Fourfold Symmetry Research Articles

Effect of Fiber Orientation on Microstructure and Texture Evolution During the Cold‐Rolling of Al–Mg–Si Alloy

A material with a strong double fibrous texture is subjected to rolling with various deformation paths—unidirectionally and with 90° rotations about the normal direction (cross‐rolling). Additionally, the orientation of the initial fiber is manipulated to force unlikely grain rotations. The purpose of these procedures is to study the dependence between crystallographic and morphological texture changes caused by the rolling. Microstructure observations show that deformation mechanism responsible for the final microstructure depends on the initial fiber orientation. The crystallographic texture is related to the deformation mode and leads toward expected orientations; however, the initial grain boundaries alignment has a strong impact on the final microstructure. Unidirectional rolling results in typical orientations along the β‐fiber in all investigated cases. The texture created during the more complex deformation path with inset rotations follows the geometrical constraints for fourfold symmetry, even if this required unlikely rotations toward the α‐fiber.

Wideband, polarization independent electromagnetic wave absorber using cross arrow resonator and lumped SMD resistors for C and X band applications

In this work, a polarization independent and wideband electromagnetic (EM) waves absorbing frequency selective surface (FSS) structure is presented. The unit cell of the proposed FSS consists of an assembly of cross arrow resonators with four SMD resistors mounted on it, to enhance the absorbance bandwidth. This unit cell also possesses a four-fold symmetry which makes it polarization insensitive. The designed unit cell is compact with the length and width dimensions as 0.19λL × 0.19λL, and thickness of 0.13λL, where λL is the guided wavelength corresponding to the lowest operating frequency. The proposed absorber is theoretically and experimentally tested for its absorbance, cross-polarization level, and radar cross section (RCS) characteristics. The computer-aided simulation and practical measurements indicate that the proposed absorber offers more than 90% (with a fractional bandwidth of 93%) absorbance for normal incidence at 4.5–12.4 GHz frequency band. The cross-polarization reflection coefficient analysis indicates that the proposed FSS configuration behaves as an absorber and not a polarization convertor. The input impedance plot, surface current distribution, and E-field distribution of the unit cell were also analyzed and presented to understand the absorbance mechanism. The RCS of the proposed FSS is compared with the RCS of a reflective (metallic) sheet to analyze its suitability for practical applications (RCS reduction) within the working band. The 3D simulated and 2D calculated RCS results indicate that the proposed FSS is suitable for wideband EM wave absorber applications.

A novel modified circular ring-based broadband polarization-insensitive angular stable circuit analog absorber (CAA) for RCS applications

AbstractIn this study, a compact modified circular ring-based circuit analog absorber (CAA) is proposed. It comprises a resistor-loaded frequency selective surface (FSS) underneath an FR-4 substrate, and the other end is terminated with a perfect electric conductor (PEC) separated by an air-spacer. The proposed design shows a minimum −10 dB reflectance from 10.55 to 36.03 GHz (25.48 GHz bandwidth and 109.4% fractional bandwidth) with two dips at 13.5 GHz and 35.23 GHz having reflectivity −17.18 dB and −24.9 dB, respectively. The existing four-fold circular symmetry architecture shows insensitivity for different polarization angles under normal incidences and up to 45° stability for Transverse Electric (TE) and Transverse Magnetic (TM) modes under oblique incidences. The proposed cell is compact with a periodicity of 0.193λL, and a thickness of 0.09λL, where λL is the free-space wavelength corresponding to the lowest frequency of the absorption band. The novelty of the design lies in the topology of using an underneath FSS to take advantage of effective permittivity control for both broader bandwidth and better angular stability. To demonstrate the ability of the proposed design, a 28 GHz microstrip patch antenna prototype is fabricated, and its radar cross section (RCS) is measured after loading with the absorber. A 15.15 dBsm RCS reduction is observed in comparison with the PEC. The authors strongly believe that the proposed design has potential applications such as RCS reduction and radio-frequency energy harvesting.

