Macroscopic Symmetry Research Articles

Chiral spin-liquid-like state in pyrochlore iridate thin films

The pyrochlore iridates have become ideal platforms to unravel fascinating correlated and topological phenomena that stem from the intricate interplay among strong spin-orbit coupling, electronic correlations, lattice with geometric frustration, and itinerancy of the 5d electrons. The all-in-all-out antiferromagnetic state, commonly considered as the magnetic ground state, can be dramatically altered in reduced dimensionality, leading to exotic or hidden quantum states inaccessible in bulk. Here, by means of magnetotransport, resonant elastic and inelastic x-ray scattering experiments, we discover an emergent quantum disordered state in (111) Y2Ir2O7 thin films (thickness ≤30 nm) persisting down to 5 K, characterized by dispersionless magnetic excitations. The anomalous Hall effect observed below an onset temperature near 125 K corroborates the presence of chiral short-range spin configurations expressed in non-zero scalar spin chirality, breaking the macroscopic time-reversal symmetry. The origin of this chiral state is ascribed to the restoration of magnetic frustration on the pyrochlore lattice in lower dimensionality, where the competing exchange interactions together with enhanced quantum fluctuations suppress any long-range order and trigger spin-liquid-like behavior with degenerate ground-state manifold.

Ferrospintronic Order in Noncentrosymmetric Antiferromagnets: An Avenue toward Spintronic‐Based Computing, Data Storage, and Energy Harvesting

A ferroic order, ferrospintronic (FSp) order, arising in some magnetic materials lacking inversion symmetry is reported on. Emerging from a macroscopic spontaneous symmetry breaking of both the time reversal T and the spatial inversion, while maintaining the symmetry, the order parameter is given by the dipolar moment of the spin density . Herein a model is advanced that fulfills the symmetry requirements mentioned earlier and its properties are investigated. With the aid of a mean‐field theory, its stability against thermal fluctuations is studied and evidence of truly ferroic states that result from breaking its symmetry is provided. Three predictions that can be checked experimentally to distinguish this class of materials from other compounds are provided. In the first place, it is illustrated that FSp systems host the potential for multiferroic behavior. Second, it is shown that the generic FSp system responds under strain by generating spin currents that can be used in spintronic devices, therefore showing a piezospintronic effect. Finally, it is proven that domain walls in the FSp order parameter lead to magnetoresistive effects. All of the findings mentioned earlier are a significant breakthrough in spintronics and multiferroic phenomena and they have wide‐ranging implications for advancing materials and technologies, particularly in computing and energy harvesting.

Edge and skin effects in rhombus reciprocal photonic crystals.

With the development of non-Hermitian physics, the non-Hermitian skin effect (NHSE) has attracted much attention. Existing research highlights the critical roles of the periodic boundary condition (PBC) spectrum, lattice symmetry, and macroscopic symmetry of the lattice in relation to the geometry-dependent skin effect (GDSE). However, the impact of macroscopic edge geometry is frequently neglected. We find that the GDSE is highly sensitive to the edge and cannot be simply determined by the symmetries. Specifically, the GDSE can emerge at trivial interfaces of rhombus photonic crystals (PhCs) with zigzag edge and bearded edge. Furthermore, we analyze the underlying mechanisms from the perspective of point-gap topology. This work underscores important, yet frequently overlooked, aspects in two-dimensional (2D) reciprocal PhC systems and can be used to enhance design flexibility, allowing the NHSE to have better applications in areas such as lasers and highly sensitive sensors.

Two orientation effects and large anisotropy of parameters in piezo-active 2–1–2 composites based on [0 1 1]-poled crystals

