Lattice Symmetry Research Articles

A semiclassical model for charge transfer along ion chains in silicates

It has been observed in fossil tracks and experiments in the layered silicate mica muscovite the transport of charge through the cation layers sandwiched between the layers of tetrahedra-octahedra-tetrahedra. A classical model for the propagation of anharmonic vibrations along the cation chains has been proposed based on first principles and empirical functions. In that model, several propagating entities have been found as kinks or crowdions and breathers, both with or without wings, the latter for specific velocities and energies. Crowdions are equivalent to moving interstitials and transport electric charge if the moving particle is an ion, but they also imply the movement of mass, which was not observed in the experiments. Breathers, being just vibrational entities, do not transport charge. In this work, we present a semiclassical model obtained by adding a quantum particle, electron or hole to the previous model. We present the construction of the model based on the physics of the system. In particular, the strongly nonlinear vibronic interaction between the nuclei and the extra electron or hole is essential to explain the localized charge transport, which is not compatible with the adiabatic approximation. The formation of vibrational localized charge carriers breaks the lattice symmetry group in a similar fashion to the Jahn-Teller Effect, providing a new stable dynamical state. We study the properties and the coherence of the model through numerical simulations from initial conditions obtained by tail analysis and other means. We observe that although the charge spreads from an initial localization in a lattice at equilibrium, it can be confined basically to a single particle when coupled to a chaotic quasiperiodic breather. This is coherent with the observation that experiments imply that a population of charge is formed due to the decay of potassium unstable isotopes.

Reconfigurable (4, 62) and (4, 82) Archimedean plasma photonic crystals in dielectric barrier discharge

Archimedean photonic crystal has become a research area of great interest due to its various unique properties. Here, we experimentally demonstrate the realization of reconfigurable (4, 62) and (4, 82) Archimedean plasma photonic crystals (APPCs) by use of dielectric barrier discharges in air. Dynamical control on both the macrostructures including the lattice symmetry and the crystal orientation, and the microstructures including the fine structures of scattering elements has been achieved. The formation mechanisms of APPCs are studied by time-resolved measurements together with numerical simulations. Large omnidirectional band gaps of APPCs have been obtained. The tunable topology of APPCs may offer new opportunities for fabricating multi-functional and highly-integrated microwave devices.

Hydrogen diffusivity in dislocation, grain boundary, and lattice of α-Fe based on electrochemical hydrogen permeation experiments and Maxwell-Garnett calculations

We elucidate the hydrogen diffusivity in α-Fe with different dislocation densities, grain sizes, and textures obtained by different annealing after cold rolling based on electrochemical hydrogen permeation experiments and Maxwell-Garnett calculations. A unique inflection point was found to calculate the hydrogen diffusion coefficient, which reflects the threshold from accelerating to decelerating hydrogen diffusion. Texture has significant influences on hydrogen diffusion, and hydrogen atoms in α-Fe lattice diffuse along <111> direction much slower than in other directions. Based on Maxwell-Garnett calculations, the hydrogen diffusion coefficients of dislocations, grain boundaries, and α-Fe isotropic lattice are 4.4×10−4, 2.3×10−4, and 2.5×10−10 m2/s, respectively.

Negative elastic wave refraction and focusing regulation of single-phase solid phononic crystals

This paper presents the design of a single-phase solid phononic crystal (PnC) structure featuring a regular hexagonal perforation pattern. The structure manifests three negative refraction bands, encompassing one for transverse waves and two for longitudinal waves, thereby enabling simultaneous control of shear and longitudinal waves. Due to the high symmetry of the triangular lattice, the equal frequency curves corresponding to the negative refraction band approach circular shapes, suggesting a nearly isotropic negative refraction effect. This negative refraction effect is achieved through specific mass resonance modes closely related to the porous structure designed in this paper. Initially, we analyze the band structure of the PnC, followed by designing the PnC plate structure to achieve negative refraction control for transverse waves at a frequency of 32.4 kHz, with a negative refraction index of −1. Additionally, negative refraction control for longitudinal waves is attained at frequencies of 44 and 64.54 kHz. Subsequently, we scrutinize the influence of various conditions on negative refraction, including different structural parameters, incident angles, and operating frequencies, while verifying the robustness of the designed phonon crystal structure. Leveraging the negative refraction characteristics of the structure, we construct an elastic wave lens to achieve perfect imaging of shear and longitudinal waves. Finally, employing finite element simulation and analyzing focusing imaging characteristics with different source positions, we validate that the results closely align with theoretical expectations. The solid PnC structure designed in this study holds significant potential for applications in the fields of elastic wave imaging.

