Flexoelectricity in Nematic and Smectic-A Liquid Crystals

Flexoelectric effects are observed in both the nematic and smectic‐A phases of p‐butoxybenzal‐p‐($\beta$‐methylbutyl) aniline (BBMBA) and p‐cyano‐benzylidine‐p‐octyloxyaniline (CBOOA). This is the first reported observation of flexoelectricity in smectic phases. The use of a symmetric interdigital electrode in the homeotropic geometry facilitated the unambiguous separation of linear and quadratic electro‐optic effects. Both the interdigital electrodes and those liquid‐crystal deformations that are quadratic in the voltage act as optical diffraction gratings with a spacing that corresponds to the repeat distance d for adjacent electrodes. In contrast linear electro‐optic effects give rise to diffraction gratings with twice this spacing since adjacent electrodes have opposite voltages. Diffraction maxima due to the linear effects are halfway between the maxima due to the other effects. Using optical heterodyne detection, the intensity of the diffraction maxima believed to arise from the linear effect are indeed observed to be linear in the applied voltage $V (\omega)$. With homodyne detection the diffracted intensity is proportional to $V (\omega)^2$. Although previous discussions of flexoelectricity in nematics have been in terms of two flexoelectric coefficients $e_{11}$ and $e_{33}$, we present theoretical arguments that as long as $\nabla \times E=0$ there is only one true volume coefficient and that the other constant can always be included in surface effects. Our measurements of the volume coefficient $f=e_{11}+e_{33}$ are an order of magnitude larger than previously obtained values for $e_{11}$ and $e_{33}$. Measured values of f are also nearly independent of temperature, in contrast to previous theoretical models, and of similar magnitude in the smectic and nematic phases. Measurements of flexoelectric signals versus the frequency of the driving voltage obtain relaxation times for splaylike nematic fluctuations and undulation‐type smectic fluctuations.Engineering and Applied Science

Quantum states and intertwining phases in kagome materials

In solid materials, nontrivial topological states, electron correlations, and magnetism are central ingredients for realizing quantum properties, including unconventional superconductivity, charge and spin density waves, and quantum spin liquids. The Kagome lattice, made up of connected triangles and hexagons, can host these three ingredients simultaneously and has proven to be a fertile platform for studying diverse quantum phenomena including those stemming from the interplay of these ingredients. In this review, we introduce the fundamental properties of the Kagome lattice as well as discuss the complex observed phenomena seen in several emergent material systems such as the intertwining of charge order and superconductivity in some Kagome metals, modulation of magnetism and topology in some Kagome magnets, and symmetry breaking with Mott physics in the breathing Kagome insulators. We also highlight many open questions in the field as well as future research directions of Kagome systems

Chemical Symmetry Breaking

This book entitled “Chemical Symmetry Breaking” is a collective volume of state-of-the-art reports on unique nonlinear chemical and physical symmetry-breaking phenomena that were experimentally observed upon a thermally or photochemically induced phase transition in various organic condensed phases, such as metastable liquid crystals, crystals, amorphous solids, and colloidal polymer materials, only under nonequilibrium conditions. Each author summarizes the introductory section in simple terms but in detail for beginners in this field. We wish that many readers familiarize themselves with the general concepts and features of nonlinear and nonequilibrium (or out of equilibrium) complexity theory, which govern a variety of unique dynamic behaviors observed in chemistry, physics, life science and other fields, so that they may discover novel symmetry-breaking phenomena in their own research areas

Colloquium: Ice rule and emergent frustration in particle ice and beyond

Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial constraints. The second, in its more general sense, represents a prescription for the minimization of the topological charges in a constrained system. Both can lead to manifolds of high susceptibility and non-trivial, constrained disorder where exotic behaviors can appear and even be designed deliberately. In this Colloquium, we describe the emergence of geometric frustration and the ice rule in soft condensed matter. This Review excludes the extensive developments of mathematical physics within the field of geometric frustration, but rather focuses on systems of confined micro- or mesoscopic particles that emerge as a novel paradigm exhibiting spin degrees of freedom. In such systems, geometric frustration can be engineered artificially by controlling the spatial topology and geometry of the lattice, the position of the individual particle units, or their relative filling fraction. These capabilities enable the creation of novel and exotic phases of matter, and also potentially lead towards technological applications related to memory and logic devices that are based on the motion of topological defects. We review the rapid progress in theory and experiments and discuss the intimate physical connections with other frustrated systems at different length scales