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The type-II Dirac fermions are characterized by a tilted Dirac cone and sustain exotic quantum transport phenomena. Here, we show the emergence of a type-II Dirac nodal loop in the SrVO 3 / SrTiO 3 quantum well structure by density functional theory calculations and symmetry arguments. When the spin–orbit coupling (SOC) is neglected, the unavoidable crossing between two t 2 g bands gives rise to a nodal loop in the Brillouin zone, which is protected by the mirror symmetry. Such a nodal loop is fully gapped by including SOC, which results in a large spin Hall effect due to large spin Berry curvatures. Our findings add the unexplored functionality to oxide quantum wells and offer a practical platform to explore the interplay between topological fermions and spin transport phenomena. [ABSTRACT FROM AUTHOR]

Fluorographene, a fluorinated graphene-derivative, is expected to feature both high thermal conductivity and electrical insulation simultaneously, making it an emerging material for thermal management in electronic devices. In this paper, we investigated the lattice thermal conductivity and phonon transport properties of monolayer fluorographene using first-principles calculation. The solution of the fully linearized phonon Boltzmann transport equation gives the lattice thermal conductivity of monolayer fluorographene as 145.2 W m−1 K−1 at 300 K, which is about 20 times smaller than that of monolayer graphene. We systematically compared the phonon transport properties of all phonon modes in graphene and fluorographene in terms of phonon polarization. The significantly reduced thermal conductivity of fluorographene can be attributed to the lowering of both the lifetime of the flexural acoustic phonons and the group velocities of all acoustic phonons. We concluded that the broken in-plane mirror symmetry and the weaker in-plane chemical bonds induced by fluorination led to the suppression of the lattice thermal conductivity of fluorographene. Finally, we investigated the anomalously large contribution of optical phonons to the thermal transport process in fluorographene, where the large group velocities of selected optical phonons were derived from the in-plane acoustic modes of graphene. Our work provides a new approach to studying the influence of chemical functionalization on the phonon structure and exploring graphene-derived thermal management materials. [ABSTRACT FROM AUTHOR]

This study delves into the interplay of symmetry and structure in 2D systems to identify monolayers hosting valley physics together with the Rashba effect. Through high-throughput density functional theory calculations, 57 monolayers are identified exhibiting the Rashba effect, with the Rashba parameter α R spanning from 0 < α R < 2.0. The robustness of the Rashba parameters (α R) in these monolayers is primarily influenced by the physical parameters, highlighting the anti-crossing of Rashba-split bands and the Born effective charge (Z*). Among the 57 monolayers exhibiting the Rashba effect, the study identifies a subset of 23 monolayers presenting valley physics, demonstrating both in-plane and out-of-plane spin polarizations. The pronounced coupling of the valley and Rashba spin splitting is influenced by the in-plane and out-of-plane orbital contributions at the relevant K-points in the band spectra. In particular, the AB-type buckled structures feature these dual properties due to the presence of the broken inversion and mirror symmetries in them. Overall, the study eases the identification of monolayers with significant spin splitting and spin polarization, aiding in the design of high-performance 2D materials. [ABSTRACT FROM AUTHOR]

Based on the quantum valley Hall effect analogy, this work proposes a phononic crystal plate with ligament-type beams to obtain the topological valley transmission of elastic waves. A pure Bragg degenerate state appears in the high-frequency region with a resonator introduced. By rotating the central scatterer and the beams, the mirror symmetry is broken to form a topological bandgap. Subsequently, this work finds that two selective edge states also appear beside the commonly non-trivial crossing edge states in the topological bandgap by calculating the projected band and eigenvalue spectrum of the supercell with different valley Hall phases phononic crystals. Their appearance is due to band separation of the topological edge states caused by an increase in the rotation angle. Both selective edge states can transmit topologically in specific paths. They will help further to broaden the width of the frequency band of topological transmission. Besides, an elastic wave splitter is designed and demonstrated numerically, which can form two channels and three channels in different frequency bands. With the topological selective edge state disappearing, a topological corner state exists in the edge bandgap. This work provides a theoretical reference for practical applications of broadband elastic wave topological transmission and elastic energy trapping. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) Janus transition metal dichalcogenides MXY manifest novel physical properties owing to the breaking of out-of-plane mirror symmetry. Recently, the 2H phase of MoSH has been demonstrated to possess intrinsic superconductivity, whereas the 1T phase exhibits a charge density waves state. In this paper, we have systematically studied the stability and electron–phonon interaction characteristics of MoSLi. Our results have shown that both the 2H and 1T phases of MoSLi are stable, as indicated by the phonon spectrum and the ab initio molecular dynamics. However, the 1T phase exhibits an electron–phonon coupling constant that is twice as large as that of the 2H phase. In contrast to MoSH, the 1T phase of MoSLi exhibits intrinsic superconductivity. By employing the ab initio anisotropic Migdal-Eliashberg formalism, we have revealed the two-gap superconducting nature of 1T-MoSLi, with a transition temperature (Tc) of 14.8 K. The detailed analysis indicates that the superconductivity in 1T-MoSLi primarily originates from the interplay between the vibration of the phonon modes in the low-frequency region and the dz2 orbital. These findings provide a fresh perspective on superconductivity within Janus structures. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) piezoelectric nanomaterials have widely been studied recently due to their promise for various applications in technology. Investigation of vertical piezoelectricity will contribute to a deeper understanding of the intrinsic mechanism of piezoelectric effects in the 2D structures. In this paper, we report a first-principle study for the structural, electronic, piezoelectric, and transport properties of new-designed Janus WSi Z 3 H (Z = N, P, and As) monolayers. The structural stability of WSi Z 3 H is theoretically confirmed based on the energetic, phonon dispersion, and also elastic analyses. At the ground state, while WSiN 3 H is an indirect semiconductor, both WSiP 3 H and WSiAs 3 H are predicted to be direct semiconductors with smaller bandgaps. When the spin-orbit coupling effects are taken into account, a large valley spin splitting is observed at the K point of WSi Z 3 H materials. Interestingly, a giant Rashba spin splitting is found in WSiP 3 H and WSiAs 3 H with Rashba constant α R up to 770.91 meV Å. Additionally, our first-principles study indicates that Janus WSi Z 3 H monolayers are piezoelectric semiconductors with high out-of-plane piezoelectric coefficient | d 31 | , up to 0.15 pm/V, due to the broken mirror symmetry. Besides, with high electron mobilities and also possessing direct band gaps, WSiP 3 H and WSiAs 3 H monolayers are favorable for applications in optoelectronics. [ABSTRACT FROM AUTHOR]

