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There are many reports in the literature of bound states in the continuum (BICs) in systems with up–down mirror symmetry. Semiconductor-based technology requires bulk semiconductor substrates, which impose symmetry breaking in the vertical direction. In this paper, we explore the possibility of realizing BICs in a high refractive index subwavelength one-dimensional grating placed on a substrate with a refractive index that varies from 1 to almost the refractive index of the grating, while the refractive index above the grating is 1. We demonstrate that in gratings with broken up–down mirror symmetry not only symmetry-protected BICs can arise, but also Friedrich–Wintgen (FW) and interference-based (IB) BICs with diverging quality factors. The limit of the refractive index difference between the grating and the substrate supporting the BIC was found to be as little as 0.03. We also present a study of configurations composed of a finite number of grating stripes, with refractive indices corresponding to GaAs in the grating and Al-rich AlGaAs in the substrate. We demonstrate that such an all-semiconductor configuration enables Q-factors above 104 when composed of fewer than 20 periods and nearly exponential Q-factor growth with increasing numbers of grating periods. The results of this study pave the way for a new class of micro- and nano-optical cavities realised in standard all-semiconductor technology and relying on the high quality factor induced by BIC. [ABSTRACT FROM AUTHOR]

The quest for nonmagnetic Weyl semimetals with high tunability of phase has remained a demanding challenge. As the symmetry-breaking control parameter, the ferroelectric order can be steered to turn on/off the Weyl semimetals phase, adjust the band structures around the Fermi level, and enlarge/shrink the momentum separation of Weyl nodes which generate the Berry curvature as the emergent magnetic field. Here, we report the realization of a ferroelectric nonmagnetic Weyl semimetal based on indium-doped Pb1−xSnxTe alloy in which the underlying inversion symmetry as well as mirror symmetry are broken with the strength of ferroelectricity adjustable via tuning the indium doping level and Sn/Pb ratio. The transverse thermoelectric effect (i.e., Nernst effect), both for out-of-plane and in-plane magnetic field geometry, is exploited as a Berry curvature–sensitive experimental probe to manifest the generation of Berry curvature via the redistribution of Weyl nodes under magnetic fields. The results demonstrate a clean, nonmagnetic Weyl semimetal coupled with highly tunable ferroelectric order, providing an ideal platform for manipulating the Weyl fermions in nonmagnetic systems. [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]

Dimer models provide a method of constructing noncommutative crepant resolutions of affine toric Gorenstein threefolds. In homological mirror symmetry, they can also be used to describe noncommutative Landau–Ginzburg models dual to punctured Riemann surfaces. For a consistent dimer embedded in a torus, we explicitly compute the Hochschild cohomology of its Jacobi algebra in terms of dimer combinatorics. This includes a full characterization of the Batalin–Vilkovisky structure induced by the Calabi–Yau structure of the Jacobi algebra. We then compute the compactly supported Hochschild cohomology of the category of matrix factorizations for the Jacobi algebra with its canonical potential. [ABSTRACT FROM AUTHOR]

Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions. [ABSTRACT FROM AUTHOR]

We study Landau–Ginzburg orbifolds with and , where and is either the maximal group of scalar symmetries of or the intersection of the maximal diagonal symmetries of with . We construct a mirror map between the corresponding phase spaces and prove that it is an isomorphism restricted to a certain subspace of the phase space when is a prime number. When satisfies the parity condition of Ebeling–Gusein-Zade, this subspace coincides with the full space. We also show that two phase spaces are isomorphic for . [ABSTRACT FROM AUTHOR]

