Mirror Symmetry Research Articles

Enhanced wave transmission in random media with mirror symmetry

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

The second neutrino, heavy lepton and broken mirror symmetry (on the 100th anniver-sary of the birth of Emmanuel Moiseevich Lipmanov)

The second neutrino, heavy lepton and broken mirror symmetry (on the 100th anniver-sary of the birth of Emmanuel Moiseevich Lipmanov)

Noncollinear Electric Dipoles in a Polar Chiral Phase of CsSnBr3 Perovskite.

Polar and chiral crystal symmetries confer a variety of potentially useful functionalities upon solids by coupling otherwise noninteracting mechanical, electronic, optical, and magnetic degrees of freedom. We describe two phases of the 3D perovskite, CsSnBr3, which emerge below 85 K due to the formation of Sn(II) lone pairs and their interaction with extant octahedral tilts. Phase II (77 K < T < 85 K, space group P21/m) exhibits ferroaxial order driven by a noncollinear pattern of lone pair-driven distortions within the plane normal to the unique octahedral tilt axis, preserving the inversion symmetry observed at higher temperatures. Phase I (T < 77 K, space group P21) additionally exhibits ferroelectric order due to distortions along the unique tilt axis, breaking both inversion and mirror symmetries. This polar and chiral phase exhibits second harmonic generation from the bulk and pronounced electrostriction and negative thermal expansion along the polar axis (Q22 ≈ 1.1 m4 C-2; αb = -7.8 × 10-5 K-1) through the onset of polarization. The structures of phases I and II were predicted by recursively following harmonic phonon instabilities to generate a tree of candidate structures and subsequently corroborated by synchrotron X-ray powder diffraction and polarized Raman and 81Br nuclear quadrupole resonance spectroscopies. Preliminary attempts to suppress unintentional hole doping to allow for ferroelectric switching are described. Together, the polar symmetry, small band gap, large spin-orbit splitting of Sn 5p orbitals, and predicted strain sensitivity of the symmetry-breaking distortions suggest bulk samples and epitaxial films of CsSnBr3 or its neighboring solid solutions as candidates for bulk Rashba effects.

Breaking the mirror symmetry of photonic spin-orbit interaction using a geometrically symmetric chiral resonator

The symmetries of photonic spin-orbit interaction (PSOI) at waveguide interfaces provide flexible modulation capability but limit their practical implementation due to the stringent requirements of excitation conditions. This limitation can be mitigated by intentionally breaking local symmetries, offering a novel platform for achieving directional coupling and optical isolation with PSOI-based interfaces. For example, breaking the inversion symmetry of a nanofiber PSOI interface using a nanosphere scatterer reduces the required accuracy in the size and position of excitation spots. This study introduces a novel approach to break the mirror symmetry of a PSOI-based nanofiber waveguide by coupling it with a geometrically symmetric chiral gold nanohelicoid (GNH) resonator, which relaxes the original requirement of circularly polarized excitations. Finite-difference time-domain simulations demonstrate unidirectional light coupling and propagation under both circularly and linearly polarized excitations, showcasing the versatility of this hybrid symmetry-broken system. The Fano-like features observed in directionality spectra align with the GNH’s circular dichroism spectrum, emphasizing an intricate correlation between plasmonic near-field chirality and far-field scattering dichroism. This work paves the way for enhancing the functionalities of PSOI-based waveguide interfaces through locally coupling them with nanoscale chiral resonators, thereby expanding their application in quantum photonics, information transport and plasmonic nanophotonics.

Exact formulas for estimating the area of flow regions in free boundary problems

An effective technique is proposed for obtaining exact formulas for estimating the area of flow regions in two-dimensional fluid flow problems with free boundaries, that allow an exact solution in terms of elliptic functions. The effectiveness of the technique is demonstrated using a specific example of the problem of capillary waves on the surface of a liquid of finite depth. This example is characterized by mirror symmetry of the flow region, but the technique can be generalized to the case of other symmetry of the flow region.

In-plane magnetization orientation driven topological phase transition in OsCl3 monolayer

The quantum anomalous Hall effect resulting from the in-plane magnetization in the OsCl3 monolayer is shown to exhibit different electronic topological phases determined by the crystal symmetries and magnetism. In this Chern insulator, the Os-atoms form a two dimensional planar honeycomb structure with an easy-plane ferromagnetic configuration and the required non-adiabatic paths to tune the topology of electronic structure exist for specific magnetic orientations based on mirror symmetries of the system. Using density functional theory (DFT) calculations, these tunable phases are identified by changing the orientation of the magnetic moments. We argue that in contrast to the buckled system, here the Cl-ligands bring non-trivial topology into the system by breaking the in-plane mirror symmetry. The interplay between the magnetic anisotropy and electronic band-topology changes the Chern number and hence the topological phases. Our DFT study is corroborated with comprehensive analysis of relevant symmetries as well as a detailed explanation of topological phase transitions using a generic tight binding model.

