Original Symmetry Research Articles

Imaging two-dimensional generalized Wigner crystals.

The Wigner crystal1 has fascinated condensed matter physicists for nearly 90 years2-14. Signatures of two-dimensional (2D) Wigner crystals were first observed in 2D electron gases under high magnetic field2-4, and recently reported in transition metal dichalcogenide moiré superlattices6-9. Direct observation of the 2D Wigner crystal lattice in real space, however, has remained an outstanding challenge. Conventional scanning tunnelling microscopy (STM) has sufficient spatial resolution but induces perturbations that can potentially alter this fragile state. Here we demonstrate real-space imaging of 2D Wigner crystals in WSe2/WS2 moiré heterostructures using a specially designed non-invasive STM spectroscopy technique. This employs a graphene sensing layer held close to the WSe2/WS2 moiré superlattice. Local STM tunnel current into the graphene layer is modulated by the underlying Wigner crystal electron lattice in the WSe2/WS2 heterostructure. Different Wigner crystal lattice configurations at fractional electron fillings of n = 1/3, 1/2 and 2/3, where n is the electron number per site, are directly visualized. The n = 1/3 and n = 2/3 Wigner crystals exhibit triangular and honeycomb lattices, respectively, to minimize nearest-neighbour occupations. The n = 1/2 state spontaneously breaks the original C3 symmetry and forms a stripe phase. Our study lays a solid foundation for understanding Wigner crystal states in WSe2/WS2 moiré heterostructures and provides an approach that is generally applicable for imaging novel correlated electron lattices in other systems.

Stability of [formula omitted]-dimensional gravastars with variable equation of state

In this paper, we are interested to explore stable configurations of d-dimensional gravastars constructed from the interior d-dimensional de Sitter and exterior d-dimensional Schwarzschild/Reissner–Nordström (de Sitter) black holes through cut and paste approach. We consider the linearized radial perturbation preserving the original symmetries to explore their stability by using three different types of matter distributions. The resulting frameworks represent unstable structures for barotropic, Chaplygin, and phantomlike models for every considered choice of exterior geometries. However, matter contents with variable equations of state have a remarkable role to maintain the stability of gravastars. We conclude that stable structures of gravastars are obtained only for generalized variable models with exterior d-dimensional Schwarzschild/Reissner–Nordström–de Sitter black holes.

Topological Goldstone phases of matter

We consider the possibility for phases of matter in which a continuous symmetry is spontaneously broken in a \emph{topologically non-trivial} way, which, roughly, means that the action for the Goldstone modes contains a quantized topological term, and could manifest in, for example, non-trivial quantum numbers of topological defects of the order parameter. We show that, in fact, such a scenario can occur only when the system is in a non-trivial symmetry-protected topological (SPT) or symmetry-enriched topological (SET) phase with respect to the residual symmetry; or alternatively, if the original symmetry before spontaneous symmetry breaking acts on the system in an "anomalous" way. Our arguments are based on a general correspondence between topological defects of the order parameter and topological defects of a background gauge field for the residual symmetry.

Elementary Open Quantum States

It is shown that the mixed states of a closed dynamics supports a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are defined as operators of the Liouville space in the irreducible representations of the symmetry of the open system. These are tensor operators in the case of rotational symmetry. The case of translation symmetry is discussed in more detail for harmonic systems.

Revisit of the structure of Ω precipitate in Al-Cu-Mg-Ag alloys

Re-examination of the structure of Ω precipitate in Al-Cu-Mg-Ag alloys through first-principles density functional theory (DFT) calculation reveals that the widely-accepted orthorhombic structure of the ‘metastable’ Ω phase is actually tetragonal that is identical to that of the equilibrium θ phase in binary Al-Cu alloys. When the tetragonal θ (i.e. Ω) is embedded in α-Al matrix as thin plates, the elastic distortion imposed by the surrounding α-Al matrix can reduce the original 4-fold symmetry of the tetragonal structure to the 2-fold symmetry of the orthorhombic structure. The DFT calculation results also indicate that the presence of Mg and Ag at the θ/α-Al interface can dramatically facilitate the θ formation. The clarification of the Ω structure and the role of Mg and Ag in θ formation provides insights into how to facilitate precipitation of an intrinsically strong equilibrium phase as a key strengthening constituent in the microstructure.

