Spontaneous electric-polarization topology in confined ferroelectric nematics

Enantiomeric Ferroelectric Chiral Domains

Chiral ferroelectric crystals with inherent chirality and spontaneous polarization have recently gained considerable interest. However, the chiral topological texture, which provides a promising platform for exploring exotic functionalities, has never been found in enantiomeric ferroelectric crystals. Here, we report a pair of enantiomeric molecular ferroelectrics, [RFAO][ReO4] and [SFAO][ReO4] (RFAO/SFAO = (4R,5R/4S,5S)-4-fluoro-1-azabicyclo[3.2.1]octane). The enantiomers crystallize in the chiral-polar point group 2 at room temperature and undergo two ferroelectric phase transitions with an Aizu notation of 222F2 at 350 K and 432F2 at 463 K, respectively. Such phase transitions enable them to show a multistep switchable second-harmonic generation circular dichroism (SHG-CD) effect from high to low to off (inactive) SHG-CD states. More importantly, we observed spiral chiral ferroelectric domains in the enantiomers. To the best of our knowledge, this is the first discovery of chiral domains in enantiomeric ferroelectric crystals. Our breakthrough findings give new sights into the interplay between polarization and chirality and will greatly stimulate further exploration of chiral ferroelectric crystals with switchable SHG-CD and chiral domains for next-generation electronic-photonic devices.

Interface-Engineered Polar Topological Domains in Ferroelectric Nematic Liquid Crystals

Polar topological domains, distinguished by their inherent topological protection and diverse optoelectronic functionalities, have recently attracted significant interest across scientific disciplines. However, the realization of these structures in inorganic materials is often impeded by crystal symmetry constraints. In this context, ferroelectric nematic liquid crystals, characterized by spontaneous polarization and flexible polarization orientation, provide an exceptional platform for the development of polar topological domains. Despite their potential, a considerable challenge lies in identifying a straightforward yet versatile approach for engineering polar topological domains within liquid crystals. Here, this study presents an interfacial engineering strategy that effectively stabilizes a range of polar topological domains in ferroelectric nematic liquid crystals, including vortex, centrifugal vortex, and center-divergent configurations, by synergistically modulating the surface tension and interfacial tension. Utilizing a combination of experimental characterization and simulation, the role of anchoring energy is systematically investigated in the molecular alignment of liquid crystals and facilitates transitions between diverse topological structures. This research not only extends the horizons for constructing and manipulating polar topological domains but also enhances their prospective applications in topological photonics.

Ferroelectric Nematic Liquid Crystals Showing High Birefringence

High birefringence nematic liquid crystals are particularly demanded for adaptive optics applications in the infrared spectrum because it enable a thinner cell gap for achieving fast response time and improved diffraction efficiency. The emerging ferroelectric nematic liquid crystals have attracted widespread interest in soft matter due to their unique combination of ferroelectricity and fluidity. However, the birefringence, which is one of the most important optical parameters in electro-optic devices, is not large enough (<0.25) in most ferroelectric nematic materials. Here, a polar liquid crystal molecule library containing more than 60 molecules with a highly rigid and fluorinated nature is developed. The introduction of triple bonds constructs a long π-electron conjugated mesogen skeleton, significantly improving the birefringence of polar liquid crystal phases. The birefringence and dispersion properties are systematically studied, demonstrating a strong dependence on chemical structures and the type of polar phases. Furthermore, through multi-component mixing, polar liquid crystal mixtures with ultra-wide temperature range and excellent stability at or near room temperature are obtained. They possess much higher birefringence than the existing ferroelectric liquid crystal materials. The unique combination of high birefringence and fluidic ferroelectricity is expected to promote the application of polar liquid crystals in electro-optic technologies.

Impact of charge distribution on the stability of ferroelectric nematic liquid crystals

This study explores the influence of charge distribution and molecular shape on the stability of ferroelectric nematic liquid crystalline phases through atomistic simulations of DIO molecules. We demonstrate the role of dipole-dipole interactions and molecular shape in achieving polar ordering by simulating charged and chargeless topologies, and analysing positional and orientational pair-distribution functions. The charged DIO molecules exhibit head-to-tail and side-by-side parallel alignments conducive to long-range polar order, whereas the chargeless molecules show no polar ordering. The 2D x-y cross-section of the correlation pair-distribution function shows that lateral local dipoles in the molecular structure are critical for the formation of the ferroelectric phase, highlighting the importance of charge asymmetry and electrostatic interactions in stabilizing long-range polar order.