Higher categorical symmetries and gauging in two-dimensional spin systems

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries. Our framework relies on an approach to dualities whereby dual quantum lattice models only differ in a choice of module 2-category over some input fusion 2-category. Given an arbitrary two-dimensional spin system with an ordinary symmetry, we explain how to perform the (twisted) gauging of any of its sub-symmetries. We then demonstrate that the resulting model has a symmetry structure encoded into the Morita dual of the input fusion 2-category with respect to the corresponding module 2-category. We exemplify this approach by specialising to certain finite group generalisations of the transverse-field Ising model, for which we explicitly define lattice symmetry operators organised into fusion 2-categories of higher representations of higher groups.

Tolerance and breakdown of topological protection in a disordered waveguide

We consider a disordered waveguide consisting of trivial dielectric and non-trivial magnetically anisotropic material. A topologically protected edge mode appears owing to the broken time-reversal symmetry of the non-trivial lattice. While the edge mode maintains under other position and radius disorders, the protection is immediately broken by applying a radius disorder to the non-trivial lattice. This breakdown originates from donor and acceptor modes occupying the topological bandgap. Furthermore, via the calculation of the Bott index, we show that Anderson localization occurs as a metal conducting gap changes to a topological gap along with increasing disorders.

Elastic and anelastic behavior associated with magnetic ordering in the skyrmion host Cu2OSeO3

Magnetic ordering in Cu2OSeO3 occurs without any detectable changes in the lattice symmetry but involves significant coupling with strain. The strain coupling effects in Cu2OSeO3 have been investigated with a focus on the skyrmion lattice by examining elastic and anelastic properties. Resonant ultrasound spectroscopy has been used to measure these properties of a Cu2OSeO3 single crystal as a function of temperature and magnetic field. On heating, the skyrmion phase has been characterized by slightly softer elasticity compared to the helical phase. However, there were no obvious anomalies in elastic and anelastic properties associated with the boundary of the stability field of the skyrmion lattice. Evolution of elastic properties with magnetic field, passing through the stability field of the skyrmion lattice, showed a characteristic pattern of a glassy state, where an equilibrium state is never reached. These imply that coupling of the skyrmions with strain is extremely weak in Cu2OSeO3, leading to glassy or liquidlike behavior of skyrmions. Three Debye-like loss peaks were observed near ∼40, ∼50, and ∼60K. The relaxation mechanism for the 40 K loss peak has been found to have a single relaxation time. Overlapping acoustic loss peaks in the temperature interval ∼50–62K suggest that the magnetic transitions with variable temperature in this temperature range involve freezing of some dynamic aspect(s) of the magnetic structure with an activation energy of ∼0.1–0.15 eV. Published by the American Physical Society 2024

Delocalized nonlinear vibrational modes and discrete breathers in a body centered cubic lattice

Body centered cubic (bcc) lattice with nearest and next-nearest interactions described by the β-FPUT interatomic potential is considered. Exact dynamical solutions in the form of zone-boundary delocalized nonlinear vibrational modes (DNVMs) are analyzed. 31 such solutions are revealed from the analysis of only the symmetry of the bcc lattice. Frequency response of DNVMs for the case of soft- and hard-type anharmonicity is calculated. In the case of hard-type anharmonicity, four DNVMs have frequencies bifurcating from the upper edge of the phonon spectrum and growing with the amplitude. Various quasi-discrete breathers are obtained by superimposing localizing functions upon these DNVMs. Our work demonstrates a practical approach to finding quasi-discrete breathers in higher-dimensional lattices. The obtained spatially localized long-lived vibrational modes inspire the search for various discrete breathers in bcc metals.

Strain Engineering of Twisted Bilayer Graphene: The Rise of Strain-Twistronics.