Magnetic and electronic properties of YCr1−xNixO3 (0 ≤ x ≤ 0.15) polycrystalline ceramics

In this manuscript, we have investigated the temperature evolution of magnetic and electronic properties in doped YCr1−xNixO3 (x = 0.0, 0.05, 0.10, and 0.15). While both Cr3+ and Ni2+ are magnetic, the substitution of Ni2+ for Cr3+ changes the Cr ionic state which alters the magnetic correlation as well as the electrical resistivity. The system retains its original orthorhombic-Pnma structural symmetry, but unit cell volume shows an evolution with the Ni content. While the magnetic moment below TN initially decreases then re-increases with the Ni content, the magnetic transition temperature continuously decreases with Ni doping throughout the series. The electrical resistivity data exhibit an insulating behaviour throughout the temperature range, however, the resistivity decreases with Ni doping. The nature of charge conduction is found to follow Arrhenius-type conduction behaviour in the whole series.

Theoretical study on two dimensional group IV-VI ternary compounds with large in-plane spontaneous polarization

Room temperature ultra-thin ferroelectric materials are highly desired for a wide range of applications, such as high-density non-volatile memory devices. However, the continuous thinning of the ferroelectric film is impeded by the enhanced depolarization field. Recently demonstrated two-dimensional (2D) ferroelectric sheds the light on the realization of atomically thin ferroelectric materials for advanced applications. Herein, through comprehensive first-principles calculations, we successfully designed several Janus type 2D group IV-VI ternary compounds M2XY (M = Ge, Sn; X/Y = S, Se) and ABN2 (A/B = Ge, Sn; N = S, Se) with large in-plane ferroelectric polarization. Specifically, we show that via Janus substitution to break the original symmetry, the in-plane ferroelectric polarization of the 2D ternary compounds can be tuned from 3.82 to 5.03*10−10C/m. The effective modulation of the spontaneous polarization of 2D group IV-VI ternary compounds in response to the external strain is also revealed. The bandgaps of these 2D ternary compounds are in the range of 1.6 to 2.0 eV. The dynamics and thermal stabilities of these ternary compounds were also confirmed by the phonon spectrum calculations and ab initio molecular dynamics (AIMD) simulations. The AIMD simulation also indicate that the ferroelectric order of these ternary compounds can be maintained at room temperature. This study not only expand the size of the 2D ferroelectrics family but also demonstrates a feasible strategy to tune the polarization of 2D ferroelectric materials.

Development of a Linguistic Approach to the Problem of the Computer Electrocardiogram’s Classifications

Introduction. The linguistic approach, based on the transition from the observed cyclic signal to a sequence of symbols (codeword), which characterize the dynamics of indicators from cycle to cycle, makes it possible to use the procedures of mathematical linguistics to increase the reliability of decisions. The purpose of the article is to expand the diagnostic capabilities of the linguistic approach to the analysis and interpretation of electrocardiograms (ECG). Methods. Each ECG cycle is encoded with one of four symbols characterizing changes in two indicators: traditional (cycle duration) and original (symmetry of the repolarization area). Results. Based on the processing of real clinical data of verified patients and healthy volunteers, standards of patients with chronic coronary artery disease (СAD) and healthy patients. The standards are developed using computational procedures of mathematical linguistics – the Levenshtein distance, which is the minimum number of editing operations (insertion, deletion and replacement of a character), ensuring the transition from one word to another and the frequency of occurrence of substrings in the analyzed word. On the basis of these procedures, decision rules that have been developed allow making diagnostic decisions based on the Levenshtein distance to the standards and the frequency of occurrence of one-, two- and three-symbol patterns in code words. It was found that the combination of these two methods expands the diagnostic capabilities of the linguistic approach to the analysis and interpretation of the ECG. Conclusions. It has been shown that using of the developed decision rules makes it possible to increase the sensitivity and specificity of diagnostics even in cases when the ECG does not show traditional electrocardiological signs of myocardial ischemia.