Chiral phonons in lattices with C4 symmetry

Chiral phonons were initially proposed and further verified experimentally in two-dimensional (2D) hexagonal crystal lattices. Many intriguing features brought about by chiral phonons are attributed to the pseudoangular momenta which are associated with the threefold rotational symmetry of hexagonal lattices. Here, we go beyond the hexagonal crystals and investigate the chiral phonons in systems with fourfold rotational symmetry. We clarify the symmetry requirements for the emergence of chiral phonons in both 2D square lattices and three-dimensional tetragonal lattices. For two dimensions, the realization of ${C}_{4}$ chiral phonons requires the breaking of time-reversal symmetry; while for three dimensions, they can exist on the ${C}_{4}$-invariant path in a chiral tetragonal lattice. These phonons have the advantage that they can be more readily coupled with optical transitions, which facilitates their experimental detection. We demonstrate our idea via model analysis and first-principles calculations of concrete materials, including the MnAs monolayer and the $\ensuremath{\alpha}$-cristobalite. Our work reveals chiral phonons beyond the hexagonal lattices and paves the way for further exploration of chiral phonon physics in square/tetragonal materials and metamaterials.

Effect of clustering on the orientational properties of a fluid of hard right isosceles triangles

Recent studies have shown the fluid of hard right triangles to possess fourfold and quasi-eightfold (octatic) orientational symmetries. However, the standard density-functional theory for two-dimensional anisotropic fluids, based on two-body correlations, and an extension to incorporate three-body correlations fail to describe these symmetries. To explain the origin of octatic symmetry, we postulate strong particle clustering as a crucial ingredient. We use the scaled particle theory to analyze four binary mixtures of hard right triangles and squares, three of them being extreme models for a one-component fluid, where right triangles can exist as monomeric entities together with triangular dimers, square dimers, or square tetramers. Phase diagrams exhibit a rich phenomenology, with demixing and three-phase coexistences. More important, under some circumstances the orientational distribution function of triangles has equally high peaks at relative particle angles 0, π/2, and π, signaling fourfold, tetratic order, but also secondary peaks located at π/4 and 3π/4, a feature of eightfold, octatic order. Also, we extend the binary mixture model to a quaternary mixture consisting of four types of clusters: monomers, triangular and square dimers, and square tetramers. This mixture is analyzed using the scaled particle theory under the restriction of fixed cluster fractions. Apart from the obvious tetratic phase promoted by tetramers, we found that, for certain cluster compositions, the total orientational distribution function of monomers can exhibit quasi-eightfold (octatic) symmetry. The study gives evidence on the importance of clustering to explain the peculiar orientational properties of liquid-crystal phases in some two-dimensional fluids.

Quasi-omnidirectional retroreflective metagrating for TE-polarized waves based on wave-vector reversions.

Structuring elements of gratings brings more freedom in manipulating diffraction waves, e.g., retroreflection using diffraction orders other than the 0th order. Most retroreflective metagratings (RMs) can achieve retroreflection only under one particular direction, limiting their applications. In this paper, we propose a quasi-omnidirectional RM based on wave-vector reversion for TE-polarized waves. The metagrating element is composed of four rotationally-symmetric sub-elements, which is composed of one probe and two directors on its two sides. The substrate-air-metal layer can reverse kz while directors can reverse kx. Therefore, the wave-vector k of reflected waves can be completely reversed by the sub-element, providing necessary momentum for retroreflection. The -2nd diffraction order of the metagrating is tailored to channel out waves with reversed k, leading to retroreflection. Due to the element's four-fold rotational symmetry, retroreflection can be achieved along four directions, covering all of the four quarters of azimuth angle. We demonstrate prototypes in Ku band, and the average backscattering enhancement compared with a metal plane with the same area (SAMP) along the four directions reaches up to 31.3 dB with incident angle 50.0° at 15.0 GHz. Both simulated and measured results verify our design. This work provides another perspective on retroreflection and may find applications in retroreflective functional devices.

Bias-dependent two-phase anisotropy in magnetoresistance of a GaMnAs-based magnetic tunnel junction

We report unique two-phase anisotropy in the tunnel magnetoresistance (TMR) of a GaMnAs-based magnetic tunnel junction, obtained by investigating the magnetic-field-direction dependence with various applied bias voltages. The TMR shows two-fold symmetry about the axis at a low bias voltage, while at higher bias voltages, it shows four-fold symmetry about the 〈100〉 axis in the large magnetic field H region. Considering modified Jullière’s model and multiple bands with different anisotropic features, we can well reproduce the experimental TMR characteristics. Our results will lead to novel functionalities using TMRs with different symmetries in multi-orbital materials.