The layer-by-layer stacked van der Waals structures (termed vdW hetero/homostructures) offer a new paradigm for materials design-their physical properties can be tuned by the vertical stacking sequence as well as by adding a mechanical twist, stretch, and hydrostatic pressure to the atomic structure. In particular, simple twisting and stacking of two layers of graphene can form a uniform and ordered Moiré superlattice, which can effectively modulate the electrons of graphene layers and lead to the discovery of unconventional superconductivity and strong correlations. However, the twist angle of twisted bilayer graphene (tBLG) is almost unchangeable once the interlayer stacking is determined, while applying mechanical elastic strain provides an alternative way to deeply regulate the electronic structure by controlling the lattice spacing and symmetry. In this review, diverse experimental advances are introduced in straining tBLG by in-plane and out-of-plane modes, followed by the characterizations and calculations toward quantitatively tuning the strain-engineered electronic structures. It is further discussed that the structural relaxation in strained Moiré superlattice and its influence on electronic structures. Finally, the conclusion entails prospects for opportunities of strained twisted 2D materials, discussions on existing challenges, and an outlook on the intriguing emerging field, namely "strain-twistronics".

Simultaneously enhanced of energy storage and energy harvesting performances of [(Bi0.5Na0.5)TiO3–BaTiO3] ceramics by addition of SrTiO3

As is well known, relaxor dielectrics are characterized by high energy storage efficiency (η), while high recoverable energy storage density (Wrec) can be achieved by anti-ferroelectric ceramics. Herein, our approach is to find relaxor- anti-ferroelectric coexistence phases of (Bi0.5Na0.5)TiO3- BaTiO3 ceramics for achieving high performance in energy storage and energy harvesting as well. Therefore, [(0.9-x) ( Bi0.5Na0.5)TiO3-xSrTiO3-0.1BaTiO3] (abbreviation (0.9-x) NBT-0.1BT-xST) (0.0 ≤ x ≤ 0.4) were synthesized via the solid-state reaction route in air. The tolerance factor (τ) increased from 0.9901 to 0.9998 when ST-content increased from 0.0 to 0.4, indicating an increase in crystal lattice symmetry. The FT-IR de-convolution vibration modes shown in the TiO6 octahedra exhibit two peaks at ∼550 and 650 cm−1, which indicate present coexistence phases of the crystal structure. Ferroelectric to relaxor phase crossover has been detected by the addition of ST with the present anti-ferroelectric phase in particular dopant ST = 0.2. The increasing into the diffused phase transition (γ) is signified by enhancement of the relaxor degree of NBT-BT at high content of ST. The rapidly suppressed remnant polarization (Pr) at high content of ST is due to substitute iso-valence (Sr2+) by tri-valence (Bi3+) and mono-valence (Na1+). Ultrahigh Wrec = 1.13 J/ cm3 with excellent η = 92.62% were obtained at ST = 0.3 at low electric field (E = 110 kV cm−1). A remarkable response of the strain with a high converse piezoelectric coefficient ( d33* = 390.47 pm V−1) at ST = 0.2 was obtained due to decreasing the non-revisable 180° domain switching. Based on the obtained results, the addition of ST to NBT-BT ceramics can provide a head start in the implementation of ceramic capacitors for potential effective into energy harvesting and energy storage applications.

Extending intergranular normal-stress distributions using symmetries of linear-elastic polycrystalline materials

Intergranular normal stresses (INS) are critical in the initiation and evolution of grain boundary damage in polycrystalline materials. To model the effects of such microstructural damage on a macroscopic scale, knowledge of INS is usually required statistically at each representative volume element subjected to various loading conditions. However, calculating INS distributions for different stress states can be cumbersome and time-consuming. This study proposes a new method to extend the existing INS distributions to arbitrary loading conditions using the symmetries of a polycrystalline material composed of randomly oriented linear-elastic grains with arbitrary lattice symmetry. The method relies on a fact that INS distributions can be accurately reproduced from the first (typically) ten statistical moments, which depend trivially on just three stress invariants and a few material invariants due to assumed isotropy and material linearity of the polycrystalline model. While these material invariants are complex averages, they can be extracted numerically from a few existing INS distributions and tabulated for later use. Practically, only three such INS distributions at properly selected loadings are required to provide all relevant material invariants for the first 11 statistical moments, which can then be used to reconstruct the INS distribution for arbitrary loading conditions. The proposed approach is demonstrated to be accurate and feasible for an arbitrarily selected linear-elastic material under various loading conditions.