Topological defects induced by air inclusions in ferroelectric nematic liquid crystals with ionic doping

We report an experimental study on how topological defects induced by cylindrical air inclusions in the ferroelectric nematic liquid crystal RM734 are influenced by ionic doping, including an ionic surfactant and ionic polymer. Our results show that subtle differences in molecular structure can lead to distinct surface alignments and topological defects. The ionic surfactant induces a planar alignment, with two -1/2 line defects adhering to the cylindrical bubble surface. In contrast, the ionic polymer promotes homeotropic alignment, resulting in a -1 polar disclination around the cylindrical bubble. By numerical simulations, we verify that these topological defects are vertical lines with two dimensional polarization fields. These configurations differ from the boojums and hedgehog defects induced by air inclusions in nematic liquid crystals, highlighting the significant role of broken inversion symmetry.

Chiral π domain walls composed of twin half-integer surface disclinations in ferroelectric nematic liquid crystals

Ferroelectric nematic liquid crystals are polar fluids characterized by microscopic orientational ordering and macroscopic spontaneous polarizations. Within these fluids, domain walls that separate regions of different polarizations are ubiquitous. We demonstrate that the π walls in films of the polar fluids consist of twin half-integer surface disclinations spaced horizontally, enclosing a subdomain where the polarization exhibits left- or right-handed π twists across the film. The degenerate geometric arrangements of the twin disclinations generate kinks and antikinks, parting subdomains of opposite chirality, like the spin-up and spin-down in Ising chains. The hierarchical structures dictate that field-driven polar switching undergo two-step annihilations of the surface disclinations. These findings provide an insight for both comprehending other walls in the polar fluids and domain engineering crucial for advancing their nonlinear and optoelectronic applications.

Half-integer topological defects paired via string micelles in polar liquids

Ferroelectric nematic (NF) liquid crystals present a compelling platform for exploring topological defects in polar fields, while their structural properties can be significantly altered by ionic doping. In this study, we demonstrate that doping the ferroelectric nematic material RM734 with cationic polymers enables the formation of polymeric micelles that connect pairs of half-integer topological defects. Polarizing optical microscopy reveals that these string defects exhibit butterfly textures, featured with a 2D polarization field divided by Néel-type kink walls into domains exhibiting either uniform polarization or negative splay and bend deformations. Through analysis of electrophoretic motion and direct measurements of polarization divergences, we show that the string micelles are positively charged, and their side regions exhibit positive bound charges. To elucidate these observations, we propose a charge double-layer model for the string defects: the positively charged cationic polymer chains and densely packed RM734 molecules form a Stern charge layer, while small anionic ions and positive bound charges constitute the charge diffusion layer. Notably, our experiments indicate that only cationic polymer doping effectively induces the formation of these unique string defects. These findings enhance our understanding of ionic doping effects and provide valuable insights for engineering polar topologies in liquid crystal systems.

Broadband Spin and Orbital Momentum Modulator Using Self-Assembled Nanostructures

The structural symmetry of solids plays an important role in defining their linear and nonlinear optical properties. The quest for versatile, cost-effective, large-scale, and defect-free approaches and materials platforms for tailoring structural and optical properties on demand is underway since decades. A self-assembled spherulite material comprised of synthesized molecules with large dipole moments aligned azimuthally, forming a vortex polarity with spontaneously broken symmetry, is experimentally demonstrated. This unique self-assembled structure enables new linear and nonlinear light-matter interactions, including generating optical vortex beams with complex spin states and on-demand topological charges at the fundamental, doubled, and tripled frequencies. This work will likely enable numerous applications in areas such as high-dimensional quantum information processing with large capacity and high security, spatiotemporal optical vortices, and a novel optical manipulation and trapping platform.