Biaxial strain tuned magnetic anisotropy of ferromagnetic penta-MnN2 monolayer

Ferromagnetic (FM) materials with high Curie temperature, large spin polarization ratio and large perpendicular magnetic anisotropic (PMA) are the basis of constructing practical spintronic devices. Using first-principles calculations, electronic property, magnetism and magnetic anisotropic energy (MAE) of penta-MnN2 monolayer are investigated. The calculated results indicate that penta-MnN2 monolayer is FM half-metal and exhibits PMA. The PMA is induced by Mn atom of 0.207 meV/Mn, which is one or two orders of magnitude larger than those of bulk Co (−65 μeV/atom), Fe (−1.4 μeV/atom) and Ni (2.7 μeV/atom). It is worth noting that the structure, magnetism and MAE of penta-MnN2 monolayer can be manipulated by applying biaxial strain. By applying tensile strain of 3%, penta-MnN2 monolayer has a second energy minimum and remains the original crystalline symmetry, but the N–N bond length has a sudden change. The MAE of Mn atom in penta-MnN2 monolayer can be enhanced by 21% with compressive strain compared to the unstrained systems. Meanwhile, the MAE decreases with the increase of tensile strain, and it exhibits a more significant decrease due to the sudden drop of N–N bond with tensile strain. These results may broaden the development of two-dimensional (2D) FM materials, which have potential applications in 2D spintronic nanodevices.

Laser-Induced Electron Symmetry Restoration in Oriented Molecules Made Simple.

Electron symmetry determines many important properties of molecules, from selection rules for photoelectron spectroscopy to symmetry selection rules for chemical reactions. The original electron symmetry is broken if a laser pulse changes the initial state, typically the ground state g, to a superposition of g and an excited state e with different irreducible representations (IRREPs). Quantum dynamics simulations for two examples, the oriented benzene and LiCN molecules, show that the original electron symmetry can be restored by means of a reoptimized π-laser pulse which transfers the component in the excited state e to another state e', or to several others with the same IRREP as the ground state. This method lends itself to much easier experimental applications than all previous ones because it allows the healing of electron symmetry immediately, without any attosecond constraint on the timing of the second pulse.

Floquet Engineering Correlated Materials with Unpolarized Light

Floquet engineering is a powerful tool that drives materials with periodic light. Traditionally, the light is monochromatic, with amplitude, frequency, and polarization varied. We introduce Floquet engineering via unpolarized light built from quasimonochromatic light and show how it can modify strongly correlated systems, while preserving the original symmetries. Different types of unpolarized light can realize different strongly correlated phases As an example, we treat insulating magnetic materials on a triangular lattice and show how unpolarized light can induce a Dirac spin liquid.

Density functional theory study on the influence of tension and compression deformation on the electrical and phonon properties of monolayer and bilayer graphene.

Based on first-principles calculations using density functional theory, this paper systematically studies the effects of uniaxial tension-compression deformation on the stability and electrical and thermal properties of monolayer graphene and AA stacked bilayer graphene. The study shows that the original symmetry of graphene is broken by the tensile and compression deformations, catalyzing the interlayer coupling of bilayer graphene. Its electronic energy band, phonon dispersion, and other physical properties have changed. The transition from metalloid to semiconductor has completed since the deformation weakens the stability of the graphene system to varying degrees and opens the band gap of monolayer graphene. The band gap becomes larger with the increase of tensile and compressive deformation, in which way it can be adjusted. Influenced by the tiny tensile deformation, metalloid properties are exhibited by a small band gap of intrinsic AA-stacked bilayer graphene, and then the band gap becomes larger as the deformation increases. A band gap appears in the system phonon dispersion curves when the compression deformation increases to -15%. The phonon mode softens and shows virtual frequency. The value of virtual frequency increases with the increase of compression deformation. At the very moment, the vibration mode is discontinuous, and the system is unstable.

