Number Of Topologies Research Articles

Structure Sensitivity of Metal Catalysts Revealed by Interpretable Machine Learning and First-Principles Calculations.

The nature of the active sites and their structure sensitivity are the keys to rational design of efficient catalysts but have been debated for almost one century in heterogeneous catalysis. Though the Brønsted-Evans-Polanyi (BEP) relationship along with linear scaling relation has long been used to study the reactivity, explicit geometry, and composition properties are absent in this relationship, a fact that prevents its exploration in structure sensitivity of supported catalysts. In this work, based on interpretable multitask symbolic regression and a comprehensive first-principles data set, we discovered a structure descriptor, the topological under-coordinated number mediated by number of valence electrons and the lattice constant, to successfully address the structure sensitivity of metal catalysts. The database used for training, testing, and transferability investigation includes bond-breaking barriers of 20 distinct chemical bonds over 10 transition metals, two metal crystallographic phases, and 17 different facets. The resulting 2D descriptor composing the structure term and the reaction energy term shows great accuracy to predict the reaction barriers and generalizability over the data set with diverse chemical bonds in symmetry, bond order, and steric hindrance. The theory is physical and concise, providing a constructive strategy not only to understand the structure sensitivity but also to decipher the entangled geometric and electronic effects of metal catalysts. The insights revealed are valuable for the rational design of the site-specific metal catalysts.

Localization of Chiral Edge States by the Non-Hermitian Skin Effect

Localization of Chiral Edge States by the Non-Hermitian Skin Effect

Spontaneous Atomic-Scale Polar Skyrmions and Merons on a SrTiO3 (001) Surface: Defect Engineering for Emerging Topological Orders.

The emergence of nontrivial topological order in condensed matter has been attracting a great deal of attention owing to its promising technological applications in novel functional nanodevices. In ferroelectrics, the realization of polar topological order at an ultimately small scale is extremely challenging due to the lack of chiral interaction and the critical size of the ferroelectricity. Here, we break through these limitations and demonstrate that the ultimate atomic-scale polar skyrmion and meron (∼2 nm) can be induced by engineering oxygen vacancies on the SrTiO3 (001) surface based on first-principles calculations. The paraelectric-to-antiferrodistortive phase transition leads to a novel topological transition from skyrmion to meron, indicating phase-topology correlations. We also discuss accumulating and driving polar skyrmions based on the oxygen divacancy model; these results and the recent discovery of defect engineering techniques suggest the possibility of arithmetic operations on topological numbers through the natural self-organization and diffusion features of oxygen vacancies.

Backscattering-free edge states below all bands in two-dimensional auxetic media

Unidirectional and backscattering-free propagation of sound waves is of fundamental interest in physics and highly sought-after in engineering. Current strategies utilize topologically protected chiral edge modes in bandgaps or complex mechanisms involving active constituents or nonlinearity. Here, we propose a new class of passive, linear, one-way edge states based on spin-momentum locking of Rayleigh waves in two-dimensional media in the limit of vanishing bulk modulus, which provides 100% unidirectional and backscattering-free edge propagation immune to any edge roughness at a broad range of frequencies instead of residing in gaps between bulk bands. We further show that such modes are characterized by a new topological winding number that is analogous to discrete angular momentum eigenvalues in quantum mechanics. These passive and backscattering-free edge waves have the potential to enable a new class of phononic devices in the form of lattices or continua that work in previously inaccessible frequency ranges.

Hidden skyrmion on the spin direction of the Majorana zero mode

The spin information of Majorana zero mode (MZM) has important application value in distinguishing MZM from other zero energy states. We study the spin direction of the Majorana zero mode (MZM) localized in a vortex state in a topological superconductor. We find that the topological number of the magnetic structure of the MZM is zero. However, with an increase in the vortex radius, the magnetic structure of the electron oscillates between the antiskyrmion and skyrmion (starting with the antiskyrmion), while that of the hole oscillates between the skyrmion and antiskyrmion (starting with the skyrmion). The total magnetic structure of the electron is a antiskyrmion (the topological number is −1) while that of the hole is a skyrmion (the topological number is 1). We hope these new features provide more characters for detection and regulation of MZM.