Molecular chirality is represented as broken mirror symmetry in the structural orientation of constituent atoms and plays a pivotal role at every scale of nature. Since the discovery of the chiroptic property of chiral molecules, the characterization of molecular chirality is important in the fields of biology, physics, and chemistry. Over the centuries, the field of optical chiral sensing was based on chiral light–matter interactions between chiral molecules and polarized light. Starting from simple optics-based sensing, the utilization of plasmonic materials that could control local chiral light–matter interactions by squeezing light into molecules successfully facilitated chiral sensing into noninvasive, ultrasensitive, and accurate detection. In this Review, the importance of plasmonic materials and their engineering in chiral sensing are discussed based on the principle of chiral light–matter interactions and the theory of optical chirality and chiral perturbation; thus, this Review can serve as a milestone for the proper design and utilization of plasmonic nanostructures for improved chiral sensing. [ABSTRACT FROM AUTHOR]

A PT-symmetric non-Hermitian photonic system composed of specifically designed metal structures is used to conduct arbitrary polarization transition from the equator and generate polarization vortices with exceptional point on the Poincaré sphere's poles, which induces unidirectional hyperbolic polaritons propagation due to the break of mirror symmetry. [Display omitted] [ABSTRACT FROM AUTHOR]

S. Gukov and C. Vafa proposed a characterization of rational N=(1,1)$N=(1,1)$ superconformal field theories (SCFTs) in 1+1$1+1$ dimensions with Ricci‐flat Kähler target spaces in terms of the Hodge structure of the target space, extending an earlier observation by G. Moore. The idea is refined, and a conjectural statement on necessary and sufficient conditions for such SCFTs to be rational is obtained, which is indeed proven to be true in the case the target space is T4$T^4$. In the refined statement, the algebraicity of the geometric data of the target space turns out to be essential, and the Strominger–Yau–Zaslow fibration in the mirror correspondence also plays a vital role. [ABSTRACT FROM AUTHOR]

We study the problem of computing Gopakumar–Vafa (GV) invariants for multiparameter families of symmetric Calabi–Yau threefolds admitting flops to diffeomorphic manifolds. There are infinite Coxeter groups, generated by permutations and flops, that act as symmetries on the GV-invariants of these manifolds. We describe how these groups are related to symmetries in GLSMs, and the existence of multiple mirrors. Some representation theory of these Coxeter groups is also discussed. The symmetries provide an infinite number of relations between the GV-invariants for each fixed genus. This remarkable fact is of assistance in obtaining higher-genus invariants via the BCOV recursion. This paper is based on joint work with Philip Candelas and Xenia de la Ossa. [ABSTRACT FROM AUTHOR]

In this paper, we describe non-Abelian T-dualities for a two-dimensional (2D) gauged linear sigma model (GLSM) with 풩=2 supersymmetry (SUSY). We start with the case of left and right SUSY (2,2), U(1) gauge group, and global non-Abelian symmetries. Our analysis applies to the specialization of the GLSM with the global group SU(2)×SU(2), whose original model is the resolved conifold. We analyze the dual model and compute the periods on the dual geometry, matching the effective potential for the U(1) gauge field, and discussing the coincident singularity at the conifold point. We further present the non-Abelian T-dualization of models with (0,2) SUSY, analyzing the case of global symmetry SU(2). In this case, the full non-Abelian duality can be solved. The dual geometries with and without nonperturbative corrections to the superpotential coincide. The structure of the dual nonperturbative corrections is determined based on symmetry arguments. The non-Abelian T-dualities reviewed here lead to potential new symmetries between physical theories. [ABSTRACT FROM AUTHOR]

Mirror symmetry for higher genus curves is usually formulated and studied in terms of Landau–Ginzburg models; however the critical locus of the superpotential is arguably of greater intrinsic relevance to mirror symmetry than the whole Landau–Ginzburg model. Accordingly, we propose a new approach to the A-model of the mirror, viewed as a trivalent configuration of rational curves together with some extra data at the nodal points. In this context, we introduce a version of Lagrangian Floer theory and the Fukaya category for trivalent graphs, and show that homological mirror symmetry holds, namely, that the Fukaya category of a trivalent configuration of rational curves is equivalent to the derived category of a non-Archimedean generalized Tate curve. To illustrate the concrete nature of this equivalence, we show how explicit formulas for theta functions and for the canonical map of the curve arise naturally under mirror symmetry. [ABSTRACT FROM AUTHOR]