The results of a comparative study on piezo-active 2–1–2 composites with two ferroelectric components are discussed. The composite structure combines elements of 2–2 (laminar) and 1–3 (fibrous) connectivity patterns. The first component in each composite is domain-engineered [0 1 1]-poled single crystal with macroscopic mm2 symmetry and high piezoelectric activity. The second component is a poled ferroelectric ceramic that is represented by parallel rods in the shape of an elliptic cylinder with a large ratio of semi-axes at its base. The first orientation effect is appreciable due to rotations of the main crystallographic axes X and Y around Z || OX 3 by an angle α in each crystal layer. Rotation of the ceramic rod bases by an angle γ in a polymer medium leads to the second orientation effect in the 2–1–2 composite. The two orientation effects contribute to a large anisotropy of electromechanical coupling factors k3j∗ , energy-harvesting figures of merit (FOM) (Q3j∗)2 and modified FOM F3j∗σ for a stress-driven harvester. The large level of (Q32∗)2 , (Q33∗)2 , F32∗σ and F33∗σ (these parameters are of the order of 10−11–10−10 Pa−1) indicates that the studied composites are suitable for piezoelectric sensors, transducers and energy-harvesting systems. New m—α diagrams put forward in the present study show regions wherein the large anisotropy of the effective parameters ( |k33∗ / k3f∗|⩾5 , (Q33∗/Q3f∗ )2 ⩾10 and F33∗σ/F3f∗σ⩾10 , f = 1 and 2) is achieved when changing the volume fraction m of the single crystal and the rotation angle α. As a result, the leading role of the first orientation effect is emphasised.

Irreversibility in belief dynamics: Unraveling the link to cognitive effort.

The relationship between time irreversibility in neuronal dynamics and cognitive effort is a subject of growing interest in the scientific literature. Although correlations between proxies of both concepts have been experimentally observed, the underlying precise linkage between them remains elusive. Here we investigate the case of learning in decision-making tasks; we do so by introducing a thermodynamically grounded metric-inspired by Landauer's principle-which connects time-irreversible information processing to energy consumption. Equipped with this metric, we investigate the role of macroscopic time-reversal symmetry breaking in belief dynamics for the case of an agent with finite sensitivity while performing a static two-armed bandit task-a standard setup in cognitive neuroscience. To gain insights into the belief dynamics, we analogize it to the dynamics of an active particle subject to state-dependent noise and living in a two-dimensional space. This mapping allows an analytical description of learning-induced biases. We deeply explore the case of Q-learning with forgetting the nonchosen option. In this case, learning-induced risk aversion is formally equivalent to standard thermophoresis, i.e., the net motion towards low-temperature regions. Finally, we quantify the irreversibility of belief dynamics in the steady state for different bandit configurations, sensitivity levels, and exploitative behavior. We found a strong correlation in high-sensitivity learning between heightened irreversibility in belief dynamics and improved decision-making outcomes. Notably, as the task's difficulty increases, a greater degree of irreversibility in belief dynamics becomes necessary for having superior performances; this explicitly unravels a plausible connection between time irreversibility and cognitive effort. In conclusion, our investigation reveals that irreversibility in belief dynamics bridges out-of-equilibrium statistical physics concepts and cognitive neuroscience. In decision-making contexts, this perspective offers insights into the notion of cognitive effort, suggesting a potential mechanism driving the evolution of living systems toward out-of-equilibrium structures.

Ferroelectric Smectic Liquid Crystals

Since the discovery of the first ferroelectric liquid crystal (FLC) in the chiral smectic C (SmC*) phase, ferroelectricity in liquid crystals has attracted much attention due to not only the fundamental interest but also the applications. This review focuses on the evolution of the design concept for ferroelectric smectic liquid crystals. It progresses from considering macroscopic phase symmetry to designing intermolecular interactions. For the purpose of understanding the molecular organization in smectic phases, we propose a dynamic model of constituent molecules in the smectic A (SmA) and SmC* phases based on 13C NMR studies. Then, we follow the structure–property relationship in ferroelectric SmC* liquid crystals for FLC displays. We reconsider de Vries-like materials that can provide defect-free alignment. We pay attention to the electro-optical switching in the chiral de Vries smectic A phase. Finally, we show several liquid crystals exhibiting polar smectic A phases and discuss how the polar order occurs in the highest symmetric smectic A phase.

Quest for the golden ratio universality class.

Using mode-coupling theory, the conditions for all allowed dynamical universality classes for the conserved modes in one-dimensional driven systems are presented in closed form as a function of the stationary currents and their derivatives. With an eye on the search for the golden ratio universality class, the existence of some families of microscopic models is ruled out a priori by using an Onsager-type macroscopic current symmetry. In particular, if the currents are symmetric or antisymmetric under the interchange of the conserved densities, then at equal mean densities the golden modes can only appear in the antisymmetric case and if the conserved quantities are correlated, but not in the symmetric case where at equal densities one mode is always diffusive and the second may be either Kardar-Parisi-Zhang (KPZ), modified KPZ, 3/2-Lévy, or also diffusive. We also show that the predictions of mode-coupling theory for a noisy chain of harmonic oscillators are exact.