Revealing the antipolar order in the antiferroelectric SmZA phase by means of circular alignment

Many ferroelectric nematic liquid crystals, like one of the archetype materials, DIO, do not have a direct paraelectric N to ferroelectric NF phase transition, but exhibit yet another phase between N and NF. This phase has recently been proposed to be antiferroelectric, with a layered structure of alternating polarization normal to the average director and is sometimes referred to as Smectic ZA (SmZA). We have examined the SmZA phase in circularly rubbed (CR) cells, known to discriminate between the polar NF and the non-polar N phase from the configuration of disclination lines formed. We find that the ground state of SmZA has the same disclination configuration as the non-polar N phase, demonstrating that the SmZA phase is also non-polar, i.e., it has no net ferroelectric polarization. At the same time, the SmZA texture generally has a grainy appearance, which we suggest is partly a result of the frustration related to layered order combined with the imposed twist in CR cells. We discuss possible orientations of the smectic layers, depending on the alignment conditions. While a horizontal SmZA layer structure is always compatible with surface-induced twist, a vertical layer structure would tend to break up in a twisted bookshelf structure to match non-parallel alignment directions at the two surfaces.

Fluid jets and polar domains, on the relationship between electromechanical instability and topology in ferroelectric nematic liquid crystal droplets

Ferroelectric nematic liquid crystals are a class of recently discovered fluid materials formed by highly polar molecules that spontaneously align along a common direction, giving rise to a macroscopic polarization P. Since the polarization vector is locally collinear to the optical axis n, the study of the spatial patterns of n enables deducing the structure of P. We have carried on such topological study on ferroelectric nematic droplets confined between two solid ferroelectric substrates both when the droplet is in equilibrium and during a jet-emission phase that takes place when the solid surfaces become sufficiently charged. We find that in equilibrium the droplet splits in striped domains in which P has alternating directions. When these domains extend close to the droplets' perimeter, P adopts a π-twisted structure to minimize accumulation of polarization charges. As the substrate surface charge is increased above threshold, fluid jets are emitted with a quasi-periodic pattern, a behaviour suggesting that their location is governed by an electrofluidic instability on the droplets' rim, in turn indicating the absence of specific trigger points. Soon after their emission, the jet periodicity is lost; some jets retract while other markedly grow. In this second regime, jets that grow are those that more easily connect to polar domains with P along the jet axis. Occasionally, ejection of isolated spikes also occurs, revealing locations where polarization charges have accumulated because of topological patterns extending on length scales smaller than the typical domain size.

Extended free-energy functionals for achiral and chiral ferroelectric nematic liquid crystals: theory and simulation

Polar nematic liquid crystals are new classes of condensed-matter states, where the inversion symmetry common to the traditional apolar nematics is broken. Establishing theoretical descriptions for the novel phase states is an urgent task. Here, we develop a Landau-type mean-field theory for both the achiral and chiral ferroelectric nematics. In the polar nematic states, the inversion symmetry breaking adds three new contributions: an additional odd elastic term (corresponding to the flexoelectricity in symmetry) to the standard Oseen-Frank free energy, electrostatic effect and an additional Landau term relating to the gradient of local polarization. The coupling between the scalar order parameter and polarization order should be considered. In the chiral and polar nematic state, we reveal that the competition between the twist elasticity and polarity dictates effective compressive energy arising from the quasi-layer structure. The polarization gradient is an essential term for describing the ferroelectric nature. Besides, we successfully simulate an experimentally reported structural transition in ferroelectric nematic droplets from a concentric-vortex-like to a line-disclination-mediated topology based on the developed theory. The approaches provide theoretical foundations for testing and predicting polar structures in emerging polar liquid crystals.

Polymer nanocomposite dielectrics for capacitive energy storage

Owing to their excellent discharged energy density over a broad temperature range, polymer nanocomposites offer immense potential as dielectric materials in advanced electrical and electronic systems, such as intelligent electric vehicles, smart grids and renewable energy generation. In recent years, various nanoscale approaches have been developed to induce appreciable enhancement in discharged energy density. In this Review, we discuss the state-of-the-art polymer nanocomposites with improved energy density from three key aspects: dipole activity, breakdown resistance and heat tolerance. We also describe the physical properties of polymer nanocomposite interfaces, showing how the electrical, mechanical and thermal characteristics impact energy storage performances and how they are interrelated. Further, we discuss multi-level nanotechnologies including monomer design, crosslinking, polymer blending, nanofiller incorporation and multilayer fabrication. We conclude by presenting the current challenges and future opportunities in this field.

