Symmetry Of Modes Research Articles

Structural and optical investigations on LaGaO3 synthesis by sol–gel method along with a blue luminescence property

• LaGaO 3 perovoskite material has been successfully synthesized by a simple rout called sol gel method. • The efficiency of sol–gel methods to obtain pure phase of LaGaO3 was proved. • Raman reveals 9 bands that correspond to active optical-vibrational modes of orthorhombic symmetry that is in good agreement with XRD results. • A special emphasis is put on the photoluminescence properties of this material. Temperature-dependent PL, low-temperature analysis has been carried out. This work presents the preparation of Lanthanum Gallate peroveskite (LaGaO3) by sol–gel based Pechini method at low temperatures. The structural and optical properties of the elaborated material were investigated, by means of X-ray diffraction (XRD), Raman, UV–visible and Photoluminescence (PL) Spectroscopies. The XRD pattern showed a pure orthorhombic phase of LaGaO3 annealed at 600 °C. The orthorhombic symmetry was confirmed by Raman study. The band gap energy was estimated from UV–visible diffuse reflectance spectra to be 3.64 eV. Photoluminescence spectra of LaGaO3 showed two bands in blue region. For a complete understanding of the luminescence properties, a temperature-dependent PL analysis was studied. The temperature dependence for LaGaO3 sample revealed an S-shape behavior. The S-shape phenomenon and the variation of the FWHM values as a function of temperature were discussed. Finally, the thermal activation energy was calculated from the integrated PL intensity as a function of inverse temperature in orders to determinate the thermal stability of material.

Observation of Two-dimensional Isotropic Double Dirac Cones in the Electromagnetic Dispersion Relation

We report on the first experimental observation of two-dimensional isotropic double Dirac cones in the electromagnetic dispersion relation, which were materialized by the accidental degeneracy of E1- and E2-symmetric eigenmodes on the Γ point of photonic crystals. We fabricated triangular-lattice photonic crystal slabs of the C6v symmetry on silicon-on-insulator wafers by electron beam lithography and examined their dispersion relation by high-resolution angle-resolved reflection spectroscopy in the mid-infrared range. We observed the characteristic linear dispersion of the double Dirac cones together with the polarization selection rules derived from the mode symmetries. All these observations agreed with numerical calculation of the dispersion relation and reflection spectra by the finite element method.

Evaluation of entropy driven jet symmetry transitions

Here we determine whether entropy drives planar turbulent jets into round turbulent jets. Determining when a jet flow transitions from one symmetry to the next is an important but incompletely resolved problem. The constructal view argues that the transition between symmetries of jet flows is governed by the minimization or maximization of entropy. Here we explore whether entropy increases with the transition of a planar turbulent jet into a round turbulent jet and whether entropy maximization (or minimization) predicts the same location of symmetry transition as velocity matching. We find that entropy considerations presented do not predict this transition.

Observation of parity-time symmetry in time-division multiplexing pulsed optoelectronic oscillators within a single resonator

In recent years, parity-time (PT) symmetry in optoelectronic systems has been widely studied, due to its potential applications in lasers, sensors, topological networks, and other fields. In this paper, a time-division multiplexed pulsed optoelectronic oscillator (OEO) is proposed to study the dynamics of a PT symmetry system. Two microwave pulses are used to realize the PT symmetry in a single spatial resonator based on the temporal degrees of freedom. The gain and loss of the microwave pulses and the coupling coefficient between them can then be controlled. We first demonstrate the phase diagram from PT broken to PT symmetry in the OEO system. We theoretically prove that the perturbation of a coupling-induced phase shift larger than ( 2 π ) × 10 − 2 causes the disappearance of the PT symmetry. In this experiment, the perturbation is less than ( 2 π ) × 0.5 × 10 − 2 ; thus, the phase transition of PT symmetry is observed. In addition, multipairs of PT-symmetry pulses indicate that pulsed OEO could be used to implement complex non-Hermitian Hamilton systems. Therefore, it is confirmed that pulsed OEO is an excellent platform to explore the dynamics of PT symmetry and other non-Hermitian Hamiltonian systems.

Polarization-dependent reflection of I-WP minimal-surface-based photonic crystal.