Macroscopic chiral symmetry breaking in gelation of Fmoc-amino acids: homochiral selective secondary nucleation promoted by the choice of solvent or stirring.

A racemic mixture of N-Fmoc-protected phenylalanine (2) or tryptophan (3) was found to spontaneously afford a gel enriched in either the L- or the D-form of their enantiomers stochastically. Homochiral selective secondary nucleation, promoted by the choice of solvent or stirring, was suggested as the key process for the observed phenomenon.

Computational analysis of electronic structure and optical properties of monocrystalline silicon-vacancy defect system based on density functional theory

Monocrystalline silicon is an important substrate or base material for manufacturing integrated circuit chips, mirrors, etc. However, it is a typical hard and brittle material, which is very prone to produce defects during processing. This paper investigates the electronic structure and optical properties of sphalerite monocrystalline silicon with vacancy concentrations of 1.5625%, 3.125%, 4.6875%, and 6.25% using the first principles method based on density functional theory. The results demonstrate that the introduction of impurities results in the formation of impurity bands (IB) within the band structure, thereby facilitating electronic transitions. However, vacancy defects do not alter the properties of monocrystalline silicon as an indirect semiconductor. Regarding optical properties, an increase in defect concentration leads to a decrease in the macroscopic symmetry of the system, resulting in noticeable anisotropy in each property. Also found that the main spectral peaks of the defect system are red-shifted, and the vacancy defects introduce new peaks in the near-infrared region and the visible region with increasing intensity, but the peaks in the ultraviolet region gradually decrease with the increase of the defect concentration. The refractive index peak gradually decreases with the increase of defect concentration, and the calculated average refractive index is around 1.2. In the high-energy region, the refractive index takes a very small value, and the reflection of electromagnetic waves from the doped system is also weak at this time, which indicates that the system has a high transmittance property. Importantly, there is a higher intensity of energy loss at photon energies around 16.5 eV. Consequently, these calculations are deemed valuable for advancing research and applications involving monocrystalline silicon optical mirrors.

Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice.

Recent studies of non-Hermitian periodic lattices unveiled the non-Hermitian skin effect (NHSE), in which the bulk modes under the periodic boundary conditions (PBC) become skin modes under open boundary conditions. The NHSE is a topological effect owing to the nontrivial spectral winding, and such spectral behaviors appear naturally in nonreciprocal systems. Hence prevailing approaches rely on nonreciprocity to achieve the NHSE. Here, we report the experimental realization of the geometry-dependent skin effect in a two-dimensional reciprocal system, in which the skin effect occurs only at boundaries whose macroscopic symmetry mismatches with the lattice symmetry. The role of spectral reciprocity and symmetry is revealed by connecting reflective channels at given boundaries with the spectral topology of the PBC spectrum. Our work highlights the vital role of reciprocity, symmetry, and macroscopic geometry on the NHSE in dimensionality larger than one and opens new routes for wave structuring using non-Hermitian effects.

Two UV organic-inorganic hybrid antimony-based materials with superior optical performance derived from cation-anion synergetic interactions

Finding suitable strategies to effectively enhance the optical properties of materials are the goal being pursued by researchers. Herein, cation-anion synergetic interactions strategy was proposed to develop two novel organic-inorganic hybrid antimony-based optical materials, (C3H5N2)SbF2SO4 (I) and (C5H6N)SbF2SO4 (II), which were obtained by introducing Sb3+cation containing stereochemically active lone-pair (SCALP) and organic π-conjugated cations into sulphate system. The synergistic interactions of the organic π-conjugated cations, the inorganic [SbO2F2]3− seesaw anions and the [SO4]2− distorted tetrahedra anions make their ultraviolet (UV) absorption edges approach 297 and 283 nm, respectively, and raise their birefringence up to 0.193@546 nm and 0.179@546 nm, respectively. Interestingly, although the two compounds have the same stoichiometric ratio and similar one-dimensional (1D) chain structure, they show opposite macroscopic symmetry, where the NCS compound (II) exhibits a large second-harmonic generation (SHG) response (1.6 times that of KH2PO4). The two reported compounds are found to be promising UV optical materials in the experimental tests.