A system of optimal biaxial molecules placed at the sites of a cubic lattice is studied in an extended Lebwohl-Lasher model. Molecules interact only with their nearest neighbors through the pair potential that depends on the molecule orientations. It is known that in a homogeneous system there is a direct second-order transition from the isotropic to the biaxial nematic phase, however the properties of confined systems are less known. In the present paper, the lattice has periodic boundary conditions in the X and Y directions and has two walls with planar anchoring, perpendicular to the Z direction. We have investigated the model using Monte Carlo simulations on Nx X Ny X Nz lattices, for Nx = Ny = 10; 16, Nz from 3 to 19, with and without mirror symmetry. This study is complementary to the statistical description of hard spheroplatelets near a hard wall (Phys. Rev. E 89, 062503 (2014)). The temperature dependence of the order-parameter profiles between walls is calculated for many cases of wall separations. For large wall separations, there are surface layers with biaxial ordering on both walls (≈ 4-5 lattice constants wide) and, beyond the surface layers, the order parameters have values as in a homogeneous system. For small wall separations, the isotropic-biaxial transition is shifted and the surface layers are thinner. Above the isotropic-biaxial transition the preferable orientations in both surface layers can be different. It is interesting that planar anchoring for biaxial molecules leads to uniaxial interactions on the wall. As a result, we get the planar Lebwohl-Lasher model with additional (biaxial) interactions with neighbors from the second layer, where the Kosterlitz-Thouless transition is present on the wall. [ABSTRACT FROM AUTHOR]

Symmetry perception in dot patterns is tolerant to temporal delays of up to 60 ms within and between element pairs. However, it is not known how factors effecting symmetry discrimination in static patterns might affect temporal integration in dynamic patterns. One such feature is luminance polarity. Using dynamic stimuli with increasing temporal delay (SOA) between the onset of the first and second element in a symmetric pair, we investigated how four different luminance-polarity conditions affected the temporal integration of symmetric patterns. All four luminance polarity conditions showed similar upper temporal limits of approximately 60 ms. However psychophysical performance over all delay durations showed significantly higher symmetry thresholds for unmatched-polarity patterns at short delays, but also significantly less sensitivity to increasing temporal delay relative to matched-polarity patterns. These varying temporal windows are consistent with the involvement of a fast, sensitive first-order mechanism for matched-polarity patterns, and a slower, more robust second-order mechanism for unmatched-polarity patterns. Temporal integration windows for unmatched-polarity patterns were not consistent with performance expected from attentional mechanisms alone, and instead supports the involvement of second-order mechanisms that combines information from ON and OFF channels. [ABSTRACT FROM AUTHOR]

We introduce a class of Laurent polynomials, called maximally mutable Laurent polynomials (MMLPs), which we believe correspond under mirror symmetry to Fano varieties. A subclass of these, called rigid, are expected to correspond to Fano varieties with terminal locally toric singularities. We prove that there are exactly 10 mutation classes of rigid MMLPs in two variables; under mirror symmetry these correspond one-to-one with the 10 deformation classes of smooth del Pezzo surfaces. Furthermore, we give a computer-assisted classification of rigid MMLPs in three variables with reflexive Newton polytope; under mirror symmetry these correspond one-to-one with the 98 deformation classes of three-dimensional Fano manifolds with very ample anti-canonical bundle. We compare our proposal to previous approaches to constructing mirrors to Fano varieties, and explain why mirror symmetry in higher dimensions necessarily involves varieties with terminal singularities. Every known mirror to a Fano manifold, of any dimension, is a rigid MMLP. [ABSTRACT FROM AUTHOR]

We demonstrate in microwave measurements the broadband enhancement of transmission through an opaque barrier due to mirror symmetry. This enhancement relies on constructive interference between mirror scattering paths resulting from strong internal reflections at the left and right interfaces of a multichannel cavity. We observe a strong sensitivity of the conductance to a shift of the barrier from the center of the cavity. Remarkably, the impact of mirror symmetry can be further increased by tuning the degree of disorder within the cavity. We report an additional enhancement of the conductance found by symmetrically placing randomly located scatterers. Our results illuminate the impact of symmetry and disorder correlation on transmission through complex systems. [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]