Study on the Generation of 1.9 μm Mode Superposition Conversion Laser by Double-End Off-Axis Pumping

In this paper, the Laguerre–Gaussian (LG) mode superposition is obtained by using the technology of double-end off-axis pumping Tm:YLF crystal, and the LG mode superposition is achieved by combining the extra-cavity conversion method. The impact of changing the off-axis distance on the order of Hermite–Gaussian (HG) mode and the topological charge of LG mode is studied. The results show that when the off-axis distance of the pump source at both ends is tuned, when the off-axis distance is in the range of 260 μm~845 μm, the single-ended 0~10 order HG mode can be obtained. Subsequently, the mode converter is placed to obtain the LG mode beam, and the double-end simultaneously pumps the crystal to obtain the superimposed LG mode. The tuning off-axis quantity changes the topological charge number. When P = 0, l1=l2, the superimposed LG mode is a single-ring spot, and the vortex beam center’s dark hollow area increases with the topological charge number. When P = 0, l1=−l2, the superimposed LG mode is a petal-like spot. The number of petals differs from the topological charges of two opposite numbers. Finally, in the case of changing the topological charge number of the double-ended LG mode, the output of the vortex array structured beams of the tuning mode order 1.9 μm Tm:YLF is completed in the case of conversion and superposition.

Topology of Hořava–Lifshitz black holes in different ensembles

In this paper, we study topological numbers for uncharged and charged static black holes obtained in z=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=3$$\\end{document} Hořava–Lifshitz gravity theory in different ensembles, where z measures the degree of anisotropy between space and time. We first calculate the topological numbers for the uncharged black holes by changing the value of the dynamic coupling constant, and find that the black holes with spherical and flat horizons have the same topological number. When the black hole’s horizon is hyperbolic, different values of the coupling constant generate different topological numbers, which can be 1, 0 or -1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-1$$\\end{document}. This shows that the coupling constant plays an important role in the topological classification. Then we study the topological numbers for the charged black holes in different ensembles. The black hole with a spherical horizon has the same topological number in canonical and grand canonical ensembles. When the horizons are flat or hyperbolic, they have different topological numbers in canonical and grand canonical ensembles. Therefore, the topological numbers for the uncharged black holes are parameter dependent, and those for the charged black holes are ensemble dependent.

Bloch Point Quadrupole Constituting Hybrid Topological Strings Revealed with Electron Holographic Vector Field Tomography.

Topological magnetic (anti)skyrmions are robust string-like objects heralded as potential components in next-generation topological spintronics devices due to their low-energy manipulability via stimuli such as magnetic fields, heat, and electric/thermal current. While these 2D topological objects are widely studied, intrinsically 3D electron-spin real-space topology remains less explored despite its prevalence in bulky magnets. 2D-imaging studies reveal peculiar vortex-like contrast in the core regions of spin textures present in antiskyrmion-hosting thin plate magnets with S4 crystal symmetry, suggesting a more complex 3D real-space structure than the 2D model suggests. Here, holographic vector field electron tomography captures the 3D structure of antiskyrmions in a single-crystal, precision-doped (Fe0.63Ni0.3Pd0.07)3P (FNPP) lamellae at room temperature and zero field. These measurements reveal hybrid string-like solitons composed of skyrmions with topological number W = -1 on the lamellae's surfaces and an antiskyrmion (W = + 1) connecting them. High-resolution images uncover a Bloch point quadrupole (four magnetic (anti)monopoles that are undetectable in 2D imaging) which enables the observed lengthwise topological transitions. Numerical calculations corroborate the stability of hybrid strings over their conventional (anti)skyrmion counterparts. Hybrid strings result in topological tuning, a tunable topological Hall effect, and the suppression of skyrmion Hall motion, disrupting existing paradigms within spintronics.

EDIT: A data inspection tool for smart contracts temporal behavior modeling and prediction

Modeling and predicting the behavior of nodes and users in blockchains provide opportunities for business strategy optimization. Indeed, the number of interactions of a node is strictly related to its balance and its prediction may be used for analytics purposes and investment strategies. However, the amount and diversity of information stored on the blockchain demand advanced tools for the modeling and analysis of blockchain data. Such tools should be able to capture the dynamicity and interaction of multiple independent actors, considering a large number of variables and dynamic interaction graph topologies. This is exacerbated by the use of smart contracts, programs stored in blockchain blocks that bring automation to blockchain’s operations and thus increasing the variability of the resulting interaction graphs. Existing modeling methodologies are unable to keep track of all these details, as they are not able to capture the temporal variability of the network.In this paper, we propose a novel framework for modeling and predicting the behavior of smart contracts on a blockchain. We propose the concept of temporal smart contracts networks, i.e., graphs representing the temporal evolution of interactions and data flow. Our framework allows the creation of temporal smart contract networks with different granularity levels by considering different interaction patterns between smart contracts, externally owned accounts, and internal transactions. Thanks to these graphs, we are able to model features such as the node in degree and amount of ether received by a smart contract, which are directly related to its behavior. We incorporate our modeling approach in Ethereum Data Inspection Tool (EDIT), a novel tool able to model interactions and predict them based on historical data. We test different machine learning models to predict features extracted by EDIT, hence allowing for the prediction of the overall behavior of the smart contract. We test EDIT on the Ethereum blockchain and model several temporal smart contracts networks, which represent the interactions and the data flow resulting from about 4 000 000 consecutive blocks. The evaluation of different real case studies shows that the proposed framework is able to predict, with a mean absolute error close to 1%, the evolution of several interesting properties (e.g., amount of received ether) related to both accounts and smart contracts.