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

We study ’t Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the “anomaly cocycle” using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group H^3(G,U(1)) × H^2(G,U(1))H3(G,U(1))×H2(G,U(1)). The first factor captures the anomaly in the internal symmetry group G, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving G and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

Generalized Boundary Integral Equation Method for Boundary Value Problems of Two-D Isotropic Lattice Laplacian

Generalized Boundary Integral Equation Method for Boundary Value Problems of Two-D Isotropic Lattice Laplacian

Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns.

We study hyperuniform properties in various two-dimensional periodic and quasiperiodic point patterns. Using the histogram of the two-point distances, we develop an efficient method to calculate the hyperuniformity order metric, which quantifies the regularity of the hyperuniform point patterns. The results are compared with those calculated with the conventional running average method. To discuss how the lattice symmetry affects the order metric, we treat the trellis and Shastry-Sutherland lattices with the same point density as examples of periodic lattices, and Stampfli hexagonal and dodecagonal quasiperiodic tilings with the same point density as examples of quasiperiodic tilings. It is found that the order metric for the Shastry-Sutherland lattice (Stampfli dodecagonal tilings) is smaller than the other in the periodic (quasiperiodic) tiling, meaning that the order metric is deeply related to the lattice symmetry. Namely, the point pattern with higher symmetry is characterized by the smaller order metric when their point densities are identical. Order metrics for several other quasiperiodic tilings are also calculated.

Robustness of magnetocrystalline anisotropy and coercivity in Fe–Co–B

As a potential candidate for critical chemical element free permanent magnet, (Fe0.7Co0.3)2B, shows promising intrinsic magnetic properties, including large magnetization, high Curie temperature and moderate magnetocrystalline anisotropy (MCA). Still, the coercivity that has been achieved is relatively low. To understand and improve coercivity, we study the robustness of MCA related to the fluctuation of chemical composition and the structural distortion and its effect on coercivity in (Fe0.7Co0.3)2B from first principles DFT (density functional theory) calculation and micromagnetic simulation. A fluctuation of cobalt content of 10%, or 1% isotropic lattice strain, or 2% tetragonal distortion reduces MCA energy up to 30%. By considering randomly distributed local MCA energy reduction up to 30%, the calculated coercivity of anisotropic bulk magnets reduced from 3.6 kOe to 2.2 kOe. Rational microstructure design, such as grain size refinement and development of strong crystal texture of MCA easy-axis (i.e., degree of alignment for (Fe0.7Co0.3)2B grains), can enhance coercivity and mitigate the effect of local MCA reduction. In addition to acceptable intrinsic magnetic properties, the promising hard magnetic phase needs good MCA robustness to facilitate the development of practical magnets.

Charge state-dependent symmetry breaking of atomic defects in transition metal dichalcogenides

The functionality of atomic quantum emitters is intrinsically linked to their host lattice coordination. Structural distortions that spontaneously break the lattice symmetry strongly impact their optical emission properties and spin-photon interface. Here we report on the direct imaging of charge state-dependent symmetry breaking of two prototypical atomic quantum emitters in mono- and bilayer MoS2 by scanning tunneling microscopy (STM) and non-contact atomic force microscopy (nc-AFM). By changing the built-in substrate chemical potential, different charge states of sulfur vacancies (VacS) and substitutional rhenium dopants (ReMo) can be stabilized. VacS−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathrm{Vac}}_{{{{{{{{\\rm{S}}}}}}}}}^{-1}$$\\end{document} as well as ReMo0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathrm{Re}}}_{{{{{{{{\\rm{Mo}}}}}}}}}^{0}$$\\end{document} and ReMo−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathrm{Re}}_{{\\rm{Mo}}}^{-1}$$\\end{document} exhibit local lattice distortions and symmetry-broken defect orbitals attributed to a Jahn-Teller effect (JTE) and pseudo-JTE, respectively. By mapping the electronic and geometric structure of single point defects, we disentangle the effects of spatial averaging, charge multistability, configurational dynamics, and external perturbations that often mask the presence of local symmetry breaking.