Effects of anisotropic surface drift diffusion on the strained heteroepitaxial nanoislands subjected to electromigration stressing

A systematic study based on self-consistent dynamical simulations is presented for the morphological evolutionary behavior of an isolated thin Ge/Si nanoisland (quantum dot) on a rigid substrate exposed to electromigration forces. This morphological evolution is basically induced by the anisotropic surface drift diffusion, driven by the capillary forces, the lattice mismatch stresses, and the wetting potential. In this study, we have mainly focused on the size and shape development kinetics of quantum dots, known as the “Stranski–Krastanov” (SK) morphology, influenced by applied electromigration stresses. Emphasis is given to the effects of rotational symmetry associated with the anisotropic diffusivity in 2D space (i.e., quantum wires in 3D). The pointed bullet-shaped “Stranski–Krastanov” islands with high aspect ratios, ξ = 0.77, are formed at the cathode edge, while the whole nanoisland slightly creeps out of the initial computational domain. The favorable configuration of the Ge20/Si80 alloy test module, which resulted in ζ = 0.37 enhancement in the contour surface area, has a dome shape attached to the [010] top surface of the Si substrate with a zone axis of {010}/⟨001⟩. The anisotropic surface diffusion dyadic has a fourfold rotational symmetry axis [001] lying on the (001) plane of the Si substrate, and its major axis is tilted at about ϕ = 45° from the applied electrostatic field extended along the longitudinal axis [100] of the substrate. This particular experiment resulted in a SK singlet peak with a small satellite with a very small aspect ratio of ≅0.2 that may be appropriate for the conception of quantum optoelectronic devices or inter-band structures to generate photoelectrons having large energy spectra, thereby increasing the efficiency of photovoltaics exposed to solar radiations.

Highly Birefringent Anti‐Resonant Hollow‐Core Fiber with a Bi‐Thickness Fourfold Semi‐Tube Structure

AbstractThe optical performance characteristics of anti‐resonant hollow‐core fibers (known as AR‐HCFs or ARFs) are improving rapidly, but the polarization maintaining issue with these fibers remains unresolved. Although a regular nonbirefringent ARF can maintain high polarization purity under static conditions, it cannot resist mechanical disturbances. In this work, by designing a bi‐thickness semi‐tube ARF structure with fourfold rotational symmetry, the first ARF with a level of birefringence close to 10−4is fabricated. The proposed ARF features a combination of phase birefringence of 9.1 × 10−5, a minimum loss of 185 dB km−1, a bandwidth of 133 nm, and single‐mode operation. Furthermore, the ARF shows high resistance to fiber bending and wide‐range temperature variations, thus confirming that this carefully designed ARF can serve as a practical workhorse in polarization‐related optical fiber applications.

Higher-order topological superconductors from Weyl semimetals

We propose that doped Weyl semimetals with {time-reversal and certain crystalline symmetries} are natural candidates to realize higher-order topological superconductors, which exhibit a fully gapped bulk while the surface hosts robust gapless chiral hinge states. We show that in such a doped Weyl semimetal, a featureless finite-range attractive interaction favors a p+ip pairing symmetry. By analyzing its topological properties, we identify such a chiral pairing state as a higher-order topological superconductor, which depending on the existence of a four-fold rotoinversion symmetry, is either intrinsic, {meaning that the corresponding hinge states can only be removed by closing the bulk gap, rather than modifying the surface states}, or extrinsic. We achieve this understanding via various methods recently developed for higher-order topology, including Wannier representability, Wannier spectrum, and defect classification approaches. For the four-fold rotoinversion symmetric case, we provide a complete classification of the higher-order topological superconductors. We show that such second-order topological superconductors exhibit chiral hinge modes that are robust in the absence of interaction effects but can be eliminated at the cost of introducing surface topological order.

