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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]

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]

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]

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]

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]

Ionospheric dynamics exhibits a distinct hemispheric asymmetry, influenced primarily by the Interplanetary Magnetic Field (IMF) By component, dipole tilt, or a combination of both. Previous studies have indicated a reduction in these asymmetries during substorms. In this study, we conduct a superposed epoch analysis using ground magnetometer data from the northern hemisphere to examine the impact of substorms on ionospheric current asymmetry. This analysis uses the assumption of mirror symmetry between the northern and southern hemispheres when IMF By and dipole tilt are reversed. We observe a significant reduction in nightside equivalent current asymmetry indicating the IMF By and dipole tilt have minimal influence on the substorm current. On the other hand, we find that substorms exert minimal or negligible effects on dayside currents. This difference in response between nightside and dayside currents emphasizes the need to incorporate nightside dynamics into existing climatological models, which presently rely mainly on upstream parameters due to a lack of robust parameters effectively representing them. Our findings provide important insights for future modeling efforts, highlighting the distinct interactions between substorms and ionospheric currents across different hemispheric regions. Key Points: Substorms can reduce interhemispheric asymmetries in the nightside ionospheric currents induced by Interplanetary Magnetic Field (IMF) By and dipole tiltSubstorms have little impact on dayside currents, and the IMF and dipole tilt has little impact on substorm currentsThis study can guide the development of future climatological models of ionospheric currents that currently rely only on upstream parameters [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]

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]

Ferrocene derivatives show a wide range of pharmacological activities in the medical field, especially in the anti‐tumor field, and can be used as candidate drugs or lead compounds for the treatment of tumors and other diseases. And α‐phenethylamine is an important intermediate for the preparation of fine chemical products. (R)‐(+)‐1‐Phenethylamine ferrocenecarboxylic acid/(S)‐(−)‐1‐phenethylamine ferrocenecarboxylic acid were prepared, named compounds 1 and 2, respectively. Single crystal X‐ray diffraction showed that compounds 1 and 2 crystallized in the orthorhombic system space group P212121, and the crystal structures of compounds 1 and 2 exhibited mirror symmetry. The inhibitory effect of two compounds on SW480, MDA‐MB‐231, and H1299 cells was tested by MTT colorimetry. The IC50 values of the compounds against cancer cells were also calculated. The anti‐cancer effect was more pronounced for compounds in the S‐configuration. Compound 2 made the wild‐type cancer cells undergo apoptosis, thus preventing cancer; it also had the function of helping the cell gene repair defects. [ABSTRACT FROM AUTHOR]

The diffraction pattern from the recently reported aperiodic 'einstein', or 'hat', monohedral tiling [Smith et al. (2023). arXiv:2303.10798v1] has been analyzed. The structure is the hexagonal mta net, a kite tiling, with aperiodic vertex deletions. A large model's diffraction pattern displays a robust sixfold periodicity in plane group p6. A repeating, roughly triangular motif of 'diffused intensity' arises between the strongest Bragg peaks. The motif contains high‐density regions of discrete 'satellite' peaks, rather than continuous 'diffuse scattering', breaking mirror symmetry, consistent with the chiral hat tiling. [ABSTRACT FROM AUTHOR]

Origami metasurfaces have emerged as a versatile platform for dynamically manipulating electromagnetic waves due to their numerous advantages, including cost‐effectiveness, lightweight nature, and diverse structural transformations. They are particularly well‐suited for reconfigurable chiroptical responses that can find utility in various applications. However, current research has primarily focused on modulating spectral properties like optical chirality and resonant frequencies, which may limit their practical applications. Herein, an origami metasurface enabled by a simple yet highly effective deformation method is proposed to achieve simultaneous tunable chirality and wavefront manipulation, which expands the modulation freedom of mechanical deformation in chiral metasurfaces. The planar metasurface with spin‐insensitive transmittance is bulked into 3D metasurfaces to break the mirror symmetry, thereby triggering pronounced chiral responses. Additionally, through the implementation of propagation phase design, two types of meta‐atoms with distinct phase responses are interleaved to create a chiral anomalous reflector that spin‐selectively modulates the reflection beam. The experimental results agree well with the simulation results and theoretical predictions, verifying the high quality of the proposed design that may offer untapped potential for applications such as reconfigurable photonics devices. [ABSTRACT FROM AUTHOR]

We study the mod 2 cohomology of real Calabi–Yau threefolds given by real structures that preserve the torus fibrations constructed by Gross. We extend the results of Castaño–Bernard–Matessi and Arguz–Prince to the case of real structures twisted by a Lagrangian section. In particular, we find exact sequences linking the cohomology of the real Calabi–Yau with the cohomology of the complex one. Applying Strominger–Yau–Zaslow mirror symmetry, we show that the connecting homomorphism is determined by a "twisted squaring of divisors" in the mirror Calabi–Yau, that is, by D↦D2+DL$D \mapsto D^2 + DL$ where D$D$ is a divisor in the mirror and L$L$ is the divisor mirror to the twisting section. We use this to find an example of a connected (M−2)$(M-2)$‐real quintic threefold. [ABSTRACT FROM AUTHOR]

