搜索结果：Chirality

Chirality is a fundamental molecular property that governs stereospecific behavior in chemistry and biology. Capturing chirality in machine learning models remains challenging due to the geometric complexity of stereochemical relationships and the limitations of traditional molecular representations that often lack explicit stereochemical encoding. Existing approaches to chiral molecular representation primarily focus on central chirality, relying on handcrafted stereochemical tags or limited 3D encodings, and thus fail to generalize to more complex forms such as axial chirality. In this work, we introduce ChiDeK (Chiral Determinant Kernels), a framework that systematically integrates stereogenic information into molecular representation learning. We propose the chiral determinant kernel to encode the SE(3)-invariant chirality matrix and employ cross-attention to integrate stereochemical information from local chiral centers into the global molecular representation. This design enables explicit modeling of chiral-related features within a unified architecture, capable of jointly encoding central and axial chirality. To support the evaluation of axial chirality, we construct a new b

We reveal a previously unknown continuous symmetry and conservation law in the equations of linear isotropic elasticity, which describe the chirality of elastic waves. We show that the integral chirality is determined by the population imbalance between right- and left-handed transverse phonons, whereas the local chirality density generally involves both transverse and longitudinal wave components. We also introduce the related concepts of acoustic helicity and ``false chirality''. The theory is illustrated with simple interference fields exhibiting distinct distributions of chirality, spin angular momentum, and false chirality. Our results establish chirality as a fundamental property of elastic waves and provide a general theoretical framework for chiral acoustic phenomena.

We introduce the concept of purely electronic chirality (PEC), which arises in the absence of structural chirality. In condensed matter physics and chemistry, chirality has conventionally been understood as a mirror-image asymmetry in crystal or molecular structures. We demonstrate that certain electronic orders exhibit chirality-related properties without atomic displacement. Specifically, we investigate quadrupole orders to realize such purely electronic chirality with handedness that can be tuned by magnetic fields. As a representative example, we analyze a model featuring $120^circ$ antiferro quadrupole orders on a distorted kagomé lattice, predicting various chirality-related responses in the nonmagnetic ordered phase of URhSn. Furthermore, as a phonon analog, chiral phonons can emerge in achiral crystals through coupling with the PEC order. Our results provide a distinct origin of chirality and a fundamental basis for exploring the interplay between electronic and structural chirality.

Recently, the projection of the electron's spin on its crystal momentum has been proposed as a metric to quantify electronic chirality of Bloch states in crystals, which is expected to affect a wide range of physical properties, such as magnetoelectric and optical responses. However, a direct experimental quantification of this chirality metric over an entire iso-energy surface has remained elusive. Here, we have used spin- and angle-resolved photoemission spectroscopy to directly probe the electronic chirality by measuring the bulk spin texture of Kramers-Weyl and Weyl cones in RhSi, a chiral topological semimetal with strong spin-orbit coupling (SOC). After quantifying the SOC splitting of Weyl cones, we determine their spin direction along different azimuthal angles to extract energy dependent the deviations (up to ~40°) from perfect parallel spin-momentum locking. From these deviations we define an energy-dependent normalized electron chirality density (NECD), a directly accessible metric of bulk electronic chirality. In RhSi, the NECD decreases from 1 at the Kramers-Weyl point to ~0.8 at ~200 meV below it. Finally, we show that this experimentally grounded NECD provides predic

Optical chirality density is widely used as a scalar measure of the chiral properties of electromagnetic fields and their interaction with matter. However, in anisotropic and structured media, a single scalar quantity is generally insufficient to capture the full complexity of chiral field-matter coupling. In this work, we go beyond the conventional optical chirality density and introduce a set of tensor measures of electromagnetic chirality based on the Lipkin formalism. These tensor quantities provide a richer and more physically transparent description of chiral electromagnetic fields, particularly in an anisotropic environment. The physical meaning of individual tensor components is discussed, and their role in characterizing different aspects of electromagnetic chirality is clarified. The proposed approach reveals multiple, complementary measures of field chirality that naturally emerge in anisotropic cases and are directly relevant to the interaction of structured electromagnetic fields with matter.

Recent years have witnessed growing interest in chiral phonons, lattice vibrations carrying angular momentum and exhibiting handedness, as revealed by helicity-dependent optical phenomena. Despite this progress, a quantitative characterization of phonon chirality as a dynamical property has remained elusive. In this work, we propose a theoretical framework to quantify the dynamical chirality of lattice vibrations. We introduce two quantitative measures: momentum-resolved dynamical chirality, which provides a mode- and wave-vector-resolved picture of phonon chirality, and the bulk dynamical chirality, which characterizes the collective behavior of thermally populated chiral phonons. Using first-principles calculations for both chiral and achiral materials, we demonstrate how these quantities capture the handedness and population imbalance of phonon modes and serve as a means to distinguish the enantiomers of chiral crystals.