Topology of ferroelectric nematic droplets: the case driven by flexoelectricity or depolarization field

The recent discovery of ferroelectric nematics provides new opportunities for exploring polar topology in liquid matter. Here, we report numerous potential polarization topological states (e.g., polar vortex-like and line disclination mediated structures) in confined ferroelectric nematics with similar free-energy levels. In the experiment, they appear according to the confinement size and surface anchoring conditions. Based on a minimal analytical approach, we reveal that the topological transformation is balanced among the nematic elasticity, the polarization gradient, the flexoelectric and the depolarization interactions.

Response of helielectric nematics under an in-plane electric field

In traditional chiral nematic liquid crystals, the apolar cholesterics, the dielectric effect is the main driving force for responding to an electric field. The emerging polar chiral nematics, dubbed helielectric nematics, are the polar counterparts of the cholesterics. The head-to-tail symmetry breaking of the new matter state enables it to respond sensitively to the polarity of an electric field. Here, we report on the observation of a sequential polar winding/unwinding process of polarization helices under an electric field applied perpendicular to the helical axes, which behaves distinctly from the unwinding of the apolar cholesteric helices. Understanding the helix-unwinding behaviors provides insights for developing switchable devices based on helielectric nematics.

Fluid Ferroelectric Filaments

Freestanding slender fluid filaments of room-temperature ferroelectric nematic liquid crystals are described. They are stabilized either by internal electric fields of bound charges formed due to polarization splay or by external voltage applied between suspending wires. The phenomenon is similar to those observed in dielectric fluids, such as deionized water, except that in ferroelectric nematic materials the voltages required are three orders of magnitudes smaller and the aspect ratio is much higher. The observed ferroelectric fluid threads are not only unique and novel but also offer measurements of basic physical quantities, such as the ferroelectric polarization and viscosity. Ferroelectric nematic fluid threads may have practical applications in nano-fluidic micron-size logic devices, switches, and relays.

Transformation of polar nematic phases in the presence of an electric field

Only a few years have passed since the discovery of polar nematics, and now they are becoming the most actively studied liquid-crystal materials. Despite numerous breakthrough findings made recently, a theoretical systematization is still lacking. In the present paper, we take a step toward systematization. The powerful technique of molecular-statistical physics has been applied to an assembly of polar molecules influenced by electric field. Three polar nematic phases were found to be stable at various conditions: the double-splay ferroelectric nematic N_{F}^{2D} (observed in the lower-temperature range in the absence of or at low electric field), the double-splay antiferroelectric nematic N_{AF} (observed at intermediate temperature in the absence of or at low electric field), and the single-splay ferroelectric nematic N_{F}^{1D} (observed at moderate electric field at any temperature below transition into paraelectric nematic N and in the higher-temperature range (also below N) at low electric field or without it. A paradoxical transition from N_{F}^{1D} to N induced by application of higher electric field has been found and explained. A transformation of the structure of polar nematic phases at the application of electric field has also been investigated by Monte Carlo simulations and experimentally by observation of polarizing optical microscope images. In particular, it has been realized that, at planar anchoring, N_{AF} in the presence of a moderate out-of-plane electric field exhibits twofold splay modulation: antiferroelectric in the plane of the substrate and ferroelectric in the plane normal to the substrate. Several additional subtransitions related to fitting the confined geometry of the cell by the structure of polar phases were detected.

Planar Spin Glass with Topologically Protected Mazes in the Liquid Crystal Targeting for Reconfigurable Micro Security Media

The planar spin glass pattern is widely known for its inherent randomness, resulting from the geometrical frustration. As such, developing physical unclonable functions (PUFs)-which operate with device randomness-with planar spin glass patterns is a promising candidate for an advanced security systems in the upcoming digitalized society. Despite their inherent randomness, traditional magnetic spin glass patterns pose considerable obstacles in detection, making it challenging to achieve authentication in security systems. This necessitates the development of facilely observable mimetic patterns with similar randomness to overcome these challenges. Here, a straightforward approach is introduced using a topologically protected maze pattern in the chiral liquid crystals (LCs). This maze exhibits a comparable level of randomness to magnetic spin glass and can be reliably identified through the combination of optical microscopy with machine learning-based object detection techniques. The "information" embedded in the maze can be reconstructed through thermal phase transitions of the LCs in tens of seconds. Furthermore, incorporating various elements can enhance the optical PUF, resulting in a multi-factor security medium. It is expected that this security medium, based on microscopically controlled and macroscopically uncontrolled topologically protected structures, may be utilized as a next-generation security system.