Via correspondence theorems, rational log Gromov–Witten invariants of the plane can be computed in terms of tropical geometry. For many cases, there exists a range of algorithms to compute tropically: for instance, there are (generalised) lattice path counts and floor diagram techniques. So far, the cases for which there exist algorithms do not extend to non‐stationary rational descendant log Gromov–Witten invariants, that is, those where Psi‐conditions do not have to be matched up with the evaluation of a point. The case of rational descendant log Gromov–Witten invariants satisfying point conditions (without Psi‐conditions) and one Psi‐condition of any power combined with a line plays a particularly important role, because it shows up in mirror symmetry as contributions to coefficients of the J$J$‐function. We provide recursive formulas to compute those numbers via tropical methods. Our method is inspired by the tropical proof of the WDVV equations. We also extend our study to counts involving two lines, both paired up with a Psi‐condition, appearing with power 1. [ABSTRACT FROM AUTHOR]

Conventional coherent absorption occurs only when two incident beams exhibit mirror symmetry with respect to the absorbing surface, i.e., the two beams have the same incident angles, phases, and amplitudes. This study proposes a more general metasurface paradigm for coherent perfect absorption with impinging waves from arbitrary asymmetric directions. By exploiting excitation of unidirectional evanescent waves, the output can be fixed at one reflection direction for any amplitude and phase ofthe control wave. It shows theoretically and confirm experimentally that the relative amplitude of the reflected wave can be tuned continuously from zero to unity by changing the phase difference between the two beams, i.e., switching from coherent perfect absorption to full reflection. It hopes that this study will open up promising possibilities for wave manipulation via evanescent waves engineering with applications in optical switches, optical computing, one-side sensing, photovoltaics, and radar cross-section control. [ABSTRACT FROM AUTHOR]

2D Janus transition metal dichalcogenides (TMDs) have attracted attention due to their emergent properties arising from broken mirror symmetry and self‐driven polarization fields. While it has been proposed that their vdW superlattices hold the key to achieving superior properties in piezoelectricity and photovoltaic, available synthesis has ultimately limited their realization. Here, the first packed vdW nanoscrolls made from Janus TMDs through a simple one‐drop solution technique are reported. The results, including ab initio simulations, show that the Bohr radius difference between the top sulfur and the bottom selenium atoms within Janus MSeS${\rm{M}}_{{\rm{Se}}}^{\rm{S}}$ (M = Mo, W) results in a permanent compressive surface strain that acts as a nanoscroll formation catalyst after small liquid interaction. Unlike classical 2D layers, the surface strain in Janus TMDs can be engineered from compressive to tensile by placing larger Bohr radius atoms on top (MSSe)${\rm{M}}_{\rm{S}}^{{\rm{Se}}})\ $to yield inverted C scrolls. Detailed microscopy studies offer the first insights into their morphology and readily formed Moiré lattices. In contrast, spectroscopy and FETs studies establish their excitonic and device properties and highlight significant differences compared to 2D flat Janus TMDs. These results introduce the first polar Janus TMD nanoscrolls and introduce inherent strain‐driven scrolling dynamics as a catalyst to create superlattices. [ABSTRACT FROM AUTHOR]

Chirality is a curious phenomenon that appears in various forms. While the concept of molecular (RS‐)chirality is ubiquitous in chemistry, there are also more intricate forms of structural chirality. One of them is the enantiomorphism of crystals, especially molecular crystals, that describes the lack of mirror symmetry in the unit cell. Its relation to molecular chirality is not obvious, but still an open question, which can be addressed with chiroptical tools. Vibrational circular dichroism (VCD) denotes chiral infrared (IR) spectroscopy that is susceptible to both, the molecular as well as the intermolecular space by means of vibrational transitions. When carried out in the solid state, VCD delivers a very rich set of non‐local contributions that are determined by crystal packing and collective motion. Since its discovery in the 1970s, VCD has become the method of choice for the determination of absolute configurations, but its applicability reaches beyond towards the study of different crystal forms and polymorphism. This brief review summarises the theoretical concepts of crystal chirality and how computations of solid‐state VCD can shed light into the intimate connection of chiral structure and vibrational optical activity. [ABSTRACT FROM AUTHOR]

Plasmonic chiral nanostructures provide a novel route for extraordinary optical properties, such as light polarization control and enhancing chiroptical signals of molecules. The symmetry of chiral nanostructures, such as helices, gyroids, and irregular tetrahedrons, is strongly correlated to chiroptical responses; therefore, it is an important design parameter. In a previous study, a synthetic strategy is demonstrated for 432‐symmetric chiral gold nanoparticles by breaking the mirror symmetry of a 4/m3¯$\overline 3 $ 2/m‐symmetric crystal structure on a high‐index surface. Herein, the aim is to extend the chiral symmetry of gold nanoparticles and their chiroptical responses. The symmetry of gold nanoparticles can be modulated by inducing single or multiple twin planes in seed nanoparticles. The 32‐symmetric chiral gold nanoplates, referred to as 32 helicoids, are successfully synthesized using 3 2/m‐symmetric triangular and hexagonal plates. The growth mechanism of the 32 helicoids, which results in two different characteristic morphologies, is analyzed. The 32 helicoids are significantly important owing to their optical activity over a wide range from the visible to the near‐infrared region. This investigation provides an insight that symmetry control of the nanomorphology can represent an important research direction in chiral plasmonic applications. [ABSTRACT FROM AUTHOR]