Configuration of transition-metal atoms on iridium-doped graphene

Our theoretical calculation and analysis show that the configuration of transition-metal (TM) atoms on iridium-doped graphene depends on the number of the d-state valence electrons of the TM atoms. TM atoms with three or less d-state valence electrons prefer to form a horizontal configuration and destroy the original C3v symmetry of the substrate. If there are more than three (but not five) d-state valence electrons in a TM atom, the TM atom selects the site just on the top of the iridium atoms and thus forms a vertical configuration, and the C3v symmetry of the iridium-doped graphene remains. For TM atoms with five d-state valence electrons and a closed s shell, the TM atoms and the iridium-doped graphene prefer to form an inclined configuration. The configuration regularity of the iridium-doped graphene-adsorbing TM atoms is attributed to the unique spin and orbital angular momentum of the electron in the iridium-doped graphene and the unique selection rule of the charge transfer under spin polarization.

Multifractal analysis of the symmetry of a strictly isospectral energy landscape on a square lattice

We use the Höder regularity analysis to study the symmetry breaking and recovery due to a parametric potential generated via the strictly isospectral factorization method. The initial potential is two-dimensional and periodic in the two Cartesian directions, with the symmetry group P4mm. The resulting parametric isospectral potential display a Pm symmetry for values of the parameter moderately close to the singular value γs. However, at large values of the parameter, visually around γ=γs+110, the original symmetry is recovered. For a much higher precision value of the parameter for this symmetry recovery, we show that the multifractal spectrum of the parametric potential can be conveniently used. In the latter case, we obtain γ=γs+201.085 for three decimal digits precision.

Facile synthesis of cooperative mesoporous-assembled CexSr1-xFexTi1-xO3 perovskite catalysts for enhancement beta-lactam antibiotic photodegradation under visible light irradiation

Results demonstrated in this work presented the synthesis of mesoporous Ce and Fe co-modified SrTiO3 (CexSr1-xFexTi1-xO3) perovskite materials using an innovative chelate complex approach, applying a molar excess of glycerol and citric acid monohydrate as the chelating agents. The influence of different Ce and Fe dopant concentrations (0 ≤ x ≤ 0.05) on the characteristics of the SrTiO3 catalysts were systematically investigated using multi-technique. The results showed that controlled Ce and Fe contents significantly altered the physical and chemical properties of the materials. The diffractogram confirmed that all prepared samples crystallized in a typical perovskite structure of SrTiO3 without deviation in the original cubic symmetry in perovskite structure when introduced Ce and Fe in the lattice. Likewise, the microscopy verified the uniformity and particle size reduction of the catalysts with increasing doping contents. In addition, all prepared samples illustrated mesoporosity and BET surface area slightly increased with increasing the doping elements and represented smaller than pure SrTiO3 sample. The Ce atom, replacing some Sr2+ in the lattice, was represented in Ce3+ and Ce4+ valence states mixture. At the same time, Fe atoms, presenting Fe3+ and Fe4+ oxidation states, cannot be incorporated by substituting Ti4+ ions in the SrTiO3 lattice structure, only incorporated with the interstitial site, as confirmed by XPS and XANES measurements. The Ce and Fe dopants improved the absorptivity towards a longer wavelength, resulting in decreasing bandgap energy. Their photocatalytic performance towards beta-lactam antibiotic degradation under visible light irradiation using an LED source was also evaluated. The Ce0.04Sr0.96Fe0.04Ti0.96O3 sample exhibited the best photocatalytic degradation of amoxicillin (67.4%) and demonstrated more activity than the pure SrTiO3 sample about 27 times. In the end, the synergistic effect of Ce and Fe dopants to help enhance the photocatalytic activity and the recycling ability were also detailed.

Symmetrically scaled coexisting behaviors in two types of simple jerk circuits

PurposeThe purpose of this paper is to develop two types of simple jerk circuits and to carry out their dynamical analyses using a unified mathematical model.Design/methodology/approachTwo types of simple jerk circuits only involve a nonlinear resistive feedback channel composited by a nonlinear device and an inverter. The nonlinear device is implemented through parallelly connecting two diode-switch-based series branches. According to the classifications of switch states and circuit types, a unified mathematical model is established for these two types of simple jerk circuits, and the origin symmetry and scale proportionality along with the origin equilibrium stability are thereby discussed. The coexisting bifurcation behaviors in the two types of simple jerk systems are revealed by bifurcation plots, and the origin symmetry and scale proportionality are effectively demonstrated by phase plots and attraction basins. Moreover, hardware experimental measurements are performed, from which the captured results well validate the numerical simulations.FindingsTwo types of simple jerk circuits are unified through parallelly connecting two diode-switch-based series branches and a unified mathematical model with six kinds of nonlinearities is established. Especially, the origin symmetry and scale proportionality for the two types of simple jerk systems are discussed quantitatively. These jerk circuits are all simple and inexpensive, easy to be physically implemented, which are helpful to explore chaos-based engineering applications.Originality/valueUnlike previous works, the significant values are that through unifying these two types of simple jerk systems, a unified mathematical model with six kinds of nonlinearities is established, upon which symmetrically scaled coexisting behaviors are numerically disclosed and experimentally demonstrated.