Two pairs of pure enantiomers of high-nuclearity chiral lanthanide–oxo clusters with the formulas [Y14(L)16(μ3-OH)16(H2O)20]·(ClO4)10·xH2O (x ≈ 55; L = L -L− for L -Y14; L = D -L− for D -Y14) and [Dy14(L)16(μ3-OH)16(H2O)20]·(ClO4)10·xH2O (x ≈ 67; L = L -L− for L -Dy14; L = D -L− for D -Dy14) were prepared in the presence of chiral ligands N-acetyl- L -alanine (L -HL) and N-acetyl- D -alanine (D -HL). Structural analysis showed that four cubane-like units as building blocks sharing vertices formed the lanthanide–oxo cluster unit {(ClO4)2@[Y12(μ3-OH)16]}18+ with two ClO4− as anion templates. The remaining Y3+ ions were connected to the opposite position of {(ClO4)2@[Y12(μ3-OH)16]}18+ through four L -L−, respectively. High-resolution electrospray ionization mass spectrometry (HRESI-MS) captured the signals of the cluster fragment {Y12(OH)16−x(O)x} (x = 4, 5, 6, 7, 8) and the unbroken dimer of {Y12(L -L)12(OH)16−x(O)x}2 (x = 4, 5, 12) from L -Y14 in a mixed solution of methanol and dichloromethane, suggesting that {Ln12(OH)16−x(O)x} is a stable cluster unit that could be further assembled into higher-nuclearity lanthanide–oxo clusters in solution. The solid-state circular dichroism (CD) spectra of compounds L -Y14/ D -Y14 and L -Dy14/ D -Dy14 displayed mirror symmetry effects in the range of 220–250 nm. The study of magnetic properties showed that L -Dy14 had a weak antiferromagnetic interaction and displayed SMM-like behavior in the absence of a dc field. [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]

This report summarises progress made in estimating the local density of dark matter (ρ DM,⊙), a quantity that is especially important for dark matter direct detection experiments. We outline and compare the most common methods to estimate ρ DM,⊙ and the results from recent studies, including those that have benefited from the observations of the ESA/Gaia satellite. The result of most local analyses coincide within a range of ρ D M , ⊙ ≃ 0. 4 â€" 0. 6 G e V c m âˆ' 3 = 0. 011 â€" 0. 016 M ⊙ / p c 3 , while a slightly lower range of ρ D M , ⊙ ≃ 0. 3 â€" 0. 5 G e V c m âˆ' 3 = 0. 008 â€" 0. 013 M ⊙ / p c 3 is preferred by most global studies. In light of recent discoveries, we discuss the importance of going beyond the approximations of what we define as the ideal Galaxy (a steady-state Galaxy with axisymmetric shape and a mirror symmetry across the mid-plane) in order to improve the precision of ρ DM,⊙ measurements. In particular, we review the growing evidence for local disequilibrium and broken symmetries in the present configuration of the Milky Way, as well as uncertainties associated with the galactic distribution of baryons. Finally, we comment on new ideas that have been proposed to further constrain the value of ρ DM,⊙, most of which would benefit from Gaia’s final data release. [ABSTRACT FROM AUTHOR]

Purpose: To investigate the age-related tilt and decentration of crystalline lenses using a swept-source optical coherence tomography biometer (SS-OCT) (CASIA2, Tomey Corp.). Setting: Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China. Design: Cross-sectional study. Methods: The direction and magnitude of the crystalline lens were evaluated in 230 participants with ages ranging from 7 to 90 years using SS-OCT. The participants were divided into 4 age groups, and the differences among the groups were analyzed. Multiple linear regression was used to investigate the main factors influencing crystalline lens tilt and decentration. Results: The natural crystalline lens tilted toward the inferotemporal direction with a mean magnitude of 4.3 +/- 1.5 degrees (range 0.7 to 8.95 degrees). The mean decentration toward the superotemporal direction was 0.17 +/- 0.12 mm (range 0.03 to 1.15 mm). There was mirror symmetry between the right and left eyes. There were statistically significant differences in the crystalline lens tilt and decentration among the age groups. Multiple linear regression showed that changes in crystalline lens tilt depended on angle [alpha] (P <.01) and anterior chamber depth (ACD; P =.008), whereas crystalline lens decentration depended on angle [kappa] (P =.003), age (P <.01), and angle [alpha] (P =.002). Conclusions: Although there was a statistically significant difference in crystalline lens tilt and decentration among age groups, the variation in the crystalline lens position was partially affected by age. The crystalline lens tilt was greater in eyes with wider angle [alpha] and shallower ACD, whereas crystalline lens decentration was greater in younger eyes with wider angles [kappa] and [alpha]. [ABSTRACT FROM AUTHOR]