We give a recursive construction of the categorified Young symmetrizer introduced by Abel and Hogancamp (Sel Math (NS) 23:1739–1801, 2017) corresponding to the single-column partition. As a consequence, we obtain new expressions for the uncolored y-ified HOMFLYPT homology of positive torus links and the y-ified column-colored HOMFLYPT homology of positive torus knots. In the latter case, we compare with the row-colored homology of positive torus knots computed by Hogancamp and Mellit (Torus link homology, 2019), verifying the mirror symmetry conjectures of Gukov and Stošić (Geom Topol Monogr 18:309–367, 2012) and Gorsky et al. (Fund Math 243:209–299, 2018) in this case. [ABSTRACT FROM AUTHOR]

Resonant dielectric planar structures can interact selectively with light of particular helicity thus providing an attractive platform for “chiral flat optics”. The absence of mirror‐symmetry planes defines geometric chirality, and it remains the main condition for achieving strong circular dichroism. For planar optical structures such as photonic‐crystal slabs and metasurfaces, breaking the out‐of‐plane mirror symmetry is especially challenging, as it requires to fabricate meta‐atoms with a tilt, variable height, or vertically shifted positions. Although transparent substrates formally break out‐of‐plane mirror symmetries, their optical effect is typically subtle being rarely considered for enhancing optical chirality. Here it is revealed that low‐refractive‐index substrates can induce up to maximum intrinsic optical chirality in otherwise achiral metastructures so that the transparency to waves of one helicity is combined with resonant blocking of waves of the opposite helicity. This effect originates from engineering twisted photonic eigenstates of different parities. The perturbation analysis developed in terms of the resonant‐state expansion reveals how the eigenstate coupling induced by a substrate gives rise to a pair of chiral resonances of opposite handedness. The general theory is confirmed by the specific examples of light transmission in the normal and oblique directions by a rotation‐symmetric photonic‐crystal slab placed on different transparent substrates. [ABSTRACT FROM AUTHOR]

Given a holomorphic family of Bridgeland stability conditions over a surface, we define a notion of spectral network which is an object in a Fukaya category of the surface with coefficients in a triangulated DG-category. These spectral networks are analogs of special Lagrangian submanifolds, combining a graph with additional algebraic data, and conjecturally correspond to semistable objects of a suitable stability condition on the Fukaya category with coefficients. They are closely related to the spectral networks of Gaiotto–Moore–Neitzke. One novelty of our approach is that we establish a general uniqueness results for spectral network representatives. We also verify the conjecture in the case when the surface is disk with six marked points on the boundary and the coefficients category is the derived category of representations of an A 2 quiver. This example is related, via homological mirror symmetry, to the stacky quotient of an elliptic curve by the cyclic group of order six. [ABSTRACT FROM AUTHOR]

Topological crystalline insulators are known to support multiple Majorana zero modes (MZMs) at a single vortex, their hybridization is forbidden by a magnetic mirror symmetry M T . Due to the limited energy resolution of scanning tunneling microscopes and the very small energy spacing of trivial bound states, it remains challenging to directly probe and demonstrate the existence of multiple MZMs. In this work, we propose to demonstrate the existence of MZMs by studying the hybridization of multiple MZMs in a symmetry breaking field. The different responses of trivial bound states and MZMs can be inferred from their spatial distribution in a vortex. However, the theoretical simulations are very demanding since it requires an extremely large system in real space. By utilizing the kernel polynomial method, we can efficiently simulate large lattices with over 108 orbitals to compute the local density of states which bridges the gap between theoretical studies based on minimal models and experimental measurements. We show that the spatial distribution of MZMs and trivial vortex bound states differs drastically in tilted magnetic fields. The zero-bias peak elongates when the magnetic field preserves M T , while it splits when M T is broken, giving rise to an anisotropic magnetic response. Since the bulk of SnTe are metallic, we also study the robustness of MZMs against the bulk states, and clarify when can the MZMs produce a pronounced anisotropic magnetic response. [ABSTRACT FROM AUTHOR]

Bicontinuous cubic liquid crystalline (LC) phases are of particular interest due their possible applications in electronic devices and special supramolecular chirality. Herein, we report the design and synthesis of first examples of achiral bent‐shaped polycatenar dimers, capable of displaying mirror symmetry breaking in their cubic and isotropic liquid phases. The molecules have a taper‐shaped 3,4,5‐trialkoxybenzoate segment connected to rod‐like building unit terminated with one terminal flexible chain. The two segments were connected using an aliphatic spacer with seven methylene units to induce bending of the whole structure. Investigated by the small‐angle X‐ray scattering (SAXS), a double network achiral cubic phase Cub/Ia 3‾ ${\bar{3}}$ d, which is a meso‐structure, and a chiral triple network cubic phase Cub/I23[*] are formed. The molecules self‐assemble into molecular helices and progress along the networks. Interestingly, different linking groups such as ester or azo linkages and core fluorination lead to distinct local helicity, resulting in an alkyl chain volume dependent phase transition sequence Ia 3‾ ${\bar{3}}$ d(L) ‐ I23* ‐ Ia 3‾ ${\bar{3}}$ d(S). The re‐entry of Ia 3‾ ${\bar{3}}$ d phase and loss of supramolecular chirality is attributed to the delicate influence of steric effect at the mono‐substitute end and interhelix interaction. Besides, aromatic core fluorination was proved to be a successful tool stabilizing the cubic phases in these dimers. [ABSTRACT FROM AUTHOR]