Brilliantly colored butterflies and weevils are known to utilize photonic crystals for their coloration. Interestingly, the morphology of such crystals made of cuticle is based on triply periodic minimal surfaces such as gyroid and diamond surfaces. Recently, a different minimal-surface-based photonic crystal, the I-WP surface, was discovered inside the scale of a longhorn beetle. The letter I is derived from expressing the body center symmetry and WP is derived from a wrapped package. It was reported that the brilliant green color is produced by the photonic band gap existing along the [110] direction of this crystal. In this study, the polarization dependence of the reflection from this photonic crystal was investigated. A peculiar reflectance spectrum with two peaks was observed under the crossed polarizers. This characteristic is theoretically reproduced by calculating the reflectance from a finite-sized photonic crystal, and the spectral shape is explained based on the symmetry of the electromagnetic modes. In addition, inspired by this longhorn beetle, a photonic crystal structure consisting of colloidal particles is proposed, which has a similar polarization effect.

Fröhlich electron–phonon interaction Hamiltonian and potential distribution of a polar optical phonon mode in wurtzite nitride triangular nanowires

Polar optical phonon modes of wurtzite triangular nanowires (NWs) with three different cross sections, including the hemi-equilateral triangle (HET), the isosceles right triangle (IRT), and the equilateral triangle (ET), are deduced and analyzed using the dielectric continuum model. The exact and analytical phonon states of exactly confined (EC) modes in nitride NWs with HET, IRT, and ET cross sections are derived. The characteristic frequency of EC phonon modes in the triangular nitride NW systems is specified. Fröhlich electron–phonon interaction Hamiltonians in wurtzite NWs with three types of triangular cross sections are obtained. It is found from the numerical results that, among the three types of GaN NWs, the electron–phonon coupling of EC modes in NWs with an HET cross section is the weakest one, that in NWs with an ET cross section is the strongest one, and that in NWs with an IRT cross section is in the middle. The electrostatic potentials of EC modes in HET NWs are neither symmetric nor antisymmetric. The potential functions of EC modes in the ET NW structures have one (three) symmetric axis (axes) as the quantum numbers p and q take fractions (integers). The potential functions of EC modes in IRT NWs behave either symmetrically or anti-symmetrically, which are closely dependent on the parities of the quantum numbers p and q. With the increase of order-number of EC modes, the electron–phonon coupling becomes weaker and weaker. This reveals that cross-sectional morphology of quantum structures has an important influence on the symmetries of phonon modes and electron–phonon coupling strengths in low-dimensional quantum systems.

Cerium metal oxidation studied by IR reflection-absorption and Raman scattering spectroscopies

Oxidation of cerium metal is a complex process which is strongly affected by the presence of water vapor in the oxidative atmosphere. Here, we explore, by means of infrared reflection-absorption spectroscopy (IRRAS) and Raman scattering spectroscopies, thin oxide films, formed on cerium metal during oxidation, under dry vs ambient (humid) air conditions (∼0.2% and ∼50% relative humidities, respectively) and compare them with a thin film of CeO2 deposited on a Si substrate. Complementary analysis of the thin films using x-ray diffraction and focused ion beam-scanning electron microscopy enables the correlation between their structure and spectroscopic characterizations. The initial oxidation of cerium metal results in the formation of highly sub-stoichiometric CeO2−x . Under dry air conditions, a major fraction of that oxide reacts with oxygen to form CeO∼2, which is spectroscopically detected by Raman scattering F 2g symmetry mode and by IRAAS F 1u symmetry mode, splitted into doubly-degenerate transverse optic and mono-degenerate longitudinally optic (LO) modes. In contrast, under ambient (humid) conditions, the oxide formed is more heterogenous, as the reaction of CeO2−x diverges towards the dominant formation of Ce(OH)3. Prior to the spectral emergence of Ce(OH)3, hydrogen ions incorporate into the highly sub-stoichiometric oxide, as manifested by Ce–H local vibrational mode detected in the Raman spectrum. The spectroscopic response of the thin oxide layer thus formed is more complex; particularly noted is the absence of the LO mode. It is attributed to the high density of microstructural and compositional defects in the oxide layer, which results in a heterogenous dielectric nature of the thin film, far from being representable by a single phase of CeO∼2.