In this paper, we present a detailed study on the phase diagrams of superconducting topological surface states, especially, focusing on the interplay between crystalline symmetry and topology of the effective BdG Hamiltonian. We show that for the 4 x 4 kinematic Hamiltonian of the normal state, a mirror symmetry M can be defined, and for the M-odd pairings, the classification of the 8 x 8 BdG Hamiltonian is ℤ ⊕ ℤ, and the timereversal symmetry is broken intrinsically. The topological non-trivial phase can support chiral Majorana edge modes, and can be realized in the thin films of iron-based superconductor such as FeSeTe. [ABSTRACT FROM AUTHOR]

Aksentijevic–Gibson complexity is an original complexity measure based on the amount of change in a string or 2D array that has been successfully implemented on data from psychology to physics. The key ingredient to computing the measure is a change symmetry (CS)—a novel form of structure (also known as generalised palindrome) which represents a central or mirror symmetry based on the redundant arrangement not of symbols but of changes. This results in patterns that although globally symmetrical do not appear as such when inspected locally. We used this property to (a) affect the registration of a target, (b) prime the symmetry judgment of 2D arrays and (c) faces using 1D patterns possessing change symmetry. In Experiment 2, we applied the lock and key principle to complete the prime without showing its structure at once. In Experiments 3 and 4, we presented subjects with fast sequences of CSs such that the configuration of an individual pattern was masked by the subsequent pattern leaving only the structural "essence" of the prime symmetry. The results strongly support the contention that higher-level hidden structure of change symmetry successfully primes the symmetry perception of 2D arrays as well as facial attractiveness. [ABSTRACT FROM AUTHOR]

Let X be a closed symplectic manifold equipped with a Lagrangian torus fibration over a base Q. A construction first considered by Kontsevich and Soibelman produces from this data a rigid analytic space Y, which can be considered as a variant of the T-dual introduced by Strominger, Yau, and Zaslow. We prove that the Fukaya category of tautologically unobstructed graded Lagrangians in X embeds fully faithfully in the derived category of (twisted) coherent sheaves on Y, under the technical assumption that π2(Q) vanishes (all known examples satisfy this assumption). The main new tool is the construction and computation of Floer cohomology groups of Lagrangian fibres equipped with topological infinite rank local systems that correspond, under mirror symmetry, to the affinoid rings introduced by Tate, equipped with their natural topologies as Banach algebras. [ABSTRACT FROM AUTHOR]

The moduli spaces of flat SL 2 - and PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of "Global topology of the Hitchin system". [ABSTRACT FROM AUTHOR]

Bacterial suspensions show turbulence-like spatiotemporal dynamics and vortices moving irregularly inside the suspensions. Understanding these ordered vortices is an ongoing challenge in active matter physics, and their application to the control of autonomous material transport will provide significant development in microfluidics. Despite the extensive studies, one of the key aspects of bacterial propulsion has remained elusive: The motion of bacteria is chiral, i.e., it breaks mirror symmetry. Therefore, the mechanism of control of macroscopic active turbulence by microscopic chirality is still poorly understood. Here, we report the selective stabilization of chiral rotational direction of bacterial vortices in achiral circular microwells sealed by an oil/water interface. The intrinsic chirality of bacterial swimming near the top and bottom interfaces generates chiral collective motions of bacteria at the lateral boundary of the microwell that are opposite in directions. These edge currents grow stronger as bacterial density increases, and, within different top and bottom interfaces, their competition leads to a global rotation of the bacterial suspension in a favored direction, breaking the mirror symmetry of the system. We further demonstrate that chiral edge current favors corotational configurations of interacting vortices, enhancing their ordering. The intrinsic chirality of bacteria is a key feature of the pairing order transition from active turbulence, and the geometric rule of pairing order transition may shed light on the strategy for designing chiral active matter. [ABSTRACT FROM AUTHOR]