Bound states in the continuum (BICs) have been engineered in periodic photonic systems to achieve diverse polarization behavior in momentum space. By breaking C2z symmetry of photonic crystal slabs (PhCS), purely circular polarization, which hold significant potential for applications in topological physics and chiral optics, can be achieved near the BICs. In this study, the intriguing phenomenon of BICs on the degenerate band of PhCS with a triangular lattice featuring cylindrical holes are investigated. Unlike previous studies that mainly focused on BICs on non‐degenerate photonic bands, this research reveals a sophisticated interplay between BICs and Dirac points on the more intricate degenerate photonic band. This interaction gives birth to two pairs of purely circular polarizations with opposite chirality, even without breaking any symmetry of the PhCS. Additionally, It is find that by further breaking the σz mirror symmetry of the PhCS, these purely circular polarization states can be significantly amplified. This findings not only enrich the polarization responses of high‐Q photonic devices but also enables the modulation of chiral light, laying the groundwork for the creation of high‐quality optical devices with precisely engineered polarization properties. [ABSTRACT FROM AUTHOR]

In this paper, we briefly survey some developments in gauged linear sigma models (GLSMs). Specifically, we give an overview of progress on constructions of GLSMs for various geometries, GLSM-based computations of quantum cohomology, quantum sheaf cohomology, and quantum K theory rings, as well as two-dimensional abelian and nonabelian mirror constructions. [ABSTRACT FROM AUTHOR]

ABSTRACT The lattice loop formed by adjacent coupling of tunnel diode LC oscillators has been shown to generate topological defects due to broken mirror symmetry, which rotate in the opposite direction to the rotating pulse. Leveraging the injection locking of the rotational dynamics of these topological defects can lead to a subharmonic injection locking scheme with a large division ratio. This paper aims to enhance the design by elucidating the relationship between loop size, the number of topological defects, and the division ratio. Furthermore, we perform bifurcation analysis of the injection locking system, demonstrating that when the external signal strength reaches a certain threshold, defect pinning by the external signal occurs, leading to an extension of the lock range. The dynamics of topological defects are well suited to the so‐called progressive multiphase injection locking. In this paper, we clarify the degree of lock range extension achieved by introducing this technique. [ABSTRACT FROM AUTHOR]

In this note, we explain how mirror symmetry for basic local models in the Gross–Siebert program can be understood through the nontoric blowup construction described by Gross–Hacking–Keel. This is part of a program to understand the symplectic geometry of affine cluster varieties through their SYZ fibrations. [ABSTRACT FROM AUTHOR]

Mirror symmetry was first observed in worldsheet string constructions, and was shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi–Yau manifolds. It opened up a new field in pure mathematics, and was utilised in the area of enumerative geometry. Spinor–Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the Heterotic String, which includes the metric the antisymmetric tensor field and the Wilson line moduli. In terms of the toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas Spinor–Vector Duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of Spinor–Vector Duality in the effective field theory compactifications of string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited Spinor–Vector Duality and resolving the orbifold singularities, hence generating a smooth, effective field theory limit with an imprint of the Spinor–Vector Duality. Just like mirror symmetry, the Spinor–Vector Duality can be used to study the properties of complex manifolds with vector bundles. Spinor–Vector Duality offers a top-down approach to the "Swampland" program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not. [ABSTRACT FROM AUTHOR]

This paper presents an investigation into one- and three-dimensional harmonic oscillators with time-dependent mass and frequency, within the framework of the Dunkl formalism, which is constituted by replacing the ordinary derivative with the Dunkl derivative. To ascertain a general form of the wave functions the Lewis-Riesenfeld method was employed. Subsequently, an exponentially changing mass function in time was considered and the parity-dependent quantum phase, energy eigenvalues, and the corresponding wave functions were derived in one dimension. The findings revealed that the mirror symmetries affect the wave functions, thus the associated probabilities. Finally, the investigation was extended to the three-dimensional case, where it was demonstrated that, as with the solution of the radial equation, the solutions of the angular equation could be classified according to their mirror symmetries. [ABSTRACT FROM AUTHOR]

Recently, the orbital coupling in 2D materials has been demonstrated to have a significant impact on the magnetic anisotropy (MA) of CrTe2. The Te atomic layers on the surface layers determine the magnetocrystalline anisotropy (MCA) of the system due to orbital coupling. Herein, Cr2Te3$\left(\text{Cr}\right)_{2} \left(\text{Te}\right)_{3}$ is proposed to investigate the surface and middle layers of Te atoms on MA. The MCA of Cr2Te3$\left(\text{Cr}\right)_{2} \left(\text{Te}\right)_{3}$ consists of in‐plane and out‐of‐plane components, which are contributed by the surface layer and middle layer, respectively. Due to the lack of Cr–Te–Cr chemical bonds in the z‐axis, the surface layer produces px/py$p_{x} / p_{y}$ coupling and results in the in‐plane MA. In addition, a tensile strain can enhance the pz/py$p_{z} / p_{y}$ coupling on the middle layer and lead to the out‐of‐plane MCA. At the same time, the out‐of‐plane MCA breaks the vertical mirror symmetry and an anomalous Hall effect has been detected on monolayer (1L) Cr2Te3$\left(\text{Cr}\right)_{2} \left(\text{Te}\right)_{3}$. Based on this result, an anomalous Hall device is designed to record and read information. The opposing contribution of the surface and middle layers provides a completely new way to understand 2D materials. [ABSTRACT FROM AUTHOR]