Design and Innovation of English Teaching Methods in Colleges and Universities Based on Topological Number Theory

Abstract This research delves into the innovative application of topological number theory to reform English language teaching methodologies in higher education. We introduce and assess a novel approach to English teaching in colleges and universities, inspired by the principles of topological number theory. Our methodology leverages a unique model for recognizing handwritten English based on visual topological cognition, applying the insights of topological cognition theory to enhance English language instruction. The empirical analysis reveals a low word error rate of just 9.42% for our model, outperforming traditional models like the CRNN, which exhibits a 15.12% error rate. In a 10-week instructional experiment, students taught using the topological approach demonstrated significant improvements across all dimensions of English learning compared to their peers in a control group. The findings underscore the substantial potential of topological number theory in elevating English language teaching in colleges, offering significant benefits in teaching effectiveness and student motivation.

Analysis of carrying capacity of higher education based on topological number theory in the context of ecological theory of education

Abstract This paper focuses on analyzing the educational carrying capacity of colleges and universities by using topological number theory and the educational carrying capacity development index. The scale range of the educational carrying capacity of colleges and universities can be determined by identifying relevant definitions of topological space and some topological invariants. Using the relevant definitions of topological space to divide the college education-bearing intervals of different regions and combining the human development index and imbalance coefficient processing, we construct the formula of the balanced and sufficient development index of college education-bearing capacity, which is used to analyze the education bearing capacity of colleges and universities. Analyze different states of college education carrying capacity based on the college education carrying capacity bearing structure. Examine the educational carrying capacity of colleges and universities by examining their educational resource allocation with the help of human and financial resources. The results show that the teacher-student ratio of the urban function expansion area is 0.052, which is the smallest teacher-student ratio among all the districts, indicating that although the district is rich in teachers’ resources, the balanced and sufficient development index of the educational carrying capacity of colleges and universities in District A and District D is high, and the top two rankings have been maintained for a long period in the process of development, and the index of the balanced and sufficient development of education in District A will be 60 in 2021, which is in the area of the development of higher value of the educational carrying capacity.

Universal Platform of Point-Gap Topological Phases from Topological Materials.

Whereas point-gap topological phases are responsible for exceptional phenomena intrinsic to non-Hermitian systems, their realization in quantum materials is still elusive. Here, we propose a simple and universal platform of point-gap topological phases constructed from Hermitian topological insulators and superconductors. We show that (d-1)-dimensional point-gap topological phases are realized by making a boundary in d-dimensional topological insulators and superconductors dissipative. A crucial observation of the proposal is that adding a decay constant to boundary modes in d-dimensional topological insulators and superconductors is topologically equivalent to attaching a (d-1)-dimensional point-gap topological phase to the boundary. We furthermore establish the proposal from the extended version of the Nielsen-Ninomiya theorem, relating dissipative gapless modes to point-gap topological numbers. From the bulk-boundary correspondence of the point-gap topological phases, the resultant point-gap topological phases exhibit exceptional boundary states or in-gap higher-order non-Hermitian skin effects.

Thermodynamic topology and photon spheres in the hyperscaling violating black holes

It was shown that a standard ring of light can be imagined outside the event horizon for stationary rotating four-dimensional black holes with axial symmetry using the topological method (Cunha, 2020; Wei and Shao-Wen, 2020). Based on this concept, in this paper, we investigate the topological charge and the conditions of existence of the photon sphere (PS) for a hyperscaling violation (HSV) black hole with various values of the parameters of this model. Then, after carrying out a detailed analysis, we show the conventional topological classes viz Q=−1 for the mentioned black hole and Q=0 for the naked singularities. Also, we propose a new topological class for naked singularities (Q=+1) with respect toz≥1. We also determined thatz≥2, it either shows a naked singularity form with total topological charge+1or has no solution. Therefore, we have the black hole solution only in1≤z<2. Then, we will use two different methods, namely the temperature (Duan’s topological current Φ-mapping theory) and the generalized Helmholtz free energy method, to study the topological classes of our black hole. By considering the black hole mentioned, we discuss the critical and zero points (topological charges and topological numbers) for different parameters of hyperscaling violating black holes, such as (z,θ¯) and other free parameters, and study their thermodynamic topology. We observe that for a given value of the parameters 1≤z<2, θ¯, and other free parameters, there exist two total topological charges (Qtotal=−1,0) with the same phase structure for the T method and total topological numbers (W=+1) for the generalized Helmholtz free energy method. Additionally, we summarize the results for each study as photon sphere, temperature, and generalized Helmholtz free energy in some figures and tables. Finally, we compare our findings with other related studies in the literature.