We propose a simple implementation to obtain super-broadband geometric phase devices (GPD) by means of circular polarization converter (CPC) with mirror symmetry. We demonstrate that the best choice of wideband GPDs and CPCs is a mirror symmetric structure. Based on a two-rotation model on the Poincaré sphere, optimization parameters and time are significantly reduced. The CPC can be extended to super-broadband GPD, such as polarization gratings (PGs), by using geometric phase holography. We simulate diffraction efficiencies of the super-broadband PGs. In the normal incident case, the diffraction efficiency is over 99% in 420–945 nm, and in the oblique incident case, the first-order diffraction efficiency is over 90% in the range of ±30°. The super-broadband GPDs show potential advantages in wide color display and spectral imaging. [ABSTRACT FROM AUTHOR]

Families of exact coherent states in elliptical pipe flow obtained from the travelling-wave solutions in circular pipe flow by a continuation approach are found. Results are given in a regime of the aspect ratio $A$ in which the laminar flow is linearly stable. The results suggest the possibility of two distinct classes of solutions of elliptical travelling waves at higher values of $A$ : (i) rotationally symmetric centre-mode states that collapse towards the pipe centre and (ii) rotationally asymmetric vortex–wave interaction states with additional mirror symmetry exhibiting organization of the waves around a critical layer. These are the first calculations of three-dimensional travelling waves in elliptical pipes. Investigation of these states has the potential to provide fresh insight into the relationship between exact coherent structures in Poiseuille flow in pipes and channels. [ABSTRACT FROM AUTHOR]

Nanostructured metals are usually strong because the ultrahigh density of internal boundaries restricts the mean free path of dislocations. Usually, they are also more brittle because of their diminished work-hardening ability. Nanotwinned materials, with coherent interfaces of mirror symmetry, can overcome this inherent trade-off. We show a bulk nanostructuring method that produces a multiscale, hierarchical twin architecture in a hexagonal closed-packed, solute-free, and coarse-grained titanium (Ti), with a substantial enhancement of tensile strength and ductility. Pure Ti achieved an ultimate tensile strength of almost 2 gigapascals and a true failure strain close to 100% at 77 kelvin. The multiscale twin structures are thermally stable up to 873 kelvin, which is above the critical temperature for many applications in extreme environments. Our results demonstrate a practical route to achieve attractive mechanical properties in Ti without involving exotic and often expensive alloying elements. [ABSTRACT FROM AUTHOR]

[Display omitted] The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at three different orders in a 3D phononic crystal with nontrivial bulk topology originated from the synergy of mirror symmetry of the unit cell and a non-symmorphic glide symmetry of the lattice. The multitude of topological states brings diverse possibilities of wave manipulations. Through judicious engineering of the boundary modes, we experimentally demonstrate two functionalities at different dimensions: 2D negative refraction of sound wave enabled by a first-order topological surface state with negative dispersion, and a 3D acoustic interferometer leveraging on second-order topological hinge states. Our work showcases that topological modes at different orders promise diverse wave steering applications across different dimensions. [ABSTRACT FROM AUTHOR]

We show how to use Gromov-Witten invariants to determine the matter content of F-theory compactifications on elliptically fibered Calabi-Yau manifolds X over Hirzebruch surfaces. To determine the representations of these matter multiplets under the gauge algebra g , we use toric methods to embed the weight lattice of g into the integer homology lattice of X. We then apply mirror symmetry to determine whether classes in this lattice which correspond to weights of given representations are represented by irreducible curves. Applying mirror symmetry efficiently to such geometries requires obtaining good approximations to their Mori cones. We propose an algorithm for obtaining such approximations. When the algorithm yields a smooth cone, we find that the latter in fact coincides with the Mori cone of X and already contains information on the matter content of compactifications on X. Our algorithm relies on studying toric ambient spaces for the Calabi-Yau hypersurface X which are merely birationally equivalent to fibrations over Hirzebruch surfaces. We study the flops relating such varieties in detail. [ABSTRACT FROM AUTHOR]

We continue our study on the hypergeometric system $E(3,6)$ that describes period integrals of the double cover family of K3 surfaces. Near certain special boundary points in the moduli space of the K3 surfaces, we construct the local solutions and determine the so-called mirror maps expressing them in terms of genus 2 theta functions. These mirror maps are the K3 analogues of the elliptic $\lambda $ -function. We find that there are two nonisomorphic definitions of the lambda functions corresponding to a flip in the moduli space. We also discuss mirror symmetry for the double cover K3 surfaces and their higher dimensional generalizations. A follow-up paper will describe more details of the latter. [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]