Two‐dimensional (2D) Janus materials are a fascinating class of materials resulting from their unique electronic and magnetic properties induced by mirror symmetry breaking. However, 2D Janus materials with intrinsic magnetism remain rather rare, casting a mysterious veil over magnetism. In this work, the electronic and magnetic properties of Janus Mn2GeX (X = As, Sb) monolayers using the first‐principles calculations are investigated. The results demonstrate that these Janus materials exhibit excellent mechanical and dynamic stability, indicating their potential for future applications in nanoscale spintronic devices. Interestingly, the Janus Mn2GeAs$\left(\text{Mn}\right)_{2} \text{GeAs}$ and Mn2GeSb$\left(\text{Mn}\right)_{2} \text{GeSb}$ monolayers possess exciting half‐metallic character with wide half‐metallic gaps of 0.29 and 0.18 eV, and spin gaps of 1.68 and 1.62 eV, respectively. Their calculated ground state exhibits a strong preference for ferromagnetic ordering, with a Curie temperature (Tc$T_{c}$) of 630 and 590 K, respectively. Additionally, the ferromagnetism of Janus Mn2GeX (X = As, Sb) monolayers is robust against biaxial strain ranging from −6% to 6%. Under 6% tensile strain, the calculated Tc$T_{c}$ of the Mn2GeSb$\left(\text{Mn}\right)_{2} \text{GeSb}$ monolayer is 639 K, which represents a 9% increase compared to the Tc$T_{c}$ observed in the unstrained condition. All these intriguing electronic and magnetic properties make the Janus Mn2GeX (X = As, Sb) monolayers an appealing candidate for applications in nanoscale spintronic devices. [ABSTRACT FROM AUTHOR]

Until now, research has not taken into consideration the physicochemical purine–pyrimidine symmetries of the genetic code in the transcription and translation processes of proteinogenesis. Our Supersymmetry Genetic Code table, developed in 2022, is common and unique for all RNA and DNA living species. Its basic structure is a purine–pyrimidine symmetry net with double mirror symmetry. Accordingly, the symmetry of the genetic code directly shows its organisation based on the principle of nucleotide Watson–Crick and codon–anticodon pairing. The maximal purine–pyrimidine symmetries of codons show that each codon has a strictly defined and unchangeable position within the genetic code. We discovered that the physicochemical symmetries of the genetic code play a fundamental role in recognising and differentiating codons from mRNA and the anticodon tRNA and aminoacyl-tRNA synthetases in the transcription and translation processes. These symmetries also support the wobble hypothesis with non-Watson–Crick pairing interactions between the translation process from mRNA to tRNA. The Supersymmetry Genetic Code table shows a specific arrangement of the second base of codons, according to which it is possible that an anticodon from tRNA recognises whether a codon from mRNA belongs to an amino acid with two or four codons, which is very important in the purposeful use of the wobble pairing process. Therefore, we show that canonical and wobble pairings essentially do not lead to misreading and errors during translation, and we point out the role of physicochemical purine–pyrimidine symmetries in decreasing disorder according to error minimisation and preserving the integrity of biological processes during proteinogenesis. [ABSTRACT FROM AUTHOR]

Motivated by constructions appearing in mirror symmetry, we study special representatives of complexified Kähler classes, which extend the notions of constant scalar curvature and extremal representatives for usual Kähler classes. In particular, we provide a moment map interpretation, discuss a possible correspondence with compactified Landau–Ginzburg models, and prove existence results for such special complexified Kähler forms and their large volume limits in certain toric cases. [ABSTRACT FROM AUTHOR]

Scientific observation has led to the discovery of recurring patterns in nature. Symmetry is the property of an object showing regularity in parts on a plane or around an axis. There are several types of symmetries observed in the natural world and the most common are mirror symmetry, radial symmetry, and translational symmetry. Symmetries can be continuous or discrete. A discrete symmetry is a symmetry that describes non-continuous changes in an object. A continuous symmetry is a repetition of an object an infinite number of times. A consequence of continuous symmetry is the existence of conservation laws. A natural system with discrete and continuous symmetries displays several physical properties, such as the existence of long-range order. Geometric shapes exhibit symmetry as mirror reflections of each other. Symmetry in nature has been a model of beauty since the beginning of civilization. Since the earliest times, nature itself has manifestly been a model, evincing regularity in sundry forms and occurrences–from minerals and plants to the anatomy of living beings, to the regularly recurring stellar constellations. For Ancient Greek philosophers, proportion, symmetry, and harmony, were the basics to determine whether something is beautiful or not. Ancient Greek philosophers were known for bringing logic and rational thinking to phenomena that were previously explained by mythology and Gods. They observed the natural world around them and used their knowledge to answer questions about the proportion in observable objects and the origin of Earth. The Greek words summetria and summetros appear frequently in the Timaeus, defined as parts with each other and with the whole. Plato has a very rough concept of symmetry, and when he uses "beauty" to characterize the so-called Platonic Solids in the Timaeus, he seems to be emphasizing their regularity and indirectly their symmetry. Plato believes the four elements (earth, air, fire, water) have been constructed by the Demiurge, or a divine craftsman who appoints order in an otherwise chaotic universe. Minerals are representative examples of beauty, order, and symmetry in inorganic materials. Well-formed minerals (crystals) are a collection of equivalent faces related by symmetry. The goal of this paper is to relate the perspective of symmetry in ancient Greek philosophy with the modern scientific evidence of the geometric description of crystal structures. The five Platonic solids are ideal models of geometrical patterns that occur throughout the world of minerals. In this paper, minerals serve as a model of connecting the symmetry theory in Plato's philosophy and modern advances in mineralogy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The elliptic Fourier transform is a common method of describing the shape of objects by an unique sequence of coefficients that allow comparing the shapes by mathematical methods. However, the raw coefficients contain unnecessary data unrelated to the shape, which does not provide a correct comparison. For this reason, the coefficients are normalized. This removes some of the superfluous data, but leaves information about mirror symmetry and the order in which the contour vertices are declared, that are encoded in the signs of the coefficients. This also interferes with shape comparison. The paper describes an algorithm for harmonizing the coefficients, leveling the influence of the information mentioned. Based on the example of attachment organs of monogeneans, the advantages of using harmonized coefficients for comparing the shapes of biological structures are shown. [ABSTRACT FROM AUTHOR]