Thermodynamic topology of black holes from bulk-boundary, extended, and restricted phase space perspectives

In this article, we investigate the thermodynamic topology of some black holes, namely AdS Reissner Nordstrom (R–N), AdS Einstein–Gauss–Bonnet (EGB), and AdS Einstein-power-Yang–Mills (EPYM), from different frameworks: bulk-boundary (BB) and restricted phase space (RPS). Using the generalized off-shell Helmholtz free energy method, we calculate the thermodynamic topology of the selected black holes in each space separately and determine their topological classifications. We show that the addition of GB terms, dimensions, and other factors do not affect the topological classes of black holes in both spaces. The calculations and plots indicate that the AdS R–N and AdS EGB black holes show similar behavior and their topological numbers sets in both spaces, i.e., BB and RPS, are similar and equal to (W=+1). However, AdS EPYM black holes show an interesting behavior. In addition to BBT and RPS, we also consider the extended phase space thermodynamics (EPST) and evaluate the thermodynamic topology for AdS EPYM black hole. The changing (r−τ) in both spaces shows similar behavior. Also, the topological number and the total topological numbers for this black hole in the BB, RPS and EPS thermodynamics are completely same, i,e., (ωBBT=ωRPS=ωEPST=+1,−1) or WBBT=WRPS=WEPST=0. An important point is that the Einstein–Yang–Mills black hole has thermodynamic topology equivalence in three spaces. The present result may be due to the non-linear YM charge parameter and the difference between the gauge and gravity corrections in the above black holes.

Quantum geometric tensor and the topological characterization of the extended Su–Schrieffer–Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su–Schrieffer–Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss–Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric, which leads to ill-defined non-integer topological Euler numbers. Nevertheless, the non-integer “Euler number” provides valuable insights and an upper bound for the absolute values of the Chern numbers.

A scheme for realizing nonreciprocal interlayer coupling in bilayer topological systems

Nonreciprocal interlayer coupling is difficult to practically implement in bilayer non-Hermitian topological photonic systems. In this work, we identify a similarity transformation between the Hamiltonians of systems with nonreciprocal interlayer coupling and on-site gain/loss. The similarity transformation is widely applicable, and we show its application in one- and two-dimensional bilayer topological systems as examples. The bilayer non-Hermitian system with nonreciprocal interlayer coupling, whose topological number can be defined using the gauge-smoothed Wilson loop, is topologically equivalent to the bilayer system with on-site gain/loss. We also show that the topological number of bilayer non-Hermitian C6v-typed domain-induced topological interface states can be defined in the same way as in the case of the bilayer non-Hermitian Su–Schrieffer–Heeger model. Our results show the relations between two microscopic provenances of the non-Hermiticity and provide a universal and convenient scheme for constructing and studying nonreciprocal interlayer coupling in bilayer non-Hermitian topological systems. This scheme is useful for observation of non-Hermitian skin effect in three-dimensional systems.Graphical

Various matching keys for asymmetric topology encryption

With the fast development of quantum computer technology, one has to focus on the security of information running in real networks. Topological coding is a technology of basic topological structure, number theory and algebra has potential application value in asymmetric encryption system. The public key and private key of topological graph encryption system designed by topological coding may be able to resist attacks equipped with artificial intelligence technology and quantum computer. In order to further investigate topology encoding, we propose new techniques for designing public and private keys using graph coloring and labeling.

Bulk-local-density-of-state correspondence in topological insulators

In the quest to connect bulk topological quantum numbers to measurable parameters in real materials, current established approaches often necessitate specific conditions, limiting their applicability. Here we propose and demonstrate an approach to link the non-trivial hierarchical bulk topology to the multidimensional partition of local density of states (LDOS), denoted as the bulk-LDOS correspondence. In finite-size topologically nontrivial photonic crystals, we observe the LDOS partitioned into three distinct regions: a two-dimensional interior bulk area, a one-dimensional edge region, and zero-dimensional corner sites. Contrarily, topologically trivial cases exhibit uniform LDOS distribution across the entire two-dimensional bulk area. Our findings provide a general framework for distinguishing topological insulators and uncovering novel aspects of topological directional band-gap materials, even in the absence of in-gap states.

Superconductivity in monolayer and few-layer graphene. II