Using hybrid density functional calculation, we study the atomic and electronic structures of p-type dopants, B, Al and Ga, in 4H-SiC. For B, depending on the growth condition, it can occupy both Si and C sites. In contrast, Al and Ga on the C sites exhibit too high formation energy to exist in a significant amount. In 4H-SiC, there exist two types of Si sites in wurtzite-like and zincblende-like local coordination, respectively. Our calculations suggest that the dopant atoms have negligible preference occupying the two sites. In neutral charge state, all the dopants exhibit significant distortions from the structure in the negatively charged state. For most cases, our calculations yield three distorted structures, in which the most stable one has the dopant atom displaced along its bond with one of the surrounding equatorial Si or C atoms, lowering the C3v symmetry to Cs symmetry (i.e., a mirror symmetry only). Among the three dopant elements, Al on Si sites exhibits overall the lowest formation energy and the shallowest acceptor level. Nevertheless, it is not a hydrogenic dopant with the acceptor level 0.12 eV above the valence band maximum based on calculation using a 400-atom supercell. Its corresponding defect state exhibits apparent localization along the [0001] direction, but it is relatively delocalized in the (0001) plane. [ABSTRACT FROM AUTHOR]

Biological homochirality is modelled using chemical reaction mechanisms that include autocatalytic and inhibition reactions as well as input and output flows. From the mathematical point of view, the differential equations associated with those mechanisms have to exhibit bistability. The search for those bifurcations can be carried out using stoichiometric network analysis. This algorithm simplifies the mathematical analysis and can be implemented in a computer programme, which can help us to analyse chemical networks. However, regardless of the reduction to linear polynomials, which is made possible by this algorithm, in some cases, the complexity and length of the polynomials involved make the analysis unfeasible. This problem has been partially solved by extending the stoichiometric matrix with rows that code the duality relations between the different reactions occurring in the network given as input. All these facts allow us to analyse 28 different network models, highlighting the basic requirements needed by a chemical mechanism to have spontaneous mirror symmetry breaking. [ABSTRACT FROM AUTHOR]

We prove an equivalence of twoA∞-functors, via Orlov’s Landau–Ginzburg/ Calabi–Yau (LG/CY) correspondence. One is the Polishchuk–Zaslow mirror symmetry functor of elliptic curves, and the other is a localized mirror functor from the Fukaya category of T² to a category of noncommutative matrix factorizations. As a corollary, we prove that the noncommutative mirror functor LMLt gr realizes homological mirror symmetry for any t. [ABSTRACT FROM AUTHOR]

We consider the multiple Calabi–Yau mirror phenomenon which appears in Berglund–Hübsch–Krawitz (BHK) mirror symmetry. We show that for any pair of Calabi–Yau orbifolds that are BHK mirrors of a loop–chain-type pair of Calabi–Yau threefolds in the same weighted projective space the periods of the holomorphic nonvanishing form coincide. [ABSTRACT FROM AUTHOR]

Using heuristics from mirror symmetry, combinations of Gross, Hacking, Keel, Kontsevich, and Siebert have given combinatorial constructions of canonical bases of "theta functions" on the coordinate rings of various log Calabi-Yau spaces, including cluster varieties. We prove that the theta bases for cluster varieties are determined by certain descendant log Gromov-Witten invariants of the symplectic leaves of the mirror/Langlands dual cluster variety, as predicted in the Frobenius structure conjecture of Gross-Hacking-Keel. We further show that these Gromov-Witten counts are often given by naive counts of rational curves satisfying certain geometric conditions. As a key new technical tool, we introduce the notion of "contractible" tropical curves when showing that the relevant log curves are torically transverse. [ABSTRACT FROM AUTHOR]

In this paper, we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Givental formalism. As results, we prove the finite generation property and holomorphic anomaly equation for the associated FJRW theory. Via general LG-LG mirror theorem, our results also hold for the Saito-Givental theory of the Fermat cubic singularity. [ABSTRACT FROM AUTHOR]