The wrapped Fukaya category for semi-toric Calabi–Yau

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

High Q chiroptical responses with maximum chirality in all-dielectric metasurfaces driven by quasi-bound states in the continuum

Chiral metasurfaces have attracted considerable attention because of their immense potential for diverse applications requiring chiral light-matter interactions. Recently, boosted by a mechanism based on the concept of bound states in the continuum (BICs), high Q factor chiroptical resonances have been exhibited by breaking the inversion symmetries of planar metasurfaces. However, the optical chirality of these chiral metasurfaces is generally intolerable with respect to the structural geometries, especially the geometric asymmetry. Here, we present a novel chiral quasi-BIC with strong optical chirality in an all-dielectric metasurface. By simultaneously breaking the in-plane C2 rotational and mirror symmetries, the chiral metasurface shows enhanced chiroptical resonances with near-unity CD (∼0.996) and high Q factors (∼2274) at terahertz frequencies. Further analyses based on numerical simulations reveal that the CD of the chiroptical resonance depicts exceptional remarkable tolerableness to the geometry asymmetry δ when δ are present in a broad range, while the corresponding Q factor is modulated accordingly. The results may develop a novel approach to manipulating the advanced optical chirality for potential applications requiring strong CD with enhanced light-matter interactions.

Field-free magnetization switching through large out-of-plane spin–orbit torque in the ferromagnetic CoPt single layers

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

Continuously Geometrical Tuning to Boost Circular Dichroism in 3D Chiral Metamaterials

AbstractChiral 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.

Chiral Stacking Identification of Two-Dimensional Triclinic Crystals Enabled by Machine Learning.

Chiral materials possess broken inversion and mirror symmetry and show great potential in the application of next-generation optic, electronic, and spintronic devices. Two-dimensional (2D) chiral crystals have planar chirality, which is nonsuperimposable on their 2D enantiomers by any rotation about the axis perpendicular to the substrate. The degree of freedom to construct vertical stacking of 2D monolayer enantiomers offers the possibility of chiral manipulation for designed properties by creating multilayers with either a racemic or enantiomerically pure stacking order. However, the rapid recognition of the relative proportion of two enantiomers becomes demanding due to the complexity of stacking orders of 2D chiral crystals. Here, we report the unambiguous identification of racemic and enantiomerically pure stackings for layered ReSe2 and ReS2 using circular polarized Raman spectroscopy. The chiral Raman response is successfully manipulated by the enantiomer proportion, and the stacking orders of multilayer ReSe2 and ReS2 can be completely clarified with the help of second harmonic generation and scanning transmission electron microscopy measurements. Finally, we trained an artificial intelligent Spectra Classification Assistant to predict the chirality and the complete crystallographic structures of multilayer ReSe2 from a single circular polarized Raman spectrum with the accuracy reaching 0.9417 ± 0.0059.

Polarity-driven three-dimensional spontaneous rotation of a cell doublet

Mechanical interactions between cells play a fundamental role in the self-organization of organisms. How these interactions drive coordinated cell movement in three dimensions remains unclear. Here we report that cell doublets embedded in a three-dimensional extracellular matrix undergo spontaneous rotations. We investigate the rotation mechanism and find that it is driven by a polarized distribution of myosin within cell cortices. The mismatched orientation of this polarized distribution breaks the doublet mirror symmetry. In addition, cells adhere at their interface through adherens junctions and with the extracellular matrix through focal contacts near myosin clusters. We use a physical theory describing the doublet as two interacting active surfaces to show that rotation is driven by myosin-generated gradients of active tension whose profiles are dictated by interacting cell polarity axes. We also show that three-dimensional shape symmetries are related to broken symmetries of the myosin distribution in cortices. To test for the rotation mechanism, we suppress myosin clusters using laser ablation and generate new myosin clusters by optogenetics. Our work clarifies how polarity-oriented active mechanical forces drive collective cell motion in three dimensions.

Homological mirror symmetry for hypertoric varieties, I: Conic equivariant sheaves

Homological mirror symmetry for hypertoric varieties, I: Conic equivariant sheaves

From Topological Nodal-Line Semimetals to Quantum Spin Hall Insulators in Tetragonal SnX Monolayers (X=F, Cl, Br, I)

Abstract Two-dimensional (2D) topological materials have recently garnered significant interest due to their profound physical properties and promising applications for future quantum nanoelectronics. Achieving various topological states within one type of materials is, however, seldom reported. Based on first-principles calculations and tight-binding models, we investigate topological electronic states in a novel family of 2D halogenated tetragonal stanene (T-SnX, X = F, Cl, Br, I). All the four monolayers are found being unusual topological nodal-line semimetals (NLSs), protected by a glide mirror symmetry. When spin-orbit coupling (SOC) is turned on, T-SnF and TSnCl are still ascertained as topological NLSs due to the remaining band inversion, primarily composed of Sn pxy orbitals, while T-SnBr and T-SnI become quantum spin Hall insulators. The phase transition is ascribed to moving up in energy of Sn s orbitals and increasing of SOC strengths. The topology origin in the materials is uniformly rationalized through elementary band representations. The robust and diverse topological states found in the 2D T-SnX monolayers position them as an excellent material platform for the development of innovative topological electronics.