Lorentz‐violating type‐II Dirac nodal line semimetals (DNLSs), hosting curves of band degeneracy formed by two dispersion branches with the same sign of slope, represent a novel state of matter. While being studied extensively in theory, convincing experimental evidence of type‐II DNLSs remain elusive. Recently, vanadium‐based kagome materials have emerged as a fertile ground to study the interplay between lattice symmetry and band topology. This work studies the low‐energy band structure of double‐kagome‐layered CsV8Sb12 and identifies it as a scarce type‐II DNLS protected by mirror symmetry. This work observes multiple DNLs consisting of type‐II Dirac cones close to or almost at the Fermi level via angle‐resolved photoemission spectroscopy (ARPES), which provides an electronic explanation for the nonsaturating magnetoresistance effect as observed. First‐principles theory analyses show that spin‐orbit coupling only opens a small gap, resulting in effectively gapless ARPES spectra, yet generating large spin Berry curvature. These type‐II DNLs, together with the interaction between a low‐energy van Hove singularity and quasi‐one‐dimensional band as observed in the same material, suggest CsV8Sb12 as an ideal platform for exploring novel transport properties. [ABSTRACT FROM AUTHOR]

The target mono‐BF2 complex is weakly emissive in fluid solution because radiationless decay of the excited‐singlet state is promoted through an intramolecular N⋅⋅⋅H−N hydrogen bond. The lack of mirror symmetry for this compound is attributed to vibronic effects, as reported previously for the bis‐BF2 complex (BOPHY). Red‐shifted fluorescence is observed from single crystals, the emission quantum yield approaching 30 % with a fluorescence lifetime of 2 ns. The large Stokes shift of 5,700 cm−1 helps minimize self‐absorption. Crystallography indicates that the internal fold and twist angles are increased substantially in the crystal, but the hydrogen bond is weakened relative to solution. The crystal structure is compiled from pairs of head‐to‐tail molecules having a shift of ca. 4.1 Å and closest approach of ca. 3.5 Å. These molecular pairs are arranged in columns, which, in turn, assemble into sheets. The proximity favors excitonic coupling between individual molecules, with the coupling strength obtained by analysis of the absorption spectrum reaching ca. 1,000 cm−1. Both the ideal dipole approximation and the extended dipole methodology seriously overestimate the coupling strength, but the atomic transition charge density procedure leads to good agreement with experiment. Emission is attributed to the closely coupled molecular pair functioning in an excimer‐like manner with the exciton trapped in a local minimum. Increasing temperature causes a slight blue shift and loss of fluorescence. [ABSTRACT FROM AUTHOR]

We study the mirror symmetry on the singular locus of the Hitchin system at two levels. First, by covering it by (supports of) (BBB)‐branes, corresponding to Higgs bundles reducing their structure group to the Levi subgroup of some parabolic subgroup P, whose conjectural dual (BAA)‐branes we describe. Heuristically speaking, the latter are given by Higgs bundles reducing their structure group to the unipotent radical of P. Second, when P is a Borel subgroup, we are able to construct a family of hyperholomorphic bundles on the (BBB)‐brane and study the variation of the dual under this choice. We give evidence of both families of branes being dual under mirror symmetry via an integral functor induced by Fourier–Mukai in the moduli stack of Higgs bundles. [ABSTRACT FROM AUTHOR]

In this work, the gyrotropic semiconductor InSb into the twisted bilayer metasurface to form a magneto‐optical moiré metasurface is introduced. Through the theoretical analysis, the "moiré angle" is developed in which case the nonreciprocity and chirality with the spin‐conjugate asymmetric transmission are obtained due to the simultaneous breaking of both time‐reversal symmetry and spatial mirror symmetry. The experiments confirm that the chirality can be actively manipulated by rotating the twisted angle and the external magnetic field, realizing spin‐conjugate asymmetric transmission. Meanwhile, the two spin states also realize the nonreciprocal one‐way transmission, and their isolation spectra are also spin‐conjugate asymmetric: one is enhanced up to 48 dB, and the other's bandwidth is widened to over 730 GHz. This spin‐conjugate symmetry‐breaking effect in the MOMM brings a combination of time‐space asymmetric transmission, and it also provides a new scheme for the implementation of high‐performance THz chirality controllers and isolators. [ABSTRACT FROM AUTHOR]

In solid state physics, any symmetry breaking is known to be associated with emergence of an order parameter. However, the order parameter for molecular and crystal chirality, which is a consequence of parity and mirror symmetry breaking, has not been known since its discovery. In this article, the authors show that the order parameter for chirality can be defined by electric toroidal monopole G0 ${{G}_{0}}$. By this definition, one becomes able to discuss external field that can distinguish two different enantiomers only by physical fields. In addition, dynamics and fluctuations of the order parameter G0 ${{G}_{0}}$ can be discussed, with which one can obtain fruitful insights on a spin filtering effect called CISS (Chirality Induced Spin Selectivity). Emergence of time‐reversal‐odd dipole Mz ${{M}_{z}}$ by time propagation of G0 ${{G}_{0}}$ quantities is discussed to explain the enantioselective effect (chiral resolution) at a ferromagnetic surface. [ABSTRACT FROM AUTHOR]

