle-microsphere colloidal dimers, probing the strength of elastic binding and demonstrating self-assembly of hierarchical colloidal superstructures such as chains and arrays.

Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains that exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields.

Diversity of Knot Solitons in Liquid Crystals Manifested by Linking of Preimages in Torons and Hopfions

Topological solitons are knots in continuous physical fields classified by non-zero Hopf index values. Despite arising in theories that span many branches of physics, from elementary particles to condensed matter and cosmology, they remain experimentally elusive and poorly understood. We introduce a method of experimental and numerical analysis of such localized structures in liquid crystals that, similar to the mathematical Hopf maps, relates all points of the mediums order parameter space to their closed-loop preimages within the three-dimensional solitons. We uncover a surprisingly large diversity of naturally occurring and laser-generated topologically nontrivial solitons with differently knotted nematic fields, which previously have not been realized in theories and experiments alike. We discuss the implications of the liquid crystals non-polar nature on the knot soliton topology and how the mediums chirality, confinement and elastic anisotropy help to overcome the constrains of the Hobart-Derrick theorem, yielding static three-dimensional solitons without or with additional defects. Our findings will establish chiral nematics as a model system for experimental exploration of topological solitons and may impinge on understanding of such nonsingular field configurations in other branches of physics, as well as may lead to technological applications

Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities

Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable “optical drawing” of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the mediums chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.

Biaxial ferromagnetic liquid crystal colloids.

Significance We introduce a soft-matter system with fluidity coexisting with long-range biaxial and ferromagnetic ordering of anisotropic molecular and magnetic colloidal building blocks. The facile polar switching of this complex fluid promises technological applications and rich physical behavior arising from the properties of solid magnetic nanoparticles and their long-range ordering prompted by interactions with the host medium. The design and practical realization of composite materials that combine fluidity and different forms of ordering at the mesoscopic scale are among the grand fundamental science challenges. These composites also hold a great potential for technological applications, ranging from information displays to metamaterials. Here we introduce a fluid with coexisting polar and biaxial ordering of organic molecular and magnetic colloidal building blocks exhibiting the lowest symmetry orientational order. Guided by interactions at different length scales, rod-like organic molecules of this fluid spontaneously orient along a direction dubbed “director,” whereas magnetic colloidal nanoplates order with their dipole moments parallel to each other but pointing at an angle to the director, yielding macroscopic magnetization at no external fields. Facile magnetic switching of such fluids is consistent with predictions of a model based on competing actions of elastic and magnetic torques, enabling previously inaccessible control of light.

Optically generated adaptive localized structures in confined chiral liquid crystals doped with fullerene

We report the facile optical creation of switchable localized structures in chiral liquid crystals doped with fullerene. In a cholesteric cell unwound by vertical boundary conditions, the initially dispersed fullerenes are deposited from the bulk to the surface of confining glass plates by low-intensity illumination. This alters the surface boundary conditions and allows for the creation of localized particlelike structures with twist-bound defects (dubbed Torons) that are controlled by electric fields and arranged into patterns of interest for photonic and electro-optic applications.

Topological Switching and Orbiting Dynamics of Colloidal Spheres Dressed with Chiral Nematic Solitons

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that “dress” the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.

Plasmon–Exciton Interactions Probed Using Spatial Coentrapment of Nanoparticles by Topological Singularities

We study plasmon-exciton interaction by using topological singularities to spatially confine, selectively deliver, cotrap and optically probe colloidal semiconductor and plasmonic nanoparticles. The interaction is monitored in a single quantum system in the bulk of a liquid crystal medium where nanoparticles are manipulated and nanoconfined far from dielectric interfaces using laser tweezers and topological configurations containing singularities. When quantum dot-in-a-rod particles are spatially colocated with a plasmonic gold nanoburst particle in a topological singularity core, its fluorescence increases because blinking is significantly suppressed and the radiative decay rate increases by nearly an order of magnitude owing to the Purcell effect. We argue that the blinking suppression is the result of the radiative rate change that mitigates Auger recombination and quantum dot ionization, consequently reducing nonradiative recombination. Our work demonstrates that topological singularities are an effective platform for studying and controlling plasmon-exciton interactions.

Squirming motion of baby skyrmions in nematic fluids

Skyrmions are topologically protected continuous field configurations that cannot be smoothly transformed to a uniform state. They behave like particles and give origins to the field of skyrmionics that promises racetrack memory and other technological applications. Unraveling the non-equilibrium behavior of such topological solitons is a challenge. We realize skyrmions in a chiral liquid crystal and, using numerical modeling and polarized video microscopy, demonstrate electrically driven squirming motion. We reveal the intricate details of non-equilibrium topology-preserving textural changes driving this behavior. Direction of the skyrmion’s motion is robustly controlled in a plane orthogonal to the applied field and can be reversed by varying frequency. Our findings may spur a paradigm of soliton dynamics in soft matter, with a rich interplay between topology, chirality, and orientational viscoelasticity.A skyrmion is a topological object originally introduced to model elementary particles and a baby skyrmion is its two-dimensional counterpart which can be realized as a defect in liquid crystals. Here the authors show that an electric field can drive uniform motion of baby skyrmions in liquid crystals.

Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals

Significance While arising in theories in many branches of science, from particle physics to condensed matter and cosmology, stable three-dimensional topological solitons remained experimentally elusive until very recently. We now show that such solitons can be electrically and magnetically switched between states with the same or different Hopf indices. Richness and robustness of this switching promise technological applications in the new breeds of information displays and data storage devices, as well as may provide a test ground and new inspirations for the mathematical knot theory. Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed “preimages”) of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. The field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.