Spin current generators are critical components for spintronics-based information processing. In this work, we theoretically and computationally investigate the bulk spin photovoltaic (BSPV) effect for creating DC spin current under light illumination. The only requirement for BSPV is inversion symmetry breaking, thus it applies to a broad range of materials and can be readily integrated with existing semiconductor technologies. The BSPV effect is a cousin of the bulk photovoltaic (BPV) effect, whereby a DC charge current is generated under light. Thanks to the different selection rules on spin and charge currents, a pure spin current can be realized if the system possesses mirror symmetry or inversion-mirror symmetry. The mechanism of BSPV and the role of the electronic relaxation time τ are also elucidated. We apply our theory to several distinct materials, including monolayer transition metal dichalcogenides, anti-ferromagnetic bilayer MnBi2Te4, and the surface of topological crystalline insulator cubic SnTe. Light offers a fast and non-invasive way to generate spin-currents in materials, however, this typically requires special ingredients such as magnetic materials, or circularly polarised light. In this theory work, the authors show how the nonlinear optical effect can generate a spin current, with the only requirement being broken inversion symmetry. [ABSTRACT FROM AUTHOR]

Damping-like torque (DLT) arising from the spin Hall effect (SHE) in heavy metals and their alloys has been widely explored for applications in spin–orbit torque MRAM, auto-oscillations, spin waves, and domain wall motion. In conventional materials, the DLT efficiency is limited by intrinsic properties, while attaining strong spin–orbit coupling and higher spin-charge interconversion, with no compromise to electric properties, is the need of the hour. In this Letter, we report more than 3.5 times increase in DLT efficiency, θDL, of modified Pt-oxide by employing a better approach of low energy 20 keV O+ ion implantation. The highest fluence of O+ implantation (1 × 1017 ions cm−2) in Pt enhanced the DLT efficiency from 0.064 to 0.230 and improved the spin transmission for a smaller trade-off in the longitudinal resistivity ( ρ Pt to ρ Pt − Oxide) from 55.4 to 159.5 μΩ cm, respectively. The transverse spin Hall resistivity, ρ SH , is found to be proportional to the square of the longitudinal resistivity, i.e., ρ SH imp ∝ ρ imp 2 , implying that the enhanced SHE in O-implanted Pt is due to a side-jumping mechanism. Further, no break in the twofold as well as mirror symmetry of torques from the O-implanted Pt allows the use of spin-torque ferromagnetic resonance-based line shape analysis to quantify such torques. [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]

Achiral multi-chain (polycatenar) compounds based on the 2,7-diphenyl substituted [1]benzothieno[3,2-b]benzothiophene (BTBT) unit and a 2,6-dibromo-3,4,5-trialkoxybenzoate end group lead to materials forming bicontinuous cubic liquid crystalline phases with helical network structures over wide temperature ranges. [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]

Mirror symmetry, a three dimensional N = 4 IR duality, has been studied in detail for quiver gauge theories of the ADE-type (as well as their affine versions) with unitary gauge groups. The A-type quivers (also known as linear quivers) and the associated mirror dualities have a particularly simple realization in terms of a Type IIB system of D3-D5-NS5-branes. In this paper, we present a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories, starting from a dual pair of A-type quivers with unitary gauge groups. The construction involves a certain generalization of the S and the T operations, which arise in the context of the SL(2, ℤ) action on a 3d CFT with a U(1) 0-form global symmetry. We implement this construction in terms of two supersymmetric observables — the round sphere partition function and the superconformal index on S2 × S1. We discuss explicit examples of various (non-ADE) infinite families of mirror pairs that can be obtained in this fashion. In addition, we use the above construction to conjecture explicit 3d N = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle. [ABSTRACT FROM AUTHOR]

Based on first-principles calculations and symmetry arguments, we reveal that the non-centrosymmetric ternary tetradymite BiSbTe3 possesses exotic dual topological features of Weyl semimetallic phases with Z2 index (1:000). The results show that the helical Dirac-type surface states protected by the time-reversal symmetry are present in the vicinity of the Brillouin zone center, which is consistent with the experimental report. Furthermore, we show that four pairs of Weyl points reside exactly at the Fermi level, which are guaranteed to be located on high-symmetry planes due to mirror symmetries. The helical surface states and the projected Weyl nodes are well separated in the momentum space, facilitating their observations in experiments. This work not only uncovers a unique quantum phenomenon with dual topological features in the tetradymite family but also paves a fascinating avenue for exploring the coexistence of multi-topological states with wide applications. [ABSTRACT FROM AUTHOR]