Spontaneous generation of chirality from achiral molecules is a contemporary research topic with numerous implications for technological applications and for the understanding of the development of homogeneous chirality in biosystems. Herein, a series of azobenzene based rod‐like molecules with an 3,4,5‐trialkylated end and a single n‐alkyl chain involving 5 to 20 aliphatic carbons at the opposite end is reported. Depending on the chain length and temperature these achiral molecules self‐assemble into a series of liquid and liquid crystalline (LC) helical network phases. A chiral isotropic liquid (Iso1[*]) and a cubic triple network phase with chiral I23 lattice were found for the short chain compounds, whereas non‐cubic and achiral cubic phases dominate for the long chain compounds. Among them a mesoscale conglomerate with I23 lattice, a tetragonal phase (Tetbi) containing one chirality synchronized and one non‐synchronized achiral network, an achiral double network meso‐structure with Ia3‾ $\bar 3$ d space group and an achiral percolated isotropic liquid mesophase (Iso1) were found. This sequence is attributed to an increasing strength of chirality synchronization between the networks, combined with a change of the preferred mode of chirophilic self‐assembly between the networks, switching from enantiophilic to enantiophobic with decreasing chain length and lowering temperature. These nanostructured and mirror symmetry broken LC phases exist over wide temperature ranges which is of interest for potential applications in chiral and photosensitive functional materials derived from achiral compounds. [ABSTRACT FROM AUTHOR]

Metasurface optical holography represents an important technique for developing ultrathin diffractive optical elements. Among various designs, the metasurface devices with strong chiroptical responses offer a new degree of freedom to manipulate light fields. However, in a linear optical regime, it is usually complicated to realize strong chiroptical properties with metasurfaces. Here, nonlinear chiroptical holography using the Pancharatnam–Berry phase controlled achiral metasurface is reported. The metasurface consists of mirror symmetry breaking plasmonic meta‐atoms. Under the pumping of a fundamental wave, the achiral meta‐atoms radiate second harmonic waves with strong circular dichroism and spin dependent Pancharatnam–Berry phase. Both the amplitude and phase of the second harmonic waves can be independently and simultaneously controlled at the subwavelength scale. As a proof of concept, the spin selective nonlinear chiroptical holography is experimentally demonstrated through the second harmonic process on gold plasmonic metasurfaces. The proposed nonlinear metasurface with Pancharatnam–Berry phase and chiroptical properties open new avenues for multifunctional wavefront engineering and optical information processing. [ABSTRACT FROM AUTHOR]

The electron–phonon coupling (EPC) in semiconductors is typically much weaker than phonon–phonon scattering and its effect on lattice thermal conductivity κl has long been considered negligible. Herein, using first‐principle calculations, it is discovered that the EPC can be significant or even dominant over the intrinsic phonon–phonon scattering via doping in 2D semiconductor hexagonal boron phosphorus (h‐BP). Filling electron pocket till van Hove singularity gradually strengthens the EPC and consequently diminishes the room‐temperature κl by 25% and 80% for monolayer and bilayer h‐BP, respectively. Strikingly, at high doping levels, the EPC drives phonon transport in bilayer h‐BP to an anomalous regime where κl becomes nearly temperature (T) independent deviated from the intrinsic 1/T trend. This distinctive behavior is governed by the joint effects of horizontal mirror symmetry breaking, and weak phonon–phonon scattering stemming from the predominance of normal processes. Further considering electronic contributions, the abnormal T‐independent thermal conductivity is still reserved, thereby facilitating the experimental exploration of EPC effect on κl. This study unveils the exotic thermal transport phenomenon in one‐atom‐thick 2D semiconductors and offers a unique avenue to manipulate heat flow by externally controlling the EPC, which calls for future experimental verification. [ABSTRACT FROM AUTHOR]

We consider K3 surfaces of Picard rank 14 which admit a purely non‐symplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We show that all of these K3 surfaces admit an elliptic fibration and we compute the invariant lattices in a geometric way by using special curves of the elliptic fibration. The computation of these lattices plays an important role when one wants to study moduli spaces and mirror symmetry for lattice polarized K3 surfaces. [ABSTRACT FROM AUTHOR]

We explore the cohomological structure for the (possibly singular) moduli of SLn$\mathrm{SL}_n$‐Higgs bundles for arbitrary degree on a genus g$g$ curve with respect to an effective divisor of degree >2g−2$>2g-2$. We prove a support theorem for the SLn$\mathrm{SL}_n$‐Hitchin fibration extending de Cataldo's support theorem in the nonsingular case, and a version of the Hausel–Thaddeus topological mirror symmetry conjecture for intersection cohomology. This implies a generalization of the Harder–Narasimhan theorem concerning semistable vector bundles for any degree. Our main tool is an Ngô–type support inequality established recently which works for possibly singular ambient spaces and intersection cohomology complexes. [ABSTRACT FROM AUTHOR]

We show that the base spaces of the semiuniversal unfoldings of some weighted homogeneous singularities can be identified with moduli spaces of A∞$A_\infty$‐structures on the trivial extension algebras of the endomorphism algebras of the tilting objects. The same algebras also appear in the Fukaya categories of their mirrors. Based on these identifications, we discuss applications to homological mirror symmetry for Milnor fibers, and give a proof of homological mirror symmetry for an n$n$‐dimensional affine hypersurface of degree n+2$n+2$ and the double cover of the n$n$‐dimensional affine space branched along a degree 2n+2$2n+2$ hypersurface. Along the way, we also give a proof of a conjecture of Seidel (Proceedings of the International Congress of Mathematicians, 2002) which may be of independent interest. [ABSTRACT FROM AUTHOR]