ASb(SO4)2 (A = Rb, Cs): Two short-wave UV antimony sulfates exhibiting large birefringence

Herein, two antimony sulfates, named RbSb(SO4)2 (1) and CsSb(SO4)2 (2), have been successfully synthesized with the introduction of Sb3+ cation with stereochemically active lone pairs (SCALP) into sulfates by the conventional hydrothermal method. Both two compounds endow short UV absorption edges (281 nm and 278 nm, respectively) and large birefringence ([email protected] nm and [email protected] nm, respectively), which means that they are promising short-wave ultraviolet (UV) optical materials. Interestingly, though both of the two compounds exhibit similar 1D chained structures, and possess the same functional moieties including SbO4 seesaws and SO4 tetrahedral groups, they exhibit significantly opposite macroscopic symmetries, i.e., compound 1 crystallizes in a centrosymmetric (CS) manner (P21/n) and compound 2 in a noncentrosymmetric (NCS) manner (P212121), due to the size of cations [r(Rb+) = 1.56 Å, r(Cs+) = 1.67 Å] affects the orientation of SCALP of the adjacent Sb3+.

Multipartite nonlocality and symmetry breaking in one-dimensional quantum chains

Multipartite nonlocality is a measure of multipartite quantum correlations. In this paper we investigate the influence of symmetry-breaking perturbations upon ground-state nonlocality by considering several typical finite-size quantum models, including the transverse-field Ising chains, the $XY$($XX$) chains, and the $XXZ$ chains. We find that even a slight perturbation can reshape the nonlocality curve dramatically. For instance, in the $XY$ chains, a perturbation can induce an oscillation behavior in the nonlocality curve. A clear microscopic mechanism for the results is proposed. Furthermore, we also connect the behaviors to the macroscopic symmetry properties of the chains and make some predictions on general models.

Multiscale dynamical symmetries and selection rules in nonlinear optics.

Symmetries and their associated selection rules are extremely useful in many fields of science. For systems of electromagnetic (EM) fields interacting with matter, the symmetries of matter and the EM fields' time-dependent polarization determine the properties of the nonlinear responses, and they can be facilitated for controlling light emission and enabling ultrafast symmetry breaking spectroscopy of various properties. Here, we formulate a general theory that describes the macroscopic and microscopic dynamical symmetries (including quasicrystal-like symmetries) of EM vector fields, revealing many previously unidentified symmetries and selection rules in light-matter interactions. We demonstrate an example of multiscale selection rules experimentally in the framework of high harmonic generation. This work paves the way for novel spectroscopic techniques in multiscale systems and for imprinting complex structures in extreme ultraviolet-x-ray beams, attosecond pulses, or the interacting medium itself.

Nonlinear circular dichroism in achiral dielectric nanoparticles

We present a theoretical study of circular dichroism in the second-harmonic signal of single dielectric nanostructures with different symmetries and noncentrosymmetric materials. We show that this effect is defined not only by macroscopic (particle) and lattice symmetries but also by their relative orientation. Using symmetry and modal analysis, we provide a general and very simple formula to determine whether the dichroism exists and a chart with the most significant cases.

Resonant Chiral Effects in Nonlinear Dielectric Metasurfaces

We study the resonant enhancement of linear and nonlinear chiroptical effects in planar silicon metasurfaces with an in-plane asymmetry supporting multipolar Mie resonances and quasi-bound states in the continuum (quasi-BICs). We demonstrate theoretically and observe in experiment the pronounced linear circular dichroism at the quasi-BIC resonances originating from the interaction of modes with the substrate. We further find that both local field enhancement and third-harmonic signal are large for Mie resonances and some quasi-BIC modes due to the critical coupling. We demonstrate experimentally a strong nonlinear chiroptical response associated with high efficiency of the third-harmonic generation and large nonlinear circular dichroism varying from +0.918 ± 0.049 to −0.771 ± 0.004 for the samples with different asymmetries. We reveal the nonreciprocal nature of nonlinear chirality governed by the microscopic symmetry of nonlinearities and macroscopic symmetries of the meta-atom and metasurface lattice. We believe our results suggest a general strategy for engineering nonlinear chiroptical response in dielectric resonant metasurfaces.