The flow of time moves in one direction in any spatial position and orientation in this universe. Chiral objects, which lack mirror symmetry, retain their chirality regardless of their position or orientation. Despite being seemingly independent, time and chirality share common features such as universality -- applying to 'any position and orientation' -- and a binary nature, such as forward/backward time flow versus left/right chirality. We introduce the concept of Time Chirality and discuss the conjugate relationship between time chirality and traditional chirality. We explore how time chirality can manifest in certain magnetic states, and examine the novel physical phenomena associated with time-chiral magnetic states. This discussion offers a fresh perspective on true time reversal symmetry breaking and temporal nonreciprocity.

In condensed matter physics, a broad spectrum of physical characteristics, such as chirality, axiality, and polarity, arises as a direct consequence of the underlying symmetry of the system. We here theoretically investigate the effective coupling between chirality and axiality at their domain boundaries, mediated by polarity. Based on symmetry considerations and model analyses, we propose the concept of chirality-induced axiality via surface polarization, which refers to a phenomenon where the handedness of chirality selects an axial moment with a particular orientation by lowering its energy at the surface. We further establish the inverse process, termed axiality-induced chirality via surface polarization, whereby axiality in turn dictates the preferred chirality. These reciprocal couplings open a new pathway for stabilizing single-domain states of chirality and axiality. They further imply interfacial functionalities, including the selective adsorption of chiral and axial molecules.

We develop a theory of chirality and racemization on isotopy classes of finite loops, formulated intrinsically within the loop isotopy groupoid understood in the categorical sense. Motivated by earlier work on quasigroups \cite{InoueQuasiChirality} and by the classical medical paradigm of mirror-related enantiomers, we restrict admissible mirror transitions to those generated by intrinsic, unit-preserving symmetries. Within this framework, racemization is modeled as a two-state dynamics on isotopy classes, with an effective rate determined by the presence of mirror-isotopisms. Our main result shows that this rate vanishes if and only if no loop isotopism exists between a loop and its opposite, providing a structural criterion for chirality. A strengthened variant based on translation-generated symmetries is discussed in the appendix.

As deep learning applications extensively increase by leaps and bounds, their interpretability has become increasingly prominent. As a universal property, chirality exists widely in nature, and applying it to the explanatory research of deep learning may be helpful to some extent. Inspired by a recent study that used CNN (convolutional neural network), which applied visual chirality, to distinguish whether an image is flipped or not. In this paper, we study feature chirality innovatively, which shows how the statistics of deep learning models' feature data are changed by training. We rethink the feature-level chirality property, propose the feature chirality, and give the measure. Our analysis of feature chirality on AlexNet, VGG, and ResNet reveals similar but surprising results, including the prevalence of feature chirality in these models, the initialization methods of the models do not affect feature chirality. Our work shows that feature chirality implies model evaluation, interpretability of the model, and model parameters optimization.

In chemistry and biochemistry, chirality represents the structural asymmetry characterized by non-superimposable mirror images for a material like DNA. In physics, however, chirality commonly refers to the spin-momentum locking of a particle or quasiparticle in the momentum space. While seemingly disconnected, structural chirality in molecules and crystals can drive electronic chirality through orbital-momentum locking, i.e. chirality can be transferred from the atomic geometry to electronic orbitals. Electronic chirality provides an insightful understanding of the chirality-induced spin selectivity (CISS), in which electrons exhibit salient spin polarization after going through a chiral material, and electric magnetochiral anisotropy (EMCA), which is characterized by the diode-like transport. It further gives rise to new phenomena, such as anomalous circularly polarized light emission (ACPLE), in which the light handedness relies on the emission direction. These chirality-driven effects will generate broad impacts in fundamental science and technology applications in spintronics, optoelectronics, and biochemistry.

Chiral functionalities exhibited by systems lacking any mirror symmetry encompass natural optical activity, magnetochiral effect, diagonal current-induced magnetization, chirality-selective spin-polarized current of charged electrons or neutral neutrons, self-inductance, and chiral phonons. These phenomena are unified under the hypothesis of kinetomagnetism of chirality, which posits that any moving (charged or neutral) object in chiral systems induces magnetization in its direction of motion, consequently imparting chirality to the object due to this induced magnetization. We also found conjugate relationships among the kinetomagnetism of chirality, linear magnetoelectricity, and electric field induced directional nonreciprocity, highlighting their interconnections with magnetic, electric, and toroidal orders. The concept of the kinetomagnetism of chirality will be an essential basis for the theoretical understanding of known chiral phenomena such as natural optical activity or chiral phonons, and also the discovery of unexplored chiral functionalities.