Low‐Frequency Phonon Modes in Layered Silver‐Bismuth Double Perovskites: Symmetry, Polarity, and Relation to Phase Transitions

AbstractMetal‐halide perovskites (PSKs) are emergent materials for a large range of applications, and the layered double PSK architectures vastly enrich the opportunities to design their composition, structural properties, and optoelectronic behavior. The stability, crystal phase, and electronic bandgap depend strongly on the bonds and distortions of the octahedra lattice that are at the origin of the vibrational spectrum of these materials. This work investigates the structural dynamics of flakes of exfoliated layered Ag‐Bi bromide double PSKs by angle‐dependent polarized Raman spectroscopy and density functional theory modeling. The well‐defined orientation of the inorganic octahedra lattice with respect to the light polarization allows to correlate the angle‐dependent intensity of the Raman signal to the directionality and symmetry of the phonon modes. Low‐frequency vibrations are revealed for which a detailed microscopic and group theory assignment of the Raman modes is provided. The temperature‐dependent measurements across the phase transitions show marked changes in the phonon frequencies, reveal soft modes, and help to distinguish first from second‐order transitions as well as to determine their transition temperature. This provides highly valuable insights to improve the properties of this class of Pb‐free PSKs for applications in energy harvesting and optoelectronics.

Lattice Dynamics of Bi2Те3 and Vibrational Modes in Raman Scattering of Topological Insulators MnBi2Te4·n(Bi2Te3)

This work is devoted to the experimental study and symmetry analysis of the Raman-active vibration modes in MnBi2Te4·n(Bi2Te3) van der Waals topological insulators, where n is the number of Te–Bi–Te–Bi–Te quintuple layers between two neighboring Te–Bi–Te–Mn–Te–Bi–Te septuple layers. Confocal Raman spectroscopy is applied to study Raman spectra of crystal structures with n = 0,1,2,3,4,5,6, and ∞. The experimental frequencies of vibration modes of the same symmetry in the structures with different n are compared. The lattice dynamics of free-standing one, three, and four quintuple layers, as well as of bulk Bi2Те3(n = infty ) and MnBi2Te4(n = 0), is considered theoretically. Vibrational modes of the last two systems have the same symmetry, but different displacement fields. These fields in the case of a Raman-active mode do not contain displacements of manganese atoms for any finite n. It is shown that two vibrational modes in the low-frequency region of the spectrum (35–70 cm–1) of structures with n = 1,;2,;3,;4,;5, and 6 practically correspond to the lattice dynamics of n free quintuple Bi2Те3 layers. For this reason, the remaining two vibration modes, which are observed in the high-frequency region of the spectrum (100–140 cm–1) and are experimentally indistinguishable in the sense of belonging to quintuple or septuple layer or to both layers simultaneously, should also be assigned to vibrations in quintuple layers under immobile atoms of septuple layers.

Intrinsic Spin-Momentum Dynamics of Surface Electromagnetic Waves in Dispersive Interfaces.

Intrinsic spin-momentum locking is an inherent property of surface electromagnetic fields and its study has led to the discovery of phenomena such as unidirectional guided waves and photonic spin lattices. Previously, dispersion was ignored in spin-momentum locking, resulting in anomalies contradicting the apparent physical reality. Here, we formulate four dispersive spin-momentum equations, revealing in theory that transverse spin is locked with kinetic momentum. Moreover, in dispersive metal or magnetic materials spin-momentum locking obeys the left-hand screw rule. In addition to dispersion, structural features can affect substantially this locking. Remarkably, an extraordinary spin originating from coupling polarization ellipticities is uncovered that depends on the symmetry of the field modes. We further identify the properties of this spin-momentum locking with diverse photonic topological lattices by engineering their rotational symmetry akin to that in solid-state physics. The concept of spin-momentum locking based on photon flow properties translates easily to other classical wave fields.

Hidden conformal symmetries from Killing towers with an application to large-D/CFT

We generalize the notion of hidden conformal symmetry in Kerr/CFT to Kerr-(A)dS black holes in arbitrary dimensions. We build the SL(2, R) generators directly from the Killing tower, whose Killing tensors and Killing vectors enforce the separability of the equations of motion. Our construction amounts to an explicit relationship between hidden conformal symmetries and Killing tensors: we use the Killing tower to build a novel tensor equation connecting the SL(2,R) Casimir with the radial Klein-Gordon operator. For asymptotically flat black holes in four and five dimensions we recover previously known results that were obtained using the ``near-region'' limit and the monodromy method. We then perform a monodromy evaluation of the Klein-Gordon scalar wave equation for all Kerr-(A)dS black holes, finding explicit forms for the zero mode symmetry generators. We also extend this analysis to the large-dimensional Schwarzschild black hole as a step towards buliding a Large-D/CFT correspondence.