Mirror symmetry and Hitchin system on Deligne–Mumford curves: Strominger–Yau–Zaslow duality

Abstract We systematically study the moduli stacks of Higgs bundles, spectral curves, and Norm maps on Deligne–Mumford curves. As an application, under some mild conditions, we prove the Strominger–Yau–Zaslow duality for the moduli spaces of Higgs bundles over a hyperbolic stacky curve.

Influence of Lifshitz Transition on the Intrinsic Resistivity of Cu2N Monolayer.

The Lifshitz transition (LT), a topological structure transition of Fermi surfaces, can induce various intricate physical properties in metallic materials. In this study, through first-principles calculations, we explore the nontrivial effect of the LT on the intrinsic resistivity of the Cu2N monolayer arising from electron-phonon (el-ph) scattering. We find that when the LT is induced by electron doping, the multibranch Fermi surface simplifies into a single-band profile. Such an LT leads to a decoupling of low-frequency flexural phonons from el-ph scattering due to mirror symmetry. Consequently, the resistivity of the Cu2N monolayer at room temperature significantly decreases, approaching that of slightly doped graphene, and highlighting the Cu2N monolayer as a highly conductive two-dimensional metal. Moreover, this LT can bring about a nonlinear temperature dependence of the intrinsic resistivity at a high temperature.

Anomalous Hall effects in chiral superconductors

We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E1 and E2 representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and—as we highlight—the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, ν, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for ν = ±1, but vanishes for |ν| &amp;gt; 1. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, R ≥ ℏ/pf, the thermal Hall conductivity is finite for chiral order with |ν|≥ 2, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.

Polarization Saturation in Multilayered Interfacial Ferroelectrics.

Van der Waals polytypes of broken inversion and mirror symmetries have been recently shown to exhibit switchable electric polarization even at the ultimate two-layer thin limit. Their out-of-plane polarization has been found to accumulate in a ladder-like fashion with each successive layer, offering 2D building blocks for the bottom-up construction of 3D ferroelectrics. Here, it is demonstrated experimentally that beyond a critical stack thickness, the accumulated polarization in rhombohedral polytypes of molybdenum disulfide saturates. The underlying saturation mechanism, deciphered via density functional theory and self-consistent Poisson-Schrödinger calculations, point to a purely electronic redistribution involving: 1.Polarization-induced bandgap closure that allows for cross-stack charge transfer and the emergence of free surface charge; 2. Reduction of the polarization saturation value, as well as the critical thickness at which it is obtained, by the presence of free carriers. The resilience of polar layered structures to atomic surface reconstruction, which is essentially unavoidable in polar 3D crystals, potentially allows for the design of new devices with mobile surface charges. The findings, which are of general nature, should be accounted for when designing switching and/or conductive devices based on ferroelectric layered materials.

Topological Deformations of Manifolds by Algebraic Compositions in Polynomial Rings

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism.

Chiral photothermoelectric effect driven by high-Q quasi-bound states in the continuum

Bound states in continuum (BIC) have been proposed as a means to efficiently improve light-matter interactions in metasurfaces. While breaking the mirror symmetry of structure and developing BIC into a reachable and observable quasi-BIC, it is usually accompanied by the chiral phenomenon with high quality (Q) factor. Here, we report a spin-sensitive photodetector in the infrared (NIR) region comprising a silicon metasurface with chiral quasi-BIC, a silver layer, and a thermoelectric layer. A chiral quasi-BIC supported by a silicon metasurface can be realized under normal incidence. Based on finite element method simulations, a silicon metasurface with a silver layer shows a high Q-factor of 958.6 with a giant absorption circular dichroism of 0.83. Subsequently, we study the thermal performance of the chiral absorbers by using the heat transfer module of COMSOL. Combined with the thermoelectric material bismuth telluride, we calculate the differential photothermoelectric effects of the system under circular-polarized light irradiation. When the incident flux is 100 W cm−2, the output voltage under right-circular-polarization (left-circular-polarization) light reaches 0.59 mV (0.08 mV), which can be used for polarization detection. Therefore, our designed structure incorporating thermoelectricity broadens the applications of chiral BIC in sensors and detectors.