Narasimhan–Ramanan branes, introduced by the authors in a previous paper, consist of a family of (BBB)-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex Lagrangian subvarieties support the (BAA)-branes that are mirror dual to the Narasimhan–Ramanan (BBB)-branes. In this paper, we show that the support of these branes intersects nontrivially the locus of wobbly Higgs bundles. [ABSTRACT FROM AUTHOR]

Cholinergic signaling in the retina is mediated by acetylcholine (ACh) released from starburst amacrine cells (SACs), which are key neurons for motion detection. SACs comprise ON and OFF subtypes, which morphologically show mirror symmetry to each other. Although many physiological studies on SACs have targeted ON cells only, the synaptic computation of ON and OFF SACs is assumed to be similar. Recent studies demonstrated that gene expression patterns and receptor types differed between ON and OFF SACs, suggesting differences in their functions. Here, we compared cholinergic signaling pathways between ON and OFF SACs in the mouse retina using the patch clamp technique. The application of ACh increased GABAergic feedback, observed as postsynaptic currents to SACs, in both ON and OFF SACs; however, the mode of GABAergic feedback differed. Nicotinic receptors mediated GABAergic feedback in both ON and OFF SACs, while muscarinic receptors mediated GABAergic feedback in ON SACs only in adults. Neither tetrodotoxin, which blocked action potentials, nor LY354740, which blocked neurotransmitter release from SACs, eliminated ACh-induced GABAergic feedback in SACs. These results suggest that ACh-induced GABAergic feedback in ON and OFF SACs is regulated by different feedback mechanisms in adults and mediated by non-spiking amacrine cells other than SACs. [ABSTRACT FROM AUTHOR]

Chirality, the lack of mirror symmetry, can be mimicked in nanophotonics and plasmonics by breaking the symmetry in light-nanostructure interaction. Here we report on versatile use of nanosphere lithography for the fabrication of low-cost metasurfaces, which exhibit broadband handedness- and angle-dependent extinction in the near-infrared range, thus offering extrinsic chiro-optical behavior. We measure wavelength and angle dependence of the extinction for four samples. Two samples are made of polystyrene nanospheres asymmetrically covered by silver and gold in one case and silver only in the other case, with a nanohole array at the bottom. The other two samples are nanohole arrays, obtained after the nanosphere removal from the first two samples. Rich extrinsic chiral features are governed by different chiro-optical mechanisms in the three-dimensional plasmonic semi-shells and planar nanohole arrays. We also measure Stokes parameters in the same wavelength and incidence angle range and show that the transmitted fields follow the extrinsic chirality features of the extinction dissymmetry. We further study the influences of the nanostructured shapes and in-plane orientations on the intrinsic vs extrinsic chirality. The nanoholes are modelled as oval shapes in metal, showing good agreement with the experiments. We thus confirm that nanosphere lithography can provide different geometries for chiral light manipulation at the nanoscale, with the possibility to extend functionalities with optimized oval shapes and combination of constituent metals. [ABSTRACT FROM AUTHOR]

Chiral metamaterials possess unique optical chiral responses, and the attainment of remarkable intrinsic chirality typically necessitates the disruption of their mirror symmetry to facilitate cross‐coupling between electric and magnetic dipoles. However, achieving such symmetry breaking in a flexible and controllable manner remains challenging due to the limited range of applications afforded by available methodologies. Here, a method is proposed for fabricating robust three‐dimensional (3D) chiral metamaterials by projecting arbitrary planar chiral metasurfaces onto on‐demand height‐tunable 3D silicon structures, thereby effectively modulating their optical chiral responses through continuously tuning the degree of cross‐coupling between dipoles. Experimental and simulation results demonstrate this approach's ability to precisely control circular dichroism (CD) from a non‐chiral state to various activated and enhanced chirality. Enhancing CD with high precision and continuous control manners can naturally provide an advanced opportunity and platform for the future design and actual applications of chiral optical systems. [ABSTRACT FROM AUTHOR]

Telescopers for a function are linear differential (resp. difference) operators annihilating the definite integral (resp. definite sum) of this function. They play a key role in Wilf–Zeilberger theory and algorithms for computing them have been extensively studied in the past 30 years. In this paper, we introduce the notion of telescopers for differential forms with D-finite function coefficients. These telescopers appear in several areas of mathematics, for instance parametrized differential Galois theory and mirror symmetry. We give a sufficient and necessary condition for the existence of telescopers for a differential form and describe a method to compute them if they exist. Algorithms for verifying this condition are also given. [ABSTRACT FROM AUTHOR]

Chiral metasurfaces have attracted considerable attention because of their immense potential for diverse applications requiring chiral light-matter interactions. Recently, boosted by a mechanism based on the concept of bound states in the continuum (BICs), high Q factor chiroptical resonances have been exhibited by breaking the inversion symmetries of planar metasurfaces. However, the optical chirality of these chiral metasurfaces is generally intolerable with respect to the structural geometries, especially the geometric asymmetry. Here, we present a novel chiral quasi-BIC with strong optical chirality in an all-dielectric metasurface. By simultaneously breaking the in-plane C 2 rotational and mirror symmetries, the chiral metasurface shows enhanced chiroptical resonances with near-unity CD (∼0.996) and high Q factors (∼2274) at terahertz frequencies. Further analyses based on numerical simulations reveal that the CD of the chiroptical resonance depicts exceptional remarkable tolerableness to the geometry asymmetry δ when δ are present in a broad range, while the corresponding Q factor is modulated accordingly. The results may develop a novel approach to manipulating the advanced optical chirality for potential applications requiring strong CD with enhanced light-matter interactions. [ABSTRACT FROM AUTHOR]