Angle-Resolved Optical Characterization of a Plasmonic Triangular Array of Elliptical Holes in a Gold Layer

Plasmonic arrays are grating-like structures able to couple an incoming electromagnetic field into either localized or propagating surface plasmonic modes. A triangular array of elliptical holes in a gold layer were realized resorting to displacement Talbot lithography. Scanning electron microscopy was used to evaluate the geometrical features and finite time domain simulations were performed to verify the consistency of the design. The optical response was characterized by angle-resolved reflectance and transmittance measurements. The results demonstrate the good quality and uniformity of the array. Furthermore, the study on the dependence of the optical response on both the hexagonal lattice and the elliptical hole-defined symmetry properties was conducted allowing the distinction of their effects on both the localized and propagating plasmonic modes. The results indicate that the localized component of the plasmonic modes is mainly affected by the elliptical shape, while the propagating part is influenced by the hexagonal lattice symmetry.

Synthesis, X-ray diffraction and dielectric studies of the ceramic samples (1−x)BaTiO3⋅xPbFe2/3W1/3O3 (0≤x≤1) system

Ceramic samples of the ([Formula: see text])BaTiO3⋅xPbFe[Formula: see text]W[Formula: see text]O3, [Formula: see text] (([Formula: see text])BT⋅xPFW) system were synthesized by solid-state reactions method. The samples were characterized by X-ray diffraction (XRD) and dielectric studies, as well as by the measurements of the thermally stimulated depolarization currents (TSDC). It was found that the predominant phase in the samples is presented by the (Ba[Formula: see text]Pbx)(Ti[Formula: see text]Fe[Formula: see text]W[Formula: see text])O3 solid solutions with a perovskite structure, herewith the samples with [Formula: see text] are practically single-phase, and with [Formula: see text] contain the impurity phase BaWO4 (up to 15 mass.% at [Formula: see text]–0.90). Information has been obtained about the changes in the structural and dielectric characteristics of the solid solutions with the change of their composition. It is established that the solid solutions crystal lattice symmetry at 296 K changes from tetragonal at [Formula: see text] to cubic at [Formula: see text]. An increase in the PFW content in solid solutions causes a gradual change in their properties from ferroelectric at [Formula: see text] to relaxor ferroelectric at [Formula: see text], and then to properties similar to those of the dipole glass with weak or zero correlation between dipoles at [Formula: see text]. The addition of BT to PFW leads to rather quick degradation of the relaxor ferroelectric properties of PFW in the region [Formula: see text]–1.0.

Manifestation of the hexatic phase in confined two-dimensional systems with circular symmetry

Quasi-two-dimensional systems play an important role in the manufacture of various devices for the needs of nanoelectronics. Obviously, the functional efficiency of such systems depends on their structure, which can change during phase transitions under the influence of external conditions (for example, temperature). Until now, the main attention has been focused on the search for signals of phase transitions in continuous two-dimensional systems. One of the central issues is the analysis of the conditions for the nucleation of the hexatic phase in such systems, which is accompanied by the appearance of defects in the Wigner crystalline phase at a certain temperature. However, both practical and fundamental questions arise about the critical number of electrons at which the symmetry of the crystal lattice in the system under consideration will begin to break and, consequently, the nucleation of defects will start. The dependences of the orientational order parameter and the correlation function, which characterize topological phase transitions, as functions of the number of particles at zero temperature have been studied. The calculation results allows us to establish the precursors of the phase transition from the hexagonal phase to the hexatic one for N = 92, 136, 187, considered as an example.

Kitaev-Heisenberg model on the star lattice: From chiral Majorana fermions to chiral triplons

The interplay of frustrated interactions and lattice geometry can lead to a variety of exotic quantum phases. Here we unearth a particularly rich phase diagram of the Kitaev-Heisenberg model on the star lattice, a triangle decorated honeycomb lattice breaking sublattice symmetry. In the antiferromagnetic regime, the interplay of Heisenberg coupling and geometric frustration leads to the formation of valence bond solid (VBS) phases—a singlet VBS and a bond selective triplet VBS stabilized by the Kitaev exchange. We show that the ratio of the Kitaev versus Heisenberg exchange tunes between these VBS phases and chiral quantum spin-liquid regimes. Remarkably, the VBS phases host a whole variety of chiral triplon excitations with high Chern numbers in the presence of a weak magnetic field. We discuss our results in light of a recently synthesized star lattice material and other decorated lattice systems. Published by the American Physical Society 2024