Based on first-principles calculations and symmetry arguments, we reveal that the non-centrosymmetric ternary tetradymite BiSbTe3 possesses exotic dual topological features of Weyl semimetallic phases with Z2 index (1:000). The results show that the helical Dirac-type surface states protected by the time-reversal symmetry are present in the vicinity of the Brillouin zone center, which is consistent with the experimental report. Furthermore, we show that four pairs of Weyl points reside exactly at the Fermi level, which are guaranteed to be located on high-symmetry planes due to mirror symmetries. The helical surface states and the projected Weyl nodes are well separated in the momentum space, facilitating their observations in experiments. This work not only uncovers a unique quantum phenomenon with dual topological features in the tetradymite family but also paves a fascinating avenue for exploring the coexistence of multi-topological states with wide applications. [ABSTRACT FROM AUTHOR]

The classification of Fano varieties is an important open question, motivated in part by the MMP. Smooth Fano varieties have been classified up to dimension three: one interesting feature of this classification is that they can all be described as certain subvarieties in GIT quotients; in particular, they are all either toric complete intersections (subvarieties of toric varieties) or quiver flag zero loci (subvarieties of quiver flag varieties). There is a program to use mirror symmetry to classify Fano varieties in higher dimensions. Fano varieties are expected to correspond to certain Laurent polynomials under mirror symmetry; given such a Fano toric complete intersections, one can produce a Laurent polynomial via the Hori–Vafa mirror. In this paper, we give a method to find Laurent polynomial mirrors to Fano quiver flag zero loci in Y -shaped quiver flag varieties. To do this, we generalize the Gelfand–Cetlin degeneration of type A flag varieties to Fano Y -shaped quiver flag varieties, and describe these degenerations as toric quiver moduli spaces. We find conjectural mirrors to 99 four dimensional Fano quiver flag zero loci, and check them up to 20 terms of the period sequence. [ABSTRACT FROM AUTHOR]

The mirror P=W conjecture, formulated by Harder-Katzarkov-Przyjalkowski [27] , predicts a correspondence between weight and perverse filtrations in the context of mirror symmetry. In this paper, we revisit this conjecture through the lens of mirror symmetry for a Fano pair (X , D) , where X is a smooth Fano variety and D is a simple normal crossing divisor. We introduce its mirror object as a multi-potential analogue of a Landau-Ginzburg (LG) model, which we call the hybrid LG model. This model is expected to capture the mirrors of all irreducible components of D. We study the topological aspects, particularly the perverse filtration, and the Hodge theory of hybrid LG models, building upon the work of Katzarkov-Kontsevich-Pantev [32]. As an application, we discover an interesting upper bound on the multiplicativity of the perverse filtration for a hybrid LG model. Additionally, we propose a relative version of the homological mirror symmetry conjecture and explain how the mirror P=W conjecture naturally emerges from it. [ABSTRACT FROM AUTHOR]

We give a local algebraic condition on the coincidence of feature lines of contour curvature and slope (the latter is associated with ridges and valleys in a terrain map) for general two-dimensional scalar fields employing two newly derived feature lines. We also give a sufficient condition on the coincidence of feature lines using the reflection symmetries of the contour curves. We analyze the coincidence and separation of the different feature lines in symmetric and asymmetric terrain objects. Then, we apply the results for planar fluid flows, including simple ideal and viscous flows and a natural lake circulation. In the fluid dynamic examples, the stream function replaces the height field. The symmetry-breaking of the contour curves by boundary deformations and viscous dissipations are highlighted and discussed in each case. • Coincidence conditions on feature lines of two-dimensional scalar fields. • Application on idealized height fields with and without mirror symmetries. • Application on planar flows of ideal and real fluids. • Geometric and viscosus breaking of mirror symmetries and feature line separation. • Feature lines of a natural vortex pattern in a lake-flow. [ABSTRACT FROM AUTHOR]