Beta-delayed proton and gamma emission in the decay of 21 Mg has been measured at ISOLDE, CERN with the ISOLDE Decay Station (IDS) set-up. The existing decay scheme is updated, in particular what concerns proton transitions to excited states in 20 Ne. Signatures of interference in several parts of the spectrum are used to settle spin and parity assignments to highly excited states in 21 Na. The previously reported β p α branch is confirmed. A half-life of 120.5(4) ms is extracted for 21 Mg. The revised decay scheme is employed to test mirror symmetry in the decay and to extract the beta strength distribution of 21 Mg that is compared with theory. [ABSTRACT FROM AUTHOR]

We introduce the wrapped Donaldson--Fukaya category of a (generalized) semi-toric SYZ fibration with Lagrangian section satisfying a tameness condition at infinity. Examples include the Gross fibration on the complement of an anti-canonical divisor in a toric Calabi--Yau 3-fold.We compute the wrapped Floer cohomology of a Lagrangian section and find that it is the algebra of functions on the Hori--Vafa mirror. The latter result is the key step in proving homological mirror symmetry for this case. The techniques developed here allow the construction in general of the wrapped Fukaya category on an open Calabi--Yau manifold carrying an SYZ fibration with nice behavior at infinity. We discuss the relation of this to the algebraic vs analytic aspects of mirror symmetry. [ABSTRACT FROM AUTHOR]

Nodal chains in which two nodal rings connect at one point were recently discovered in non-symmorphic electronic systems and then generalized to symmorphic phononic systems. In this work, we identify a new class of planar nodal chains in non-symmorphic phononic systems, where the connecting rings lie in the same plane. The constituting nodal rings are protected by mirror symmetry, and their intersection is guaranteed by the combination of time-reversal and non-symmorphic twofold screw symmetry. The connecting points are fourfold degenerate while those in previous works are twofold degenerate. We found 8 out of 230 space groups that can host the proposed planar nodal chain phonons. Taking wurtzite GaN (space group No. 186) as an example, the planar nodal chain is confirmed by first-principles calculations. The planar nodal chains result in two distinct classes of drumhead surface states on the [10(–1)0] and the [0001] surface Brillouin zones. Our finding reveals a class of planar nodal chains in non-symmorphic phononic systems, expanding the catalog of topological nodal chains and enriching the family of topological surface states. [ABSTRACT FROM AUTHOR]

In this article, we investigate the potential feasibility of new Janus XMPYS (X = Se, Te; M = Mo, W; Y Al, Ga) monolayers using first-principles calculations. All eight studied monolayers are shown to be direct semiconductors with moderate bandgaps ranging from 1.30 eV to 1.47 eV. The asymmetric structure of Janus XMPYS together with the presence of heavy transition metals (M = Mo, W) results in the considerable valley and Rashba spin-splittings desirable for valleytronic and spintronic applications. It is also shown that strain can be used to modulate the spin-related properties of the proposed structures. Among XMPYS monolayers, the four with X = Se meet the band alignment requisite for overall water splitting. Moreover, these monolayers are predicted to have excellent solar-to-hydrogen efficiency of 25.61%–28.08%. Excitingly, it is found that by applying tensile strain an impressive efficiency of 39% can be achieved in SeWPAlS and SeWPGaS monolayers. • The spintronic and photocatalytic properties of XMPYS monolayers are investigated. • All studied monolayers are direct semiconductors with bandgaps in the range of 1.3–1.47 eV. • Broken mirror and inversion symmetry lead to Rashba and valley spin-splittings. • The SeMPYS monolayers satisfy the band alignment requirement for overall water splitting. [ABSTRACT FROM AUTHOR]

We present an analysis of enhanced wave transmission through random media with mirror symmetry about a reflecting barrier. The mathematical model is the acoustic wave equation, and we consider two setups, where the wave propagation is along a preferred direction: in a randomly layered medium and in a randomly perturbed waveguide. We use the asymptotic stochastic theory of wave propagation in random media to characterize the statistical moments of the frequency-dependent random transmission and reflection coefficients, which are scalar-valued in layered media and matrix-valued in waveguides. With these moments, we can quantify explicitly the enhancement of the net mean transmitted intensity, induced by wave interference near the barrier. [ABSTRACT FROM AUTHOR]

The interlayer proximity effect induced by spin-orbital coupling between the monolayers of borophosphene (BP) and MoSe2 in the stacked heterostructure is studied by first principles calculations. The proximity effect originates from the hybridization of the d orbital of the Mo atoms and the p orbital of the B atoms. This hybridization greatly improved the strength of spin-orbital coupling of the BP layer, bringing the spin-dependent valley and spin splitting about 13 meV at the K point of the conduction band of BP layer. Moreover, the existence of BP layer destroyed the mirror symmetry of MoSe2 layer, causing the Rashba splitting at the Γ point of the valence band. In addition, the calculation results indicate that both the Zeeman splitting and Rashba splitting can be modulated by the transverse electric field and the interlayer distance. [ABSTRACT FROM AUTHOR]