Solid-Liquid Crystal Biphasic Ferroelectrics with Tunable Biferroelectricity

Ferroelectricity has been separately found in numerous solid and liquid crystal materials since its first discovery in 1920. However, a single material with biferroelectricity existing in both solid and liquid crystal phases is very rare, and the regulation of biferroelectricity has never been studied. Here, solid-liquid crystal biphasic ferroelectrics, cholestanyl 4-X-benzoate (4X-CB, X = Cl, Br, and I), which exhibits biferroelectricity in both the solid and liquid crystal phases, is presented. It is noted that the ferroelectric liquid crystal phase of 4X-CB is a cholesteric one, distinct from the ordinary chiral smectic ferroelectric liquid crystal phase. Moreover, 4X-CB shows solid-solid and solid-liquid crystal phase transitions, of which the transition temperatures gradually increase from Cl to Br to I substitution. The spontaneous polarization (Ps ) of 4X-CB in both solid and liquid crystal phases can also be regulated by different halogen substitutions, where the 4Br-CB has the optimal Ps because of the larger molecular dipole moment. To the authors' knowledge, 4X-CB is the first ferroelectric with tunable biferroelectricity, which offers a feasible case for the performance optimization of solid-liquid crystal biphasic ferroelectrics.

Spontaneous periodic polarization wave in helielectric fluids

By analogy with spin waves in ferromagnetic systems, the polarization (or dipole) wave is the electric counterpart that remains elusive. Here, we discover that the helielectricity, i.e. a polarization field with helicoidal helices that corresponds to a quasi-layered chiral nematic environment, causes a spontaneous formation of large-scale polarization waves in the form of the sinusoidal function. Both experimental and theoretical analyses reveal that the polarization ordering over a threshold polarization strength violates the inherent periodicity of the polarization helices, thus penalizing the compression energy. It drives a second-order structural transition to a periodically modulated polarization wave state. The roles of chirality and confinement condition are discussed.

Electric field-induced interfacial instability in a ferroelectric nematic liquid crystal

Studies of sessile droplets and fluid bridges of a ferroelectric nematic liquid crystal in externally applied electric fields are presented. It is found that above a threshold, the interface of the fluid with air undergoes a fingering instability or ramification, resembling to Rayleigh-type instability observed in charged droplets in electric fields or circular drop-type instabilities observed in ferromagnetic liquids in magnetic field. The frequency dependence of the threshold voltage was determined in various geometries. The nematic director and ferroelectric polarization direction was found to point along the tip of the fingers that appear to repel each other, indicating that the ferroelectric polarization is essentially parallel to the director. The results are interpreted in connection to the Rayleigh and circular drop-type instabilities.

Alignment properties of a ferroelectric nematic liquid crystal on the rubbed substrates

The orientation characteristics of FNLC-919, a new material with a ferroelectric nematic phase at room temperature, were investigated. Its alignment characteristics varied greatly depending on the relative rubbing direction on both substrates of a liquid crystal cell. In a cell where the two substrates were rubbed in the same direction, they were arranged homogeneously along the rubbing direction without domains or defects in the ferroelectric nematic phase. In a cell where the two substrates were rubbed in the anti-parallel direction, the two domains were twisted in the opposite direction. We quantitatively obtained the twisted direction and angle by matching the experimental data and calculation results using Jones matrix calculations. From the electro-optical experiment, it was confirmed that the polarization direction was opposite to the rubbing direction. In addition, the wavelength and temperature dependence of birefringence was measured for FNLC-919. In a cell where the rubbing direction between two substrates was 90°, two domains of opposite directions were observed in the nematic phase. When it becomes a ferroelectric nematic phase on cooling, the twist is determined to be only in one direction. The twist direction and angle were quantitatively obtained in the nematic and ferroelectric nematic phases. It was twisted more in the ferroelectric nematic phase than in the nematic phase.