The Evolution of Oxytocin and Vasotocin Receptor Genes in Jawed Vertebrates: A Clear Case for Gene Duplications Through Ancestral Whole-Genome Duplications.

The neuronal and neuroendocrine peptides oxytocin (OT) and vasotocin (VT), including vasopressins, have six cognate receptors encoded by six receptor subtype genes in jawed vertebrates. The peptides elicit a broad range of responses that are specifically mediated by the receptor subtypes including neuronal functions regulating behavior and hormonal actions on reproduction and water/electrolyte balance. Previously, we have demonstrated that these six receptor subtype genes, which we designated VTR1A, VTR1B, OTR, VTR2A, VTR2B and VTR2C, arose from a syntenic ancestral gene pair, one VTR1/OTR ancestor and one VTR2 ancestor, through the early vertebrate whole-genome duplications (WGD) called 1R and 2R. This was supported by both phylogenetic and chromosomal conserved synteny data. More recently, other studies have focused on confounding factors, such as the OTR/VTR orthologs in cyclostomes, to question this scenario for the origin of the OTR/VTR gene family; proposing instead less parsimonious interpretations involving only one WGD followed by complex series of chromosomal or segmental duplications. Here, we have updated the phylogeny of the OTR/VTR gene family, including a larger number of vertebrate species, and revisited seven representative neighboring gene families from our previous conserved synteny analyses, adding chromosomal information from newer high-coverage genome assemblies from species that occupy key phylogenetic positions: the polypteriform fish reedfish (Erpetoichthys calabaricus), the cartilaginous fish thorny skate (Amblyraja radiata) and a more recent high-quality assembly of the Western clawed frog (Xenopus tropicalis) genome. Our analyses once again add strong support for four-fold symmetry, i.e., chromosome quadruplication in the same time window as the WGD events early in vertebrate evolution, prior to the jawed vertebrate radiation. Thus, the evolution of the OTR/VTR gene family can be most parsimoniously explained by two WGD events giving rise to the six ancestral genes, followed by differential gene losses of VTR2 genes in different lineages. We also argue for more coherence and clarity in the nomenclature of OT/VT receptors, based on the most parsimonious scenario.

Structure and Conformation Study of the O-Antigen from the Lipopolysaccharide of Cupriavidus Metallidurans CH34

Cupriavidus metallidurans is a Gram-negative bacterium that has attracted the attention of the scientific community since its discovery back in 1976. It was initially studied as a model organism for bioremediation processes due to its ability to survive in heavy metal-rich environments. However, in recent years, there is evidence that this bacterium can be a potential pathogen for humans. How C. metallidurans can survive in such different environments is unknown and prompted the following work. Its great adaptability could be explained by the structural and conformational studies of the O-antigen portion of the lipopolysaccharide, the main constituent of the outer membrane of Gram-negative bacteria, which is the one in direct contact with the external environment. Therefore, a combination of chemical and spectroscopic analyses was used to define the O-antigen structure, disclosing that it is a polysaccharide constituted of a linear tetrasaccharide repeating unit that does not resemble other structures already reported for bacteria: [4)-α-d-GalNAc-(1→3)-α-d-Qui2NAc4NHBA-(1→3)-α-l-Rha-(1→3)-α-l-Rha-(1→]. Interestingly, the molecular dynamics studies revealed that the three-dimensional structure of the O-antigen is highly flexible: it might adopt three different right-handed helix conformations described by a two, three, or four-fold symmetry. This conformational behavior could represent the reason behind the survival of C. metallidurans in different environments.