Disorder- driven gradual transition of the continuous symmetry- breaking phase transition

We study the influence of random anisotropy type quenched disorder on the phase behavior of the system, which exhibits in undistorted case the 2nd order continuous symmetry breaking phase transition. Invoking the central limit theorem we express the free energy of the system in terms of the order parameter η and the characteristic length ξ of the gauge field ϕ. The latter exhibits the Goldstone fluctuation mode and is consequently extremely susceptible to the imposed disorder. In case of negligible distribution width ΔT of the local transition temperatures the disorder converts the 2nd order transition into a discontinuous one for W<WC, where Wrepresents the disorder strength. Above the critical disorder strength WC the transition becomes gradual. However for the finite width ΔT the transition becomes gradual for any W>0. We demonstrate that for large enough values of ΔT the system behavior is dominated by the distribution of temperatures, while the details of the random field interaction term play a secondary role. The influence of distribution of local (quasi) phase transitions is in most theoretical approaches dealing with randomly perturbed systems neglected from the outset.

Experimental observation of partial parity-time symmetry and its phase transition with a laser-driven cesium atomic gas

Realization and manipulation of parity-time (PT) symmetry in multidimensional systems are highly desirable for exploring nontrivial physics and uncovering exotic phenomena in non-Hermitian systems. Here, we report the first experimental observation of partial PT (pPT) symmetry in a cesium atomic gas coupled with laser fields, where a two-dimensional pPT-symmetric optical potential for probe laser beam is created. A transition of the pPT symmetry from an unbroken phase to a broken one is observed through changing the beam-waist ratio of the control and probe laser beams, and the domains of unbroken, broken, and non-pPT phases are also discriminated unambiguously. Moreover, we develop a technique to precisely determine the location of the exceptional point of the pPT symmetry breaking by measuring the asymmetry degree of the probe-beam intensity distribution. The findings reported here pave the way for controlling multidimensional laser beams in non-Hermitian systems via laser-induced atomic coherence, and have potential applications for designing new types of light amplifiers and attenuators

Polarized Raman Response of Two-Dimensional Quasiperiodic Antiferromagnets: Configuration-Interaction versus Green’s Function Approaches

We study Raman response of Heisenberg antiferromagnets on the C5v Penrose and C8v Ammann–Beenker lattices within and beyond the Loudon–Fleury second-order perturbation scheme intending to explore optical features peculiar to quasiperiodic magnets. Within the Loudon–Fleury mechanism, we find one and only Raman-active mode of E2 symmetry without any dependence on linear incident and scattered polarizations. Beyond the Loudon–Fleury mechanism, two more symmetry species A1 and A2 are activated via dynamic ring exchange and chiral spin fluctuations, respectively, which can be extracted by the use of circular as well as linear polarizations. We employ Green’s functions on one hand and configuration-interaction wavefunctions on the other hand to calculate the multimagnon contributions to inelastic light scatterings. Demonstrating the great advantage of the configuration-interaction scheme, we reveal that a major portion of the Shastry–Shraiman fourth-order Raman intensity is mediated by multimagnon fluctuations.

Low-energy electronic structure of perovskite and Ruddlesden-Popper semiconductors in the Ba-Zr-S system probed by bond-selective polarized x-ray absorption spectroscopy, infrared reflectivity, and Raman scattering

Chalcogenides in perovskite and the related layered Ruddlesden-Popper crystal structures (chalcogenide perovskites for brevity) are an exciting family of semiconductors but remain experimentally little studied. Chalcogenide perovskites share crystal structures and some physical properties with ionic compounds such as oxide and halide perovskites, but the metal-chalcogen bonds responsible for semiconducting behavior are substantially more covalent than in these more-studied perovskites. Here, we use complementary experimental and theoretical methods to study how the mixed ionic-covalent Zr-S bonds support the electronic structure and physical properties of perovskite ${\mathrm{BaZrS}}_{3}$ and Ruddlesden-Popper ${\mathrm{Ba}}_{3}{\mathrm{Zr}}_{2}{\mathrm{S}}_{7}$. We apply theoretical methods to assign features of experimentally measured x-ray absorption spectroscopy (XAS) to particular orbital transitions, enabling a clear physical interpretation of angle-dependent, polarized XAS data measured on single-crystal samples, and an atomistic view of the covalent bonding network that facilitates charge transport. Polarized Raman measurements identify signatures of crystalline anisotropy in ${\mathrm{Ba}}_{3}{\mathrm{Zr}}_{2}{\mathrm{S}}_{7}$ and enable the first assignments of mode symmetry in this material. Infrared reflectivity reveals electronic transport properties that augur well for the use of chalcogenide perovskites in optoelectronic and energy-conversion technologies.