Spontaneous mirror symmetry breaking by formation of chiral structures from achiral building blocks and emergent polar order are phenomena rarely observed in fluids. Separately, they have both been found in certain nematic liquid crystalline phases; however, they have never been observed simultaneously. Here, we report a heliconical arrangement of achiral molecules in the ferroelectric nematic phase. The phase is thus spontaneously both polar and chiral. Notably, the pitch of the heliconical structure is comparable to the wavelength of visible light, giving selective reflection controllable by temperature or application of a weak electric field. Despite bearing resemblance to the heliconical twist-bend nematic phase, this chiral ferroelectric nematic phase arises from electrical interactions that induce a noncollinear orientation of electric dipoles. [ABSTRACT FROM AUTHOR]

Chiral metasurface based on bound state in the continuum (BIC) possesses extremely high Q factor. However, intrinsic chiral BIC only can be realized by breaking out‐of‐plane mirror symmetry with complicated 3D structures. In this work, a design of planar intrinsic chiral metasurface supporting orthogonal BICs is proposed. The coupling strength, eigenfrequency, and radiation loss of the two quasi‐BICs can be tuned by metasurface parameters. By adjusting the metasurface parameters, the two quasi‐BICs merge to an exceptional point (EP). Around EP, one of the BICs transforms to chiral BIC with circular eigenstate polarization. In the parameter space, different elliptical eigenstate polarizations with the same helicity wind around the EP. The polarizations of the quasi‐BICs nearly fully cover the Poincaré sphere by changing the geometry parameters. The superchiral fields of the quasi‐BICs will also be greatly enhanced near the EP. The simulation result shows high circular dichroism at resonance frequency. The design provides a new strategy for polarization detection and chiral light sources. [ABSTRACT FROM AUTHOR]

We consider the fourteen families W of Calabi–Yau threefolds with one complex structure parameter and Picard–Fuchs equation of hypergeometric type, like the mirror of the quintic in P 4 . Mirror symmetry identifies the masses of even-dimensional D-branes of the mirror Calabi–Yau M with four periods of the holomorphic (3, 0)-form over a symplectic basis of H 3 (W , Z) . It was discovered by Chad Schoen that the singular fiber at the conifold of the quintic gives rise to a Hecke eigenform of weight four under Γ 0 (25) , whose Hecke eigenvalues are determined by the Hasse–Weil zeta function which can be obtained by counting points of that fiber over finite fields. Similar features are known for the thirteen other cases. In two cases we further find special regular points, so called rank two attractor points, where the Hasse–Weil zeta function gives rise to modular forms of weight four and two. We numerically identify entries of the period matrix at these special fibers as periods and quasiperiods of the associated modular forms. In one case we prove this by constructing a correspondence between the conifold fiber and a Kuga–Sato variety. We also comment on simpler applications to local Calabi–Yau threefolds. [ABSTRACT FROM AUTHOR]

Non-centrosymmetric topological material has attracted intense attention due to its superior characteristics as compared with the centrosymmetric one, although probing the local quantum geometry in non-centrosymmetric topological material remains challenging. The non-linear Hall (NLH) effect provides an ideal tool to investigate the local quantum geometry. Here, we report a non-centrosymmetric topological phase in ZrTe5, probed by using the NLH effect. The angle-resolved and temperature-dependent NLH measurement reveals the inversion and ab-plane mirror symmetries breaking at <30 K, consistently with our theoretical calculation. Our findings identify a new non-centrosymmetric phase of ZrTe5 and provide a platform to probe and control local quantum geometry via crystal symmetries. [ABSTRACT FROM AUTHOR]

We introduce a conjecture on homological mirror symmetry relating the symplectic topology of the complement of a smooth ample divisor in a K3 surface to the algebraic geometry of type III degenerations. We prove it when the degree of the divisor is either 2 or 4. [ABSTRACT FROM AUTHOR]

Spin–orbit torque (SOT) induced magnetization switching in an energy-efficient and fast way has exhibited great application potential in next generation magnetic memories. However, a complicated layer structure is usually needed to break the mirror symmetry for achieving SOT induced field-free magnetization switching. Here, we report a sizeable field-free magnetization switching through large out-of-plane SOT in the chemically disordered A1-CoxPt100−x single layers within a Co composition range from 40 to 70. The largest absolute out-of-plane SOT efficiency is found at its equiatomic concentration (Co50Pt50), in which the absolute in-plane SOT efficiency also reaches the maximum value, 22.7 Oe/107 A cm−2. We further demonstrate that the symmetry dependence of field-free magnetization switching might arise from the chemically ordered L11-CoPt nano-scaled platelets formed during the sample deposition. We expect that the experimental identification of the field-free magnetization switching in the ferromagnetic CoPt single layer is desirable to simplify the applications of spin logic devices. [ABSTRACT FROM AUTHOR]

The Langlands program is a vast mathematical projection linking number theory and geometry. In high-energy physics, a connection with mirror symmetry has been suggested in string theory, but it has been little studied in low-energy physics. In the framework of the Langlands program, we present a unified description of the integer and fractional quantum Hall effect and the duality found in the fractal nature of the energy spectrum of two-dimensional Bloch electrons, statistical physics, and quantum computation. The new unified view of existing dualism presented in this paper raises the entirely new question of how each theory of physics is connected as a piece of the Langlands program. [ABSTRACT FROM AUTHOR]

Strominger–Yau–Zaslow (SYZ) proposed a way of constructing mirror pairs as pairs of torus fibrations. We apply this SYZ construction to toric Fano surfaces as complex manifolds, and discuss the homological mirror symmetry, where we consider Morse homotopy of the moment polytope instead of the Fukaya category. [ABSTRACT FROM AUTHOR]