2D materials are excellent platforms for nonlinear optical (NLO) response, especially second harmonic generation (SHG), due to its large surface to volume ratio and sub‐nanometer thickness. The SHG susceptibility strongly relies on the symmetry of materials. Constructing Janus structures can break the out‐of‐plane mirror symmetry, bringing about asymmetric charge distribution and leading to a built‐in electric field. Consequently, SHG response along the out‐of‐plane direction can be improved. In the current work, combining first‐principles calculations with independent particle approximation, the SHG response of nine Janus group‐III chalcogenide monolayers (M2XX', MM'X2) are systematically evaluated. Both extraordinary in‐plane and out‐of‐plane SHG response are revealed in all the Janus structures. Besides, cation MM'X2 Janus structures exhibit systemically higher SHG response than that of anion M2XX' due to stronger dipole. Among them, GaInTe2 possesses extremely high out‐of‐plane SHG response with d31 up to 10490.4 pm V−1 at photon energy (PE) of 4.7 eV, enabling promising applications in ultraviolet NLO devices. The SHG intensity polar plots from Janus structures display unusual rotational symmetry at different PEs allowed by the out‐of‐plane SHG components. This work provides theoretical guidelines for further experimental explorations in 2D group‐III monochalcogenide Janus structures and paves the way for their utilization in NLO devices. [ABSTRACT FROM AUTHOR]

The goal of this project was to identify the prevalence of approximate symmetry in organic P1 structures. In the November 2019 version of the Cambridge Structural Database (CSD), there are 2592 organic, P1, R ≤ 0.050 structures; complete, unique entries are available for 1407 Z = Z′ > 1 and 1049 Z = Z′ = 1 structures. All the Z > 1 structures can have approximate symmetry; the Z = 1 structures were scanned to find those composed of molecules or ions that might lie on a special position and those that have two or more large molecules or ions that are very similar. The number of Z = 1 structures so identified was 285, of which 49 were grouped with the Z > 1 structures because Zeffective > 1. The packing in each of the 1407 + 285 = 1692 structures was investigated. The 144 that should almost certainly have been described in a smaller or higher‐symmetry unit cell were removed from the list; 120 of the 144 are composed of achiral or racemic material. (About half of the Z = 1 and 89% of the Z > 1 structures are composed of enantiopure material.) Approximate periodic symmetry was found in 86% of the 1337 remaining Z > 1 structures and in 72% of the 211 remaining Z = 1 structures. About a third of the enantiomerically pure structures mimic inversion symmetry; 38% have approximate rotational symmetry. For the structures of achiral and racemic material, distorted glide or mirror symmetry is more common than is distorted inversion symmetry. Approximate rotational and glide symmetry was found to be periodic in two dimensions considerably more often than in three. In 4% of the structures, different layer types alternate or layers are related by approximate local rotations, as well as by small translations. In 5% of the structures, different parts of the molecule are segregated into two‐dimensional regions that have different approximate symmetries. More than a third of the structures that are a distorted version of a higher‐symmetry structure were determined at T ≥ 288 K. [ABSTRACT FROM AUTHOR]

The exterior algebra E$E$ on a finite‐rank free module V$V$ carries a Z/2$\mathbb {Z}/2$‐grading and an increasing filtration, and the Z/2$\mathbb {Z}/2$‐graded filtered deformations of E$E$ as an associative algebra are the familiar Clifford algebras, classified by quadratic forms on V$V$. We extend this result to A∞$A_\infty$‐algebra deformations A$\mathcal {A}$, showing that they are classified by formal functions on V$V$. The proof translates the problem into the language of matrix factorisations, using the localised mirror functor construction of Cho–Hong–Lau, and works over an arbitrary ground ring. We also compute the Hochschild cohomology algebras of such A$\mathcal {A}$. By applying these ideas to a related construction of Cho–Hong–Lau, we prove a local form of homological mirror symmetry: the Floer A∞$A_\infty$‐algebra of a monotone Lagrangian torus is quasi‐isomorphic to the endomorphism algebra of the expected matrix factorisation of its superpotential. [ABSTRACT FROM AUTHOR]

As a new degree of freedom for optical manipulation, recently, spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentums have been experimentally demonstrated with pulse shapers. Here, a spatiotemporal differentiator is proposed to generate STOVs with transverse orbital angular momentum. In order to create phase singularity in the spatiotemporal domain, the spatiotemporal differentiator is designed by breaking spatial mirror symmetry. In contrast to pulse shapers, the device proposed here is a simple one‐dimensional periodic nanostructure and thus it is much more compact. For a normal incident pulse, the differentiator generates a transmitted STOV pulse with transverse orbital angular momentum. Furthermore, the interference of the generated STOVs can be used to detect the sharp changes of pulse envelopes, in both spatial and temporal dimensions. [ABSTRACT FROM AUTHOR]