Although the phenomenon of chirality appears in many investigations of maps and hypermaps no detailed study of chirality seems to have been carried out. Chirality of maps and hypermaps is not merely a binary invariant but can be quantified by two new invariants -- the chirality group and the chirality index, the latter being the size of the chirality group. A detailed investigation of the chirality groups of maps and hypermaps will be the main objective of this paper. The most extreme type of chirality arises when the chirality group coincides with the monodromy group. Such hypermaps are called totally chiral. Examples of them are constructed by considering appropriate ``asymmetric'' pairs of generators for some non-abelian simple groups. We also show that every finite abelian group is the chirality group of some hypermap, whereas many non-abelian groups, including symmetric and dihedral groups, cannot arise as chirality groups.

We develop a structural theory of chirality for inverse semigroups and show how it propagates canonically to étale groupoids and twisted groupoid $C^*$-algebras. Starting from inverse semigroup data equipped with admissible twist information, we construct a canonical twisted universal groupoid in the sense of Paterson and introduce a mirror correspondence encoding intrinsic asymmetry. Our main result identifies a structural obstruction to mirror self-duality at the level of twisted universal groupoids and shows that this obstruction descends to an obstruction for the associated reduced twisted groupoid $C^*$-algebra to be isomorphic to its opposite. The framework is representation-independent, yet compatible with concrete germ groupoid models, and provides a unified bridge between partial symmetries, groupoid structures, and analytic invariants in noncommutative operator algebras.

We develop a structural and dynamical theory of chirality for quasigroups formulated at the level of isotopy classes. Interpreting isotopy as a gauge symmetry of re-coordinatization and mirror parastrophy as handedness reversal, we introduce a gauge-invariant continuous-time two-state Markov model in which transitions occur only between a quasigroup and its mirror. We prove that this dynamics descends to the isotopy quotient, yielding a reduced generator governed by a single class-dependent rate $k([Q])$. Symmetric mirror transitions lead to convergence toward a racemic equilibrium, whereas the vanishing condition $k([Q])=0$ characterizes dynamical chiral stability. By restricting admissible transitions to those generated by intrinsic symmetries, we show that $k([Q])=0$ is equivalent to the absence of mirror-isotopisms. A concrete example of order $7$ demonstrates the existence of structurally chiral quasigroup classes.

Molecular chirality plays an important role in chemistry and biology, allows control of biological interactions, affects drugs efficacy and safety, and promotes synthesis of new materials. In general, chirality manifests itself in optical activity (circular dichroism or circular birefringence). Chiral plasmonic nanoparticles have been recently developed for molecular enantiomer separation, chiral sensing and chiral photocatalysis. Here, we show that optical chirality of plasmonic nanoparticles exhibiting strong scattering can remain completely undetected using standard characterisation techniques, such as circular dichroism measurements. This phenomenon, which we term meso-chiral in analogy to meso-compounds in chemistry, is based on mutual cancellation of absorption and scattering chiral responses. As a prominent example, the meso-optical behaviour has been numerically demonstrated in multi-wound-SiO2/Au nanoparticles over the entire visible spectral range and in other prototypical chiral nanoparticles in narrower spectral ranges. The meso-chiral property has been experimentally verified by demonstrating chiral absorption of gold helicoid nanoparticles at the wavelength where conv

A clear understanding of chirality in spin-active electronic states is discussed in order to address confusions about chiral effects recently discovered in materials science. Electronic toroidal monopole $G_0$ can serve as a measure of chirality in this categorization, which can be clearly related to the chiral density operator in the Dirac equation. We extend the concepts of chirality not only to those of materials but also to those of physical fields, and to material-field composites. Additionally, we illustrate specific examples from physics and chemistry that demonstrate the process of acquiring chirality through the combination of seemingly achiral degrees of freedom, which we term the emergence of chirality. Interference among multiple chiralities exhibiting phenomena specific to handedness is also discussed.

It has been claimed in a number of publications that neutrinos can exhibit chirality oscillations. In this note we discuss the notion of chirality and show that chiral neutrino oscillations in vacuum do not occur. We argue that the incorrect claims to the contrary resulted from a failure to clearly discriminate between quantum fields, states and wave functions. We also emphasize the role played in the erroneous claims on the possibility of chirality oscillations by the widely spread misconceptions about negative energies.

The inherently weak chiroptical responses of natural materials limit their usage for controlling and enhancing chiral light-matter interactions. Recently, several nanostructures with subwavelength scale dimensions were demonstrated, mainly due to the advent of nanofabrication technologies, as a potential alternative to efficiently enhance chirality. However, the intrinsic lossy nature of metals and inherent narrowband response of dielectric planar thin films or metasurface structures pose severe limitations toward the practical realization of broadband and tailorable chiral systems. Here, we tackle these problems by designing all-dielectric silicon-based L-shaped optical metamaterials based on tilted nanopillars that exhibit broadband and enhanced chiroptical response in transmission operation. We use an emerging bottom-up fabrication approach, named glancing angle deposition, to assemble these dielectric metamaterials on a wafer scale. The reported strong chirality and optical anisotropic properties are controllable in terms of both amplitude and operating frequency by simply varying the shape and dimensions of the nanopillars. The presented nanostructures can be used in a plethor