Curved domain-wall fermions

Abstract We consider fermion systems on a square lattice with a mass term having a curved domain-wall. Like conventional flat domain-wall fermions, massless and chiral edge states appear on the wall. In the cases of S1 and S2 domain-walls embedded into flat hypercubic lattices, we find that these edge modes feel gravity through the induced spin or spinc connections. The gravitational effect is encoded in the Dirac eigenvalue spectrum as a gap from zero. In the standard continuum extrapolation of the square lattice, we find good agreement with the analytic prediction in the continuum theory. We also find that the rotational symmetry of the edge modes is automatically recovered in the continuum limit. Subject Index B38

Multicritical point of the three-dimensional Z2 gauge Higgs model

We investigate the multicritical behavior of the three-dimensional ${\mathbb{Z}}_{2}$ gauge Higgs model at the multicritical point (MCP) of its phase diagram, where one first-order transition line and two continuous Ising-like transition lines meet. The duality properties of the model determine some features of the multicritical behavior at the MCP located along the self-dual line. Moreover, we argue that the system develops a multicritical $XY$ behavior at the MCP, which is controlled by the stable $XY$ fixed point of the three-dimensional multicritical Landau-Ginzburg-Wilson field theory with two competing scalar fields associated with the continuous ${\mathbb{Z}}_{2}$ transition lines meeting at the MCP. This implies an effective enlargement of the symmetry of the multicritical modes at the MCP to the continuous group O(2). We also provide numerical results to support the multicritical $XY$ scenario.

Interplay of band occupation, localization, and polaron renormalization for electron transport in molecular crystals: Naphthalene as a case study

Understanding electronic properties and charge transport in organic semiconductors is important for improving organic electronic materials and devices. Here we investigate the impact of electronic band occupation, charge-carrier concentration, and symmetry of phonon modes on the electron mobility in naphthalene crystals for various temperatures. Our theoretical approach is based on the description of the electron-phonon coupling (EPC), where the coupling to low-frequency modes is treated by an effective vibrational disorder potential with local and nonlocal contributions and the coupling to high-frequency modes is included by a polaron treatment. Surprisingly, the coupling to high-frequency modes leads to an increase in the mobility in presence of the low-frequency modes, which is explained by localization and band occupation effects that further depend on the carrier density. A symmetry analysis sheds additional light on the energy dependence of the EPC, which is important to describe transport properties as a function of charge density and temperature. We also find that coupling to low-frequency phonons together with band occupation effects can lead to a vanishing slope of the mobility versus temperature that is known from experiments.

Cation distribution and site occupancy of nanoscale Cu2+-Er3+ substituted strontium hexaferrites via Raman and Mössbauer spectroscopy

In this research, we report on the cation distribution and site occupancy of Cu2+ and Er3+ ions in the hexagonal lattice of M-type strontium hexagonal ferrites with chemical composition Sr1-xCuxFe12-yEryO19 (x=0.0, 0.1, 0.2, and y=0.0, 0.4, 0.5) fabricated using sol-gel autocombustion technique. Raman analysis of the synthesized samples was conducted based on the group theory analysis of hexagonal ferrites based on the D6h symmetry. The Raman active modes based on the mode assignment and symmetry and were typical of M-type hexaferrite. Mössbauer spectroscopy shows the density of the s electron cloud at the 12k, 4f2, and 4f1 is affected by Cu2+-Er3+ substitution which indicate that all the five sexets originate from Fe3+ ion with high spin and that Er3+ ion (with d10 orbitals) occupies Fe3+ ion position at 12k, 4f2, 2a, and 2b sites in different proportion based on the Ligand theory.

Computation of transverse-electric polarized optical eigenstates in dielectric systems based on perfectly matched layer.

The optical resonance problem is an eigenproblem with an exponential-growing boundary condition imposed at infinity. This inconvenient boundary condition is caused by the openness of dielectric systems, and it is explained as the effect of retardation. Following our previous work [Jiang and Xiang, Phys. Rev. A 102, 053704 (2020)2469-992610.1103/PhysRevA.102.053704] where a perfectly-matched-layer method is developed for transverse-magnetic modes, we extend the method in this paper to transverse-electric modes and apply it to study mode symmetries. The method is implemented by introducing an extra layer to absorb outgoing waves at the far-field region, based on which we derive a damping eigenequation. A finite-element-based numerical approach is developed to compute the eigenstates of the damping eigenproblem. Our method is validated by application to the circular cavity and comparison with exact analytical solutions of whispering-gallery modes. We apply the method to the elliptic cavity to study the even- and odd-symmetric optical eigenstates. We also apply the method to trace the evolution of a pair of degenerate eigenstates with cavity shapes smoothly deformed from circles to squares.