Metamaterials consisting of subwavelength resonators offer an exciting opportunity for realizing asymmetric transmission (AT) of linearly polarized light. However, to date, only moderate/narrow‐band AT responses have been obtained in metadevices based on stacked planar nanostructures. Here, leveraging a combination of a genetic algorithm (GA) based optimization method and a membrane projection lithography (MPL) fabrication approach, a quasi‐3D metamaterial for broadband AT of linearly polarized mid‐infrared light is demonstrated. Facilitated by the customized GA, an efficient exploration of 3D plasmonic meta‐atoms with broken mirror symmetry in the light propagation direction allows the satisfaction of the rigorous conditions for AT of linearly polarized waves over a broad wavelength range. Confirmed by surface current analysis, the observed AT behavior is attributed to the resonant coupling between the plasmonic nanostructures located on the two orthogonal walls of the MPL cavities. Incorporating an advanced inverse‐design method and a state‐of‐art fabrication technique, the methodology used in the present study provides a promising route for exploiting 3D metamaterials with sophisticated functionalities via effectively exploring the high‐dimensional parametric space offered by true 3D meta‐atoms. [ABSTRACT FROM AUTHOR]

The successful fabrication of Janus transition metal dichalcogenide (TMD) monolayer has sparked extensive research interests in various fields, such as nanoelectronics, optoelectronics, valleytronics, and catalysis. Janus TMDs can not only inherit the advantages of conventional TMDs but also produce novel properties which are different from their counterparts. The breaking of vertical mirror symmetry can induce a variety of novel properties, such as Rashba spin splitting, vertical piezoelectricity, and long exciton lifetime. Moreover, the intrinsic electric field that originates from the vertical asymmetry can serve as a superior platform for tuning the interlayer coupling when forming van der Waals structures. In this mini review, the recent key research progresses of 2D Janus TMDs, including the fundamental properties and potential applications, are briefly summarized, and the existing challenges are also presented. [ABSTRACT FROM AUTHOR]

Purpose: Magnetic particle imaging (MPI) is emerging as a highly promising imaging modality. Magnetic nanoparticles (MNPs) are used as imaging tracers in MPI, and their relaxation behavior provides the foundation for its functional imaging capability. Since MNPs are also utilized in magnetic fluid hyperthermia (MFH) and MPI enables localized MFH, temperature mapping arises as an important application area of MPI. To achieve accurate temperature estimations, however, one must also take into account the confounding effects of viscosity on the MPI signal. In this work, we analyze the effects of temperature and viscosity on MNP relaxation and determine temperature and viscosity sensitivities of relaxation time constant estimations via TAURUS (TAU estimation via Recovery of Underlying mirror Symmetry) at a wide range of operating points to empower simultaneous mapping of these two parameters. Methods: A total of 15 samples were prepared to reach four target viscosity levels (0.9–3.6 mPa·$\cdot$s) at five different temperatures (25–45∘$^\circ$C). Experiments were performed on a magnetic particle spectrometer (MPS) setup at 60 different operating points at drive field amplitudes ranging between 5 and 25 mT and frequencies ranging between 1 and 7 kHz. To enable these extensive experiments, an in‐house arbitrary‐waveform MPS setup with temperature‐controlled heating capability was developed. The operating points were divided into four groups with comparable signal levels to maximize signal gain during rapid signal acquisition. The relaxation time constants were estimated via TAURUS, by restoring the underlying mirror symmetry property of the positive and negative half cycles of the time‐domain MNP response. The relative time constants with respect to the drive field period, τ̂$\hat{\tau }$, were computed to enable quantitative comparison across different operating points. At each operating point, a linear fit was performed to τ̂$\hat{\tau }$ as a function of each functional parameter (i.e., temperature or viscosity). The slopes of these linear fits were utilized to compute the temperature and viscosity sensitivities of TAURUS. Results: Except for outlier behaviors at 1 kHz, the following global trends were observed: τ̂$\hat{\tau }$ decreases with drive field amplitude, increases with drive field frequency, decreases with temperature, and increases with viscosity. The temperature sensitivity varies slowly across the operating points and reaches a maximum value of 1.18%/∘$^\circ$C. In contrast, viscosity sensitivity is high at low frequencies around 1 kHz with a maximum value of 13.4%/(mPa·$\cdot$s) but rapidly falls after 3 kHz. These results suggest that the simultaneous estimation of temperature and viscosity can be achieved by performing measurements at two different drive field settings that provide complementary temperature/viscosity sensitivities. Alternatively, temperature estimation alone can be achieved with a single measurement at drive field frequencies above 3 kHz, where viscosity sensitivity is minimized. Conclusions: This work demonstrates highly promising temperature and viscosity sensitivities for TAURUS, highlighting its potential for simultaneous estimation of these two environmental parameters via MNP relaxation. The findings of this work reveal the potential of a hybrid MPI–MFH system for real‐time monitored and localized thermal ablation treatment of cancer. [ABSTRACT FROM AUTHOR]

We introduce tropical corals, balanced trees in a half‐space, and show that they correspond to holomorphic polygons capturing the product rule in Lagrangian Floer theory for the elliptic curve. We then prove a correspondence theorem equating counts of tropical corals to punctured log Gromov–Witten invariants of the Tate curve. This implies that the homogeneous coordinate ring of the mirror to the Tate curve is isomorphic to the degree‐zero part of symplectic cohomology, confirming a prediction of homological mirror symmetry. [ABSTRACT FROM AUTHOR]