Hidden scale invariance of intermittent turbulence in a shell model

A study shows that the shell model of turbulence has a hidden scaling symmetry, which involves nonlinear transformations of shell speeds and time. This symmetry is restored statistically in the developed turbulence despite all original scaling symmetries being broken by the intermittency.

Stoichiometry and disorder influence over electronic structure in nanostructured VOx films

We present and discuss the role of nanoparticles size and stoichiometry over the local atomic environment of nanostructured VOx films. The samples have been characterized in situ using X-ray absorption near-edge structure (XANES) spectroscopy identifying the stoichiometry-dependent fingerprints of disordered atomic arrangement. In vanadium oxides, the ligand atoms arrange according to a distorted octahedral geometry depending on the oxidation state, e.g. trigonal distortion in V2O3 and tetragonal distortion in bulk VO2. We demonstrate, taking VO2 as a case study, that as a consequence of the nanometric size of the nanoparticles, the original ligands symmetry of the bulk is broken resulting in the coexistence of a continuum of distorted atomic conformations. The resulting modulation of the electronic structure of the nanostructured VOx as a function of the oxygen content reveals a stoichiometry-dependent increase of disorder in the ligands matrix. This work shows the possibility to produce VOx nanostructured films accessing new disordered phases and provides a unique tool to investigate the complex matter.

Quantum Algorithm for Solving the Continuous Hidden Symmetry Subgroup Problem

Quantum computers are expected to be able to outperform classical computers. In fact, some computational problems such as integer factorization can be solved on quantum computers substantially faster than classical computers. Interestingly, these problems can be cast in a framework of the hidden symmetry subgroup problem. However, only a few of quantum algorithms for efficiently solving this problem have been known, and the approaches used in all previous results can be applied to particular groups with specific group actions. In this paper, we introduce new technique for solving the hidden symmetry subgroup problem which can be applicable for any groups and any group actions with a certain condition. In addition, we define the continuous hidden symmetry subgroup problem on a group by employing a continuous oracle function, and prove that if the group is a metric space and the group action satisfies some condition, then the continuous hidden symmetry subgroup problem can be efficiently reduced to the continuous hidden subgroup problem. In particular, we show that there exists an efficient quantum algorithm to solve the continuous hidden symmetry subgroup problem on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {R}^{n}$ </tex-math></inline-formula> , while it has not yet been shown that the original hidden symmetry subgroup problem on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {R}^{n}$ </tex-math></inline-formula> can be efficiently solved by a quantum computer.

Massive fishnets

Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via the interpretation of individual Feynman integrals as correlators in the massless fishnet theory introduced by Gürdoğan and Kazakov. Here we seek for an analogous interpretation of the integrability of massive Feynman integrals. We contrast two approaches to define simple massive quantum field theories in four dimensions. First, we discuss spontaneous symmetry breaking in the massless bi-scalar fishnet theory. We then propose an alternative route to a massive fishnet theory by taking a double-scaling limit of mathcal{N} = 4 SYM theory on the Coulomb branch. Both approaches lead to a massive extension of the massless fishnet theory, differing in how masses enter into the propagators. In the latter theory, planar off-shell amplitudes are in one-to-one correspondence with precisely those massive Feynman integrals that were shown to be invariant under the Yangian. This suggests a re-investigation of Coulomb branch mathcal{N} = 4 SYM theory with regard to integrability. Finally, we demonstrate that in the case of spontaneous symmetry breaking, the original conformal symmetry leads to soft theorems for scattering amplitudes in the broken phase.