Mirror Symmetry Research Articles

Surface impedance and topologically protected interface modes in one-dimensional phononic crystals

When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of topological insulators, powerful tools have been developed to address these questions. In particular, when applied to one-dimensional systems with mirror symmetry, the bulk-boundary correspondence claims that the existence of interface modes is given by a topological invariant computed from the bulk properties of the PC, which ensures strong stability properties. This one-dimensional bulk-boundary correspondence has been proven in various works. Recent attempts have exploited the notion of surface impedance, relying on analytical calculations of the transfer matrix. In the present work, the monotonic evolution of surface impedance with frequency is proven for all one-dimensional PCs with mirror symmetry. This result allows us to establish a stronger version of the bulk-boundary correspondence that guarantees not only the existence but also the uniqueness of a topologically protected interface state. This correspondence is extended to a larger class of one-dimensional models that include imperfect interfaces, array of resonators, or dispersive media. Numerical simulations are proposed to illustrate the theoretical findings.

Discovery of Light-Induced Mirror Symmetry Breaking

The authors discovered the light-induced mirror symmetry breaking, paving the way for controlling mirror symmetries via light and for realizing various phenomena utilizing the mirror symmetry breaking

Towards Uncovering the Hidden Order of URu2Si2 Phase Transition

We propose a chiral charge as the hidden order parameter in URu2Si2 and present experiments to detect it by focusing on breakings of mirror and inversion symmetries at the local uranium ion.

Magnetorotational Supernova Explosions: Jets and Mirror Symmetry Violation

Magnetorotational Supernova Explosions: Jets and Mirror Symmetry Violation

Knot categorification from mirror symmetry part I: Coherent sheaves

Knot categorification from mirror symmetry part I: Coherent sheaves

Large valley splitting induced by spin-orbit coupling effects in monolayer W2NSCl.

Two-dimensional (2D) valley materials are promising materials for writing and storing information. The search for 2D materials with large valley splitting is essential for the development of spintronics and valley electronics. In this study, we theoretically design 2D W2NSCl MXenes with large valley splitting based on first-principle calculations. Due to the strong spin-orbit coupling (SOC) and the broken inversion symmetry, the W2NSCl monolayer exhibits valley splitting values of 491 meV and 83 meV at K/K' of the valence and conduction bands, respectively. The valley splitting of W2NSCl is robust to biaxial strain. Because of the broken mirror symmetry of W2NSCl, there is a Rashba effect at Γ with a Rashba parameter of 1.019 V Å. Based on the maximum localization of the Wannier function, we found the non-zero Berry curvature at K/K'. Furthermore, the non-zero Berry curvature at the K/K' valley increases monotonically with an external strain from -4% to 4%. Our finding shows that W2NSCl is a candidate material for valley electronics and spintronics applications.

Exploiting Mirror Symmetry in the 2D MoM Analysis of the Scattering by Conducting Cylinders

Exploiting Mirror Symmetry in the 2D MoM Analysis of the Scattering by Conducting Cylinders

Photo-acoustic technique with widely tuneable laser: Metasurface circular dichroism response

Chirality, an intrinsic property of certain entities in the universe, is characterized by the absence of mirror symmetry. Understanding chirality is crucial as it influences molecular interactions and properties. Circular dichroism (CD), measured using circularly polarized light, is a standard technique for probing chirality, but its sensitivity is often limited. Here, we explore extrinsic chirality (i.e. a property arising from asymmetric achiral materials when observed from out of normal incidence directions), using photo-acoustic spectroscopy (PAS). PAS allows direct measurement of local absorption, by monitoring the heat produced and transferred to the surrounding air, regardless the transmitted, reflected, and scattered light that flows away from the sample. In conventional techniques, the CD is usually measured by taking into account only the extinction as transmitted (or reflected) light. In this study, we introduce a new PAS setup that employs an oblique-incidence laser to study extrinsic chirality in silver-coated self-assembled metasurfaces. Our experimental results reveal intriguing CD trends dependent on the angle of incidence and wavelength, indicative of extrinsic chirality. This study expands the application of PAS, enabling simultaneous analysis of multiple wavelengths and providing valuable insights into chiral metasurfaces.

Periodic diffraction from an aperiodic monohedral tiling.

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

Hitchin systems: some recent advances

We give a survey of some recent advances in parabolic Hitchin systems (parabolic Beauville-Narasimhan-Ramanan correspondence, mirror symmetry for parabolic Hitchin systems), and in exact methods of solving the non-parabolic Hitchin systems. Bibliography: 55 titles.

Minimal log discrepancies of hypersurface mirrors

Abstract For certain quasismooth Calabi–Yau hypersurfaces in weighted projective space, the Berglund-Hübsch-Krawitz (BHK) mirror symmetry construction gives a concrete description of the mirror. We prove that the minimal log discrepancy of the quotient of such a hypersurface by its toric automorphism group is closely related to the weights and degree of the BHK mirror. As an application, we exhibit klt Calabi–Yau varieties with the smallest known minimal log discrepancy. We conjecture that these examples are optimal in every dimension.