Terahertz detection has been highly sought to open a range of cutting‐edge applications in biomedical, high‐speed communications, astronomy, security screening, and military surveillance. Nonetheless, these ideal prospects are hindered by the difficulties in photodetection featuring self‐powered operation at room temperature. Here, this challenge is addressed for the first time by synthesizing the high‐quality ZrGeSe with extraordinary quantum properties of Dirac nodal‐line semimetal. Benefiting from its high mobility and gapless nature, a metal‐ZrGeSe‐metal photodetector with broken mirror symmetry allows for a high‐efficiency photoelectric conversion assisted by the photo‐thermoelectric effect. The designed architecture features ultrahigh sensitivity, excellent ambient stability, and an efficient rectified signal even above 0.26 THz. Maximum responsivity larger than 0.11 A W−1, response time of 8.3 µs, noise equivalent power (NEP) less than 0.15 nW Hz−1/2, and demonstrative imaging application are all achieved. The superb performances with a lower dark current and NEP less than 15 pW Hz−1/2 are validated through integrating the van der Waals heterostructure. These results open up an appealing perspective to explore the nontrivial topology of Dirac nodal‐line semimetal by devising the peculiar device geometry that allows for a novel roadmap to address targeted terahertz application requirements. [ABSTRACT FROM AUTHOR]

In the Gross–Siebert mirror symmetry program, certain enumerations of tropical disks are encoded in combinatorial objects called scattering diagrams and broken lines. These, in turn, are used to construct a mirror scheme equipped with a canonical basis of regular functions called theta functions. This paper serves to develop the relationships between tropical disks, scattering diagrams, and broken lines in the quantum setting; for example, we express quantum theta functions in terms of refined enumerations of tropical disks.We apply these tropical descriptions to prove a refined version of the Carl–Pumperla–Siebert (Preprint) result on consistency of theta functions, and also to prove the quantum Frobenius Conjecture of Fock and Goncharov (Ann. Sci. Éc. Norm. Supér. (4) 42 (2009) 865–930). [ABSTRACT FROM AUTHOR]

Generally, the surrounding rock at the entrance of a mountain tunnel is loose, and the entrance has more slopes due to topography, which causes the tunnel entrance section to be easily destroyed under an earthquake. Based on the established slope model with a single free surface, this paper adopted the elastic wave theory to derive the analytical solution of the strain at the entrance of the mountain tunnel when the SH wave is incident perpendicularly to the bottom of the tunnel; besides, the factors affecting strain were also analyzed. The tangential strain curve at each point of the entrance section takes the centre of the elliptical tunnel as the centre of symmetry, forming symmetry between the left and right sides and mirror symmetry between the top and bottom sides. Then, large-scale shaking table model experiments were conducted to model the actual working conditions, and the correctness of the analytical solution was verified. The research can provide a theoretical reference for the seismic design of the entrance section of the high-speed railway tunnel and greatly improve the understanding of its seismic response. [ABSTRACT FROM AUTHOR]

Bound states in the continuum (BIC) have recently attracted great attention in photonics. Metasurfaces with broken inversion symmetry exhibit high‐Q resonances via quasi‐BIC, enabling low threshold lasing, sensing, and efficient nonlinear generation. Recently, chiral BICs have been investigated by using double layer structure or out‐of‐plane perturbation, requiring complicated fabrication processes. This work presents chiral quasi‐BIC by simultaneously breaking the in‐plane inversion and mirror symmetries in dielectric metasurfaces. For such a simultaneous symmetry breaking, the metasurfaces exhibit quasi‐BIC with strong chirality, resulting in near‐unity circular dichroism with high quality factor of several orders‐of‐magnitude. As the chiral quasi‐BIC appears only by in‐plane structural perturbation, it is much more feasible for practical fabrications compared with preceding results. Due to the symmetry‐protected nature of its original BIC, the proposed approach does not require fine tuning of structural parameters for observing the desired effects unlike the accidental BIC. The results presented in this work pave the way for chiral sensing with high spectral resolution, nonlinear chiroptics with high efficiency, low‐threshold circular polarized lasing, and security applications. [ABSTRACT FROM AUTHOR]

Ideal topological semimetals, which are composed of nontoxic lightweight elements and host clean Dirac/Weyl fermions near Fermi energy without contamination from other quasiparticles, are highly desirable for experimental detection and practical application. Herein, using first‐principles calculations, it is demonstrated that a new stable boron allotrope, termed "ort‐B32," harbors the needed clean Weyl fermions in a sizable energy window under modest tensile strain. Due to the protection of mirror symmetry, the band crossings form two pairs of parallel arc‐like nodal lines, running across the whole Brillouin zone in the kz=0 plane. The topological features of these nodal lines are characterized by the drumhead‐like surface state and nonzero topological invariant. Remarkably, the examination of slope index reveals that the type‐I, type‐II, and type‐III Weyl states can be found in different moment directions with the value of Fermi velocities ranging from 0 to 1.15 × 106 m s−1. These results not only establish a striking new boron allotrope, but also highlight a promising mechanically induced method for obtaining ideal Weyl semimetal. [ABSTRACT FROM AUTHOR]