Applications of Group Theory

Groups play a fundamental role in Algebra: many algebraic structures, including rings, fields, and modules, can be seen as formed by adding new operations and axioms based on groups. Researchers often use group theory to explain many kinds of phenomena. In recent years, group theory has been introduced into crystallography to further explore the macroscopic symmetry of crystals from a mathematical point of view. In this paper, the applications of group theory in crystallography and magic cubic will be discussed. Basic definitions and models of these fields are demonstrated. A finite group is a group with a finite number of elements, which are the important contents of group theory. Besides, this paper proves that n−1 elements in a n order group can completely decide the nth element and gives a method of the nth element in a commutative group of order n. The analysis suggests that the research method of group theory has an important influence on other subjects.

Bending waves localized along the edge of a semi-infinite piezoelectric plate with orthogonal symmetry

We study the propagation of bending waves along the free edge of a semi-infinite piezoelectric plate within the framework of two-variable refined plate theory (TVPT, a high-order plate theory), Reissner-Mindlin refined plate theory (RMPT, a first-order plate theory), and the classical plate theory (CPT). The piezoelectric plate has macroscopic symmetry of orthogonal mm2 The governing equations are derived using Hamilton principle. The dispersion relations for electrically open and shorted boundary conditions at the free edge are obtained analytically. The difference in dispersion property between the three plate theories is analyzed. The numerical results show that the dispersion curves predicted by TVPT and RMPT are similar and have small difference over the complete frequency range, which means both the two theories are valid for the analysis of edge waves in a piezoelectric plate. But the wave velocity calculated by CPT is much larger than the two theories above and is no longer valid for high frequency and thick plate. The electrical boundary condition at the free edge has an insignificant effect on phase velocity and group velocity which can be ignored for the analysis of edge waves in a piezoelectric plate governed by bending deformation. The velocity of bending edge waves in a semi-infinite piezoelectric plate is positively related to that of Rayleigh surface wave in a traction-free piezoelectric half-space. The edge wave velocity can be enhanced when the piezoelectric plate is considered as one with weaker anisotropy.

“Forbidden” Polarisation and Extraordinary Piezoelectric Effect in Organometallic Lead Halide Perovskites

AbstractOrganometallic lead halide perovskites are highly efficient materials for solar cells and other optoelectronic applications due to their high quantum efficiency and exceptional semiconducting properties. A peculiarity of these perovskites is the substantial ionic motion under external forces. Here, it is revealed that electric field‐and light‐induced ionic motion in MAPbX3 crystals (X = Cl, Br, I and MA = CH3NH3) leads to an unexpectedly high piezoelectric‐like response that is at low frequencies an order of magnitude larger than in ferroelectric perovskite oxides. The nominal macroscopic symmetry of the crystals is broken by redistribution of ionic species, which can be controlled deterministically by light and electric field. The revealed piezoelectric response is possibly present in other materials with significant ionic activity, but the unique feature of organometallic perovskites is the strong effect on the piezoelectric‐like response of interplay of ionic motion (MA+1 and X–1) and photoelectrons generated with illumination.

Gelation of a π-Decorated Glutamate as a Homochiral Selective Self-assembly to Obtain Macroscopic Chiral Symmetry Breaking.

An N-Fmoc and C-tBu-protected glutamate (1) bearing a phenanthrene moiety at the side residue crystalizes and gels to afford hetero- and homochiral assemblies, respectively, depending on its optical purity or solvent. When a non-stoichiometric mixture of enantiomers of 1 in acetonitrile was treated with the conditions that leave a mixture of gel and supernatant, it exhibited the self-disproportionation of enantiomers with an enrichment of the major enantiomer in the gel. Under similar conditions, a racemic mixture of 1 also provided a gel/supernatant mixture, where the gel was enriched in either of L or D-form of 1 stochastically as the result of macroscopic chiral symmetry breaking in its gelation process.