Tunable polarization properties of charge, spin, and valley in Janus VSiGeZ4 (Z = N, P, As) monolayers.

Polarization, as an important characterization of the symmetry breaking systems, has attracted tremendous attention in two-dimensional (2D) materials. Due to their significant symmetry breaking, Janus 2D ferrovalley materials provide a desirable platform to investigate the charge, spin, and valley polarization, as well as their coupling effects. Herein, using first-principles calculations, the polarization properties of charge, spin, and valley in Janus VSiGeZ4 (Z = N, P, and As) monolayers are systematically studied. The mirror symmetry breaking leads to a non-zero dipole moment and surface work function difference, indicating the presence of out-of-plane charge polarization. Magnetic properties calculations demonstrate that VSiGeN4 is a 2D-XY magnet with a Berezinskii-Kosterlitz-Thouless temperature of 342 K, while VSiGeP4 and VSiGeAs4 have an out-of-plane magnetization with a Curie temperature below room temperature. The magnetization can be rotated by applying biaxial strain, allowing manipulation of the spin polarization via nonmagnetic means. The spontaneous valley polarization is predicted to be 46, 49, and 70 meV for VSiGeN4, VSiGeP4, and VSiGeAs4, respectively, whose physical origin can be elucidated by employing the model analysis. In particular, the biaxial strain can induce the valley polarization switching from the valence (conduction) band to conduction (valence) band, but it hardly changes the valley polarization strength. Meanwhile, the valley extremum is transformed from the K' (K) to K (K') points. The present work not only provides an underlying insight into the polarization properties of Janus VSiGeZ4 but also offers a class of promising materials for spintronic and valleytronic devices.

Promising TMDC-like optical and excitonic properties of the TiBr2 2H monolayer.

The presented simulation protocol provides a solid foundation for exploring two-dimensional materials. Taking the TiBr2 2H monolayer as an example, this material displays promising TMDC-like optical and excitonic properties, making it an excellent candidate for optoelectronic and valleytronic applications. The direct band gap semiconductor (1.19 eV) is both structurally and thermodynamically stable, with spin-orbit coupling effects revealing a broken mirror symmetry in the K and K' valleys of the band structure, as confirmed by opposite values of the Berry curvature. A direct and bright exciton ground state was found, with an exciton binding energy of 0.56 eV. The study also revealed an optical helicity selection rule, suggesting selectivity in the valley excitation by specific circular light polarizations.

C-Me-graphene: an ideal two-dimensional nodal line semimetal with ultrahigh Young's modulus.

Nodal line semimetal (NLSM) has become a captivating medium for studying varieties of novel quantum phenomena. Here, based on first-principles calculations, we identify a square compound lattice (SCL) structure, namely C-Me-graphene, featuring a NLSM, wherein the nodal line of this configuration resides precisely at the Fermi energy without any extraneous bands in the vicinity, manifesting the quintessential characteristics of an ideal NLSM. As a corollary, utilizing symmetry analysis, we propose that nodal lines can be generated by exploiting the two-dimensional (2D) SCL of carbon. This is because the SCL not only satisfies time-reversal symmetry and inversion symmetry but also conforms to glide mirror symmetry. Additionally, this structure reveals remarkable mechanical attributes, exemplifying the highest Young's modulus within the realm of 2D materials, second only to graphene. Our work not only identifies an ideal carbon-based NLSM but also advances a scheme for crafting NLSMs, which would greatly enrich topological materials with exotic properties.

Circularly polarized blue fluorescence based on chiral heteroleptic six-coordinate bis-pyrazolonate-Zn2+ complexes.

Applying molecular design to chiral organo-Zn2+ complexes, a new pair of chiral heteroleptic bis-pyrazolonate-Zn2+ enantiomers [Zn(PMBP)2(1R,2R-Chxn)] (R,R-Zn2+; HPMBP = 1-phenyl-3-methyl-4-benzoyl-5-pyrazolone and 1R,2R-Chxn = (1R,2R)-cyclohexane-1,2-diamine) and [Zn(PMBP)2(1S,2S-Chxn)] (S,S-Zn2+; 1S,2S-Chxn = (1S,2S)-cyclohexane-1,2-diamine) have been synthesized and characterized in terms of photophysical and thermodynamic properties. In addition to a small Flack parameter (0.05(3)) associated with the solid-state elucidation of S,S-Zn2+, the circular dichroism (CD) and circularly polarized light (CPL) spectra for the chiral Zn2+ enantiomers show perfect mirror symmetry, establishing that the enantiopure 1,2-diamines successfully induce the optical isomerism of R,R-Zn2+ and S,S-Zn2+. As a result of the combined strong chiral induction capability of chiral 1,2-diamines and excellent photophysical properties of the pyrazolone ligand (PMBP)-, the two Zn2+ enantiomers exhibit high-quality pure blue fluorescence (ΦPL = 9-10%) and significant CPL activity (|glum| = 0.0065-0.0068). The heteroleptic strategy adopted in this study offers a new route to develop high-performance chiroptical luminophores.