Mirror symmetry breaking in systems composed of achiral molecules is of importance for the design of functional materials for technological applications as well as for the understanding of the mechanisms of spontaneous emergence of chirality. Herein, we report the design and molecular self‐assembly of two series of rod‐like achiral polycatenar molecules derived from a π‐conjugated 5,5'‐diphenyl‐2,2'‐bithiophene core with a fork‐like triple alkoxylated end and a variable single alkylthio chain at the other end. In both series of liquid crystalline materials, differing in the chain length at the trialkoxylated end, helical self‐assembly of the π‐conjugated rods in networks occurs, leading to wide temperature ranges (>200 K) of bicontinuous cubic network phases, in some cases being stable even around ambient temperatures. The achiral bicontinuous cubic Ia3‾d phase (gyroid) is replaced upon alkylthio chain elongation by a spontaneous mirror symmetry broken bicontinuous cubic phase (I23) and a chiral isotropic liquid phase (Iso1[*]). Further chain elongation results in removing the I23 phase and the re‐appearance of the Ia3‾d phase with different pitch lengths. In the second series an additional tetragonal phase separates the two cubic phase types. [ABSTRACT FROM AUTHOR]

Metasurfaces without a mirror symmetry may exhibit chiral electromagnetic response that differs substantially from any type of polarization transformation. A typical design of chiral metasurfaces is based on a complex arrangement of meta‐atoms with chiral shapes assembled into rotationally symmetric arrays. Here it is demonstrated that, in a sharp contrast to our intuition, metasurfaces that break all point symmetries can outperform their rotationally symmetric counterparts and exhibit near‐lossless maximum chirality. The authors employ the special type of high‐quality‐factor resonances—bound states in the continuum (BICs)—that are manifested in physical systems as quasi‐BICs, and allow engineering the coupling of light with resonant metasurfaces to achieve maximum chirality. A dielectric metasurface composed of pairs of rectangular bars is designed that fully transmits one circular polarization of light and resonantly reflects the other circular polarization without any polarization conversion. Proof‐of‐concept experimental results that confirm directly the prediction of maximum chiral response of the BIC‐empowered asymmetric resonant dielectric metasurfaces are presented. [ABSTRACT FROM AUTHOR]

Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180° rotation. Thus, crystallographic models of twinning require the determination of the short unit cells attached to the planes, or hyperplanes for dimensions higher than 3. Here, a method is presented to find them. Equivalently, it gives the solutions of the N‐dimensional Bézout's identity associated with the Miller indices of the hyperplane. [ABSTRACT FROM AUTHOR]

First examples of multichain (polycatenar) compounds, based on the π‐conjugated [1]benzothieno[3,2‐b]benzothiophene unit are designed, synthesized, and their soft self‐assembly and charge carrier mobility are investigated. These compounds, terminated by the new fan‐shaped 2‐brominated 3,4,5‐trialkoxybenzoate moiety, form bicontinuous cubic liquid crystalline (LC) phases with helical network structure over extremely wide temperature ranges (>200 K), including ambient temperature. Compounds with short chains show an achiral cubic phase with the double network, which upon increasing the chain length, is at first replaced by a tetragonal 3D phase and then by a mirror symmetry is broken triple network cubic phase. In the networks, the capability of bypassing defects provides enhanced charge carrier mobility compared to imperfectly aligned columnar phases, and the charge transportation is non‐dispersive, as only rarely observed for LC materials. At the transition to a semicrystalline helical network phase, the conductivity is further enhanced by almost one order of magnitude. In addition, a mirror symmetry broken isotropic liquid phase is formed beside the 3D phases, which upon chain elongation is removed and replaced by a hexagonal columnar LC phase. [ABSTRACT FROM AUTHOR]

For spintronics, it is highly desirable to obtain stable low‐dimensional materials with ferromagnetic ground state, 100% spin polarization, and high Curie temperature. Moreover, type‐II Weyl fermions are also desired for realizing high‐speed anisotropic transport. Herein, based on first‐principles calculations, the orthorhombic MnNBr monolayer is identified as a needed ferromagnetic half‐metal, which not only has a high Curie temperature (910 K), but also holds type‐II Weyl state with Lorentz symmetry broken. Analysis of the stability reveals that the MnNBr monolayer is energetically, mechanically, dynamically, and thermally stable. Remarkably, in the vicinity of the Fermi level there exist both type‐I and titled type‐II Weyl states, whose nodes form continuously distributed Weyl loops. Under intrinsic out‐of‐plane magnetization, they are robust against spin–orbital coupling due to the protection of glide mirror symmetry. Moreover, near the type‐II Weyl point, there is direction‐dependent band dispersion: the largest fermion velocities can be found in the k path of G–X (up to 6.86 × 105 m s−1), while quasi‐flat bands with negligible band dispersion can be found along the direction being parallel to G–Y. This indicates that MnNBr monolayer should be a promising candidate for further applications of high‐speed anisotropic transport and studies of strongly correlated electronic states. [ABSTRACT FROM AUTHOR]

Dirac cones in 2D carbon allotropes are generally protected by symmorphic symmetry operations. Herein, it is proposed that TPH‐graphene has Dirac cones protected by nonsymmorphic mirror symmetries. This monolayer is composed of tetragonal, pentagonal, and heptagonal carbon rings and exhibits not only good mechanical and dynamic stability but also high energetic stability. The structure has anisotropic mechanical properties, and its Young's modulus is close to that of graphene, up to 291 N m−1. The Dirac points on high‐symmetry lines Γ−X and X−S are protected by the nonsymmorphic mirror operations {m010|0,1/2,0} and {m100|0,1/2,0}, respectively. The edge states obtained from semi‐infinite structures confirm the nontrivial topological nature of these cones. The work reveals that TPH‐graphene is an excellent candidate to study nonsymmorphic‐symmetry‐protected Dirac cones in 2D carbon materials. [ABSTRACT FROM AUTHOR]