Multiple One-Way Edge Modes in Sonic Crystals With Large Chern Numbers

The quantum Hall effect (QHE) associated with Chern insulators reveals the non-trivial topological properties of two-dimensional electronic systems subject to strong magnetic field, which features finite Chern number C and chiral edge states. The latter promise robust electron transport and have received tremendous attention in both the condensed matter physics and classical systems including photonics and acoustics. In acoustics, circulating air flow has been introduced to create an effective gauge magnetic field, which breaks the time-reversal symmetry and leads to chiral edge states for acoustic waves. While the robust edge states may offer possible routes towards acoustic devices yielding unidirectional sound propagation, e.g., acoustic diodes, the mode density at the interfaces is limited by small Chern numbers of ±1. Here, we realize acoustic Chern insulators with large Chern numbers, i.e., |C|≥ 1 (|C| = 1, 2, 3, 4). The system is based on circulating air flow in a sonic crystal (SC) with fourfold rotational symmetry. The large Chern numbers are obtained by breaking multiple accidental degeneracies at (non-)high-symmetric points. Based on these Chern insulators, acoustic diodes are realized by joining structures of different Chern numbers. Up to eight propagation modes are supported on the interfaces, greatly improving the mode density and hence the propagation efficiency. Our design offers possible routes towards high-efficient and topologically robust acoustic diodes, which may further inspire acoustic non-reciprocal devices based on topological Chern insulators. Experimentally, our proposals can be realized based on angular-momentum-biased resonator arrays.

Enhancement of superconductivity by electronic nematicity in cuprate superconductors

ABSTRACT The cuprate superconductors are characterised by numerous ordering tendencies, with the electronically nematic order being the most distinct form of order. Here the intertwinement of the electronic nematicity with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconductivity. It is shown that the optimised takes a dome-like shape with the weak and strong strength regions on each side of the optimal strength of the electronic nematicity, where the optimised reaches its maximum. This dome-like shape nematic-order strength dependence of thus indicates that the electronic nematicity enhances superconductivity. Moreover, this nematic order induces the anisotropy of the electron Fermi surface, where although the original electron Fermi surface contour with the four-fold rotation symmetry is broken up into that with a residual twofold rotation symmetry, this electron Fermi surface contour with the twofold rotation symmetry still is truncated to form the disconnected Fermi arcs with the most spectral weight that locates at around the tips of the Fermi arcs. Concomitantly, these tips of the Fermi arcs connected by the scattering wave vectors construct an octet scattering model, however, the partial scattering wave vectors and their respective symmetry-corresponding partners occur with unequal amplitudes, leading to these electronically ordered states being broken both rotation and translation symmetries. As a natural consequence, the electronic structure is inequivalent between the and directions in momentum space. These anisotropic features of the electronic structure are also confirmed via the result of the autocorrelation of the single-particle excitation spectra, where the breaking of the rotation symmetry is verified by the inequivalence on the average of the electronic structure at the two Bragg scattering sites. The theory also indicates that the order parameter of the electronic nematicity achieves its maximum in the characteristic energy and then decreases rapidly as the energy moves away from the characteristic energy.

Cooperativity of steric bulk and H-bonding in coordination sphere engineering: heteroleptic PdII cages and bowls by design.

Recently developed self-assembly strategies allow to rationally reduce the symmetry of metallosupramolecular architectures. In addition, the combination of multiple ligand types without creating compound mixtures has become possible. Among several approaches to realize non-statistical heteroleptic assembly, Coordination Sphere Engineering (CSE) makes use of secondary repulsive or attractive interactions in direct vicinity of the metal nodes. Previously, we used steric congestion to turn dinuclear [Pd2L4] cages with fourfold symmetry into [Pd2L3X2] (X = solvent, halide) bowl structures. Here, we introduce a new subtype of this strategy based on balancing hydrogen bonding and repulsive interactions between ligands carrying quinoline (LQu) and 1,8-naphthyridine (LNa) donors to generate trans-[Pd2L2] and [Pd2L3L′] cages, assisted by templation of encapsulated fullerenes. Combined with steric congestion caused by acridine (LAc) donors, we further report the first example of a heteroleptic [Pd2L2L′X2] bowl. Formation, structure and fullerene binding ability of these metallo-supramolecular hosts were studied by NMR, mass spectrometry and single crystal X-ray diffraction.

Development of Resistive-Ink Based Planar and Conformal Metasurfaces for RCS Reduction

This work reports design, development and characterization of both planar and conformal Metasurfaces using resistive Ink based lossy pattern printed on top of FR-4 dielectric substrate for RADAR stealth application. Different geometrical dimensions of the proposed unit cell have been optimized numerically using CST-Microwave Studio, to achieve 20 dB reflection reduction with 60% fractional bandwidth in frequency range 10.5-19.5 GHz under normal incidence with 0.12λ_L thickness (where λ_L corresponds to lower operating frequency) and 10 dB reflection reduction up to 40° oblique angle of incidence in the given frequency spectrum for both TE and TM polarized wave. An equivalent circuit analytical modelling has also been performed to understand and verify the numerical findings which are nearly in agreement. Polarization insensitive characteristics of developed surfaces is achieved using fourfold rotation symmetry of the designed unit cell. The designed absorbers are fabricated in form of planar, cylindrically bent and 90° dihedral Metasurfaces and are characterized using ABmm Vector Network Analyzer (VNA) system and free space measurement method. A thorough different experimental measurements are performed and it is found that measured characteristics are in agreement with numerical-analytical findings.

Magnetic anisotropy and reversal in epitaxial FeGa/IrMn bilayers with different orientations of exchange bias

Epitaxial FeGa/IrMn bilayers with exchange biases along the FeGa[100] and [110] directions are prepared on MgO(001) single crystal substrates by magnetron sputtering through controlling the orientation of the external field <i>in situ</i> applied during growth. The effect of the exchange bias orientation on the magnetic switching process and the magnetic switching field are studied. The X-ray <i>φ</i>-scan indicates that the FeGa layer is epitaxially grown with a 45° in-plane rotation on the MgO(001) substrate along the FeGa(001)[110] direction and the MgO(001)[100] direction. The measurements of the angular dependence of the ferromagnetic resonance field and the corresponding fitting to the Kittel equation show that the samples have a superposition of fourfold symmetric magnetocrystalline anisotropy <inline-formula><tex-math id="M4">\begin{document}$ {K}_{1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M4.png"/></alternatives></inline-formula>, unidirectional magnetic exchange bias anisotropy <inline-formula><tex-math id="M5">\begin{document}$ {K}_{\mathrm{e}\mathrm{b}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M5.png"/></alternatives></inline-formula>, and uniaxial magnetic anisotropy <inline-formula><tex-math id="M6">\begin{document}$ {K}_{\mathrm{u}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M6.png"/></alternatives></inline-formula> with configuration of <inline-formula><tex-math id="M7">\begin{document}$ {K}_{\mathrm{e}\mathrm{b}}//\left[100\right] $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M7.png"/></alternatives></inline-formula> or <inline-formula><tex-math id="M8">\begin{document}$ {K}_{\mathrm{e}\mathrm{b}}//\left[110\right] $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M8.png"/></alternatives></inline-formula>. The combined longitudinal and transverse magneto-optical Kerr effect measurements show that sample with <inline-formula><tex-math id="M9">\begin{document}$ {K}_{\mathrm{e}\mathrm{b}}//\left[100\right] $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M9.png"/></alternatives></inline-formula> exhibits square loops, asymmetrically shaped loops, and one-sided two-step loops in different external magnetic field directions. In contrast, the sample with <inline-formula><tex-math id="M10">\begin{document}$ {K}_{\mathrm{e}\mathrm{b}}//\left[110\right] $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M10.png"/></alternatives></inline-formula> exhibits one-sided two-step and two-sided two-step loops as the magnetic field orientation changes. Because the <inline-formula><tex-math id="M11">\begin{document}$ {K}_{1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M11.png"/></alternatives></inline-formula> is superimposed by <inline-formula><tex-math id="M12">\begin{document}$ {K}_{\mathrm{u}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M12.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M13">\begin{document}$ {K}_{\mathrm{e}\mathrm{b}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M13.png"/></alternatives></inline-formula>, the in-plane fourfold symmetry of the magnetic anisotropy energy is broken. The local minima are no longer strictly along the in-plane <inline-formula><tex-math id="M14">\begin{document}$ \left\langle{100}\right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M14.png"/></alternatives></inline-formula> directions, but make a deviation angle which depends on the relative orientation and strength of magnetic anisotropy. A model based on the domain wall nucleation and propagation is proposed with considering the different orientations of <inline-formula><tex-math id="M15">\begin{document}$ {K}_{\mathrm{e}\mathrm{b}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M15.png"/></alternatives></inline-formula>, which can nicely explain the change of the magnetic switching route with the magnetic field orientation and fit the angular dependence of the magnetic switching fields, indicating a significant change of domain wall nucleation energy as the orientation of <inline-formula><tex-math id="M16">\begin{document}$ {K}_{\mathrm{e}\mathrm{b}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20220166_M16.png"/></alternatives></inline-formula> changes.

Polarization-insensitive dual-band response governed by quasi bound states in the continuum for high-performance refractive index sensing

The introduction of distortions into the metasurfaces with in-plane symmetry offers a possibility to achieve resonances with high quality (Q) factors, but such distortions make the metasurfaces sensitive to the polarization state of the incident light. Here, we propose and numerically demonstrate a polarization-insensitive dual-band refractive index (RI) sensor. In this work, the proposed metasurface is imparted with fourfold symmetry by combining two pairs of asymmetric silicon elliptical nanodisks, allowing it to acquire polarization-insensitive properties to the incident light. Two narrow-band reflection peaks with full width at half maximum (FWHM) of 3.36 nm and 4.53 nm are excited and tailored for RI sensing. Their sensitivities are 2756.67 nm/RIU and 2319.93 nm/RIU, with figure of merit (FOM) values of 820.44 RIU−1 and 532.09 RIU−1. This work provides a new approach to realize polarization-independent and high-performance RI sensor devices.

Rectangular Cylinders Formed by Compositionally Bidisperse ABC Triblock Terpolymer Blends: A Self-Consistent Field Theory Study.

Compared with traditional cylinders that have circular cross-sections, cylinders with rectangular cross-sections can endow nanomaterials with various novel optical properties and functions. In this work, the formation of the rectangular cylinders self-assembled by compositionally bidisperse ABC triblock terpolymer blends has been investigated via numerical simulations based on self-consistent field theory. The specially designed blending systems are composed of two types of linear ABC triblock terpolymers that have the same total chain lengths and the middle B block chain lengths, but different chain lengths of the side A/C blocks. By tuning the chain length fractions and the interactions between different blocks, rectangular cylinders with a fourfold symmetry pattern were successfully obtained in our simulations. Each rectangular phase domain is self-assembled together by the short and long side blocks of the same species. The simulation results indicate that the selective aggregation of the short side blocks determines the formation of the rectangular cylindrical phase, i.e., the short side blocks prefer to aggregate at the four corners within a rectangular cylindrical phase domain. This simulation result reveals a formation mechanism that is different from the mechanism proposed in previous experiments [Asai ACS Macro Lett., 2014, 3, 166-169]. Moreover, under different middle B block chain length fractions, phase diagrams as a function of the interaction parameter between different blocks and the short side block chain length fraction have been constructed. The phase diagrams show that the parameter window of the rectangular cylinders is considerably expanded by increasing the chain length fraction of the middle B blocks. Our simulation works can provide a theoretical basis for molecular design to regulate and fabricate nanomaterials with nontraditional phase domains in future experiments.

Classification of Dirac points with higher-order Fermi arcs

Dirac semimetals lack a simple bulk-boundary correspondence. Recently, Dirac materials with four-fold rotation symmetry have been shown to exhibit a higher order bulk-hinge correspondence: they display "higher order Fermi arcs," which are localized on hinges where two surfaces meet and connect the projections of the bulk Dirac points. In this paper, we classify higher order Fermi arcs for Dirac semimetals protected by a rotation symmetry and the product of time-reversal and inversion. Such Dirac points can be either linear in all directions or linear along the rotation axis and quadratic in other directions. By computing the filling anomaly for momentum-space planes on either side of the Dirac point, we find that all linear Dirac points exhibit higher order Fermi arcs terminating at the projection of the Dirac point, while the Dirac points that are quadratic in two directions lack such higher order Fermi arcs. When higher order Fermi arcs do exist, they obey either a $\mathbb{Z}_2$ (four-fold rotation axis) or $\mathbb{Z}_3$ (three- or six-fold rotation axis) group structure. Finally, we build two models with six-fold symmetry to illustrate the cases with and without higher order Fermi arcs. We predict higher order Fermi arcs in Na$_3$Bi.