Prediction of the two-dimensional ferromagnetic semiconductor Janus 2H-ZrTeI monolayer with large valley and piezoelectric polarizations.

Two-dimensional room-temperature Janus ferrovalley semiconductors with valley polarization and piezoelectric polarization offer new perspectives for designing multifunctional nanodevices. Herein, using first-principles calculations, we predict that the Janus 2H-ZrTeI monolayer is an intrinsic ferromagnetic semiconductor with in-plane magnetic anisotropy and a Curie temperature of 111 K. The Janus ZrTeI monolayer possesses a significant valley polarization of 141 meV due to time-reversal and inversion symmetry breaking. Based on the valley-contrasting Berry curvature, the anomalous valley Hall effect can be observed under an in-plane electric field. Meanwhile, the breaking of the inversion symmetry and mirror symmetry results in large longitudinal and transverse piezoelectric coefficients. By applying biaxial strain, the Janus 2H-ZrTeI monolayer can also be transformed into a Weyl nodal line semimetal. Furthermore, bilayers of ZrTeI with AB and BA stacking configurations allow the coexistence of valley polarization and ferroelectricity, enabling the manipulation of magnetism, ferroelectric polarization, and valley polarization through interlayer sliding. Our work provides a platform for studying valley polarization, piezoelectricity, and multiferroic coupling, which is significant for the application of multifunctional devices.

Symmetry-Breaking-Induced Internal Mixing Enhancement of Droplet Collision

Binary droplet collision is a basic fluid phenomenon for many spray processes in nature and industry involving lots of discrete droplets. It exists an inherent mirror symmetry between two colliding droplets. For specific cases of the collision between two identical droplets, the head-on collision and the off-center collision, respectively, show the axisymmetric and rotational symmetry characteristics, which is useful for the simplification of droplet collision modeling. However, for more general cases of the collision between two droplets involving the disparities of size ratio, surface tension, viscosity, and self-spin motions, the axisymmetric and rotational symmetry droplet deformation and inner flow tend to be broken, leading to many distinct phenomena that cannot occur for the collision between two identical droplets owing to the mirror symmetry. This review focused on interpreting the asymmetric droplet deformation and the collision-induced internal mixing that was affected by those symmetry breaking factors, such as size ratio effects, Marangoni Effects, non-Newtonian effects, and droplet self-spin motion. It helps to understand the droplet internal mixing for hypergolic propellants in the rocket engineering and microscale droplet reactors in the biological engineering, and the modeling of droplet collision in real combustion spray processes.

Mirror symmetry and new approach to constructing orbifolds of Gepner models

Motivated by the principles of the conformal bootstrap, primarily the principle of Locality, simultaneously with the requirement of space-time supersymmetry, we reconsider constructions of compactified superstring models. Starting from requirements of space-time supersymmetry and mutual locality, we construct a complete set of physical fields of orbifolds of Gepner models. To technically implement this, we use spectral flow generators to construct all physical fields from the chiral primary fields. The set of these spectral flow operators forms a so-called admissible group Gadm, which defines a given orbifold. The action of these operators produces a collection of physical fields consistent with the action of supersymmetry generators. The selection of mutually local fields from this collection is carried out using the mirror group Gadm⁎. The permutation of Gadm and Gadm⁎ replaces the original orbifold with a mirror one that satisfies the same conditions as the original one. This also implies that the resulting model is modular invariant.

Analysis of electron configurations in terms of parity-supporting rotations returns the hydrogen spectrum with consequences for the orbital model

A centrally symmetric variant of Bohr’s atomic model was constructed according to first geometric principles, and entanglement of pairs of subatomic particles through invariant rotations that stabilize the system. Its base symmetry was constrained to 2-fold rotational symmetry corresponding to 2 electrons associated with the atomic ground energy state. The theory was constructed using two sets of invariant rotations of distinguishable and indistinguishable type, derived from spherical approximations, with information regarding the initial state of the system preserved throughout the geometric transformation. Superposition of alternating structures of the two types indicates that closing of electron shells may take place via formation of mirror symmetry through rotational invariance, and quantization of energy can be reconciled with observables in quantum mechanics. The resulting solution correlates subshells s-g with unique parity-supporting states, and subsequent subshells with their imitations, having double the number of electrons of the preceding subshell of a corresponding type.

$\mu-e$ conversion in a model of electroweak scale right-handed neutrino mass

We perform a detailed analysis of the \(\mu-e\) conversion within an extended version of the standard model (SM) with mirror symmetry and low energy of the electroweak scale of the type I seesaw neutrino mass generation. After a brief introduction to the model, we derive the \(\mu-e\) conversing ratio at one-loop approximation, in which the running inside are W gauge boson or singly charged scalars accompanying with neutrinos, and neutral scalars with new leptons. We focus, mainly, on predictions of observable possibilities and constraints set on relevant couplings from the \(\mu-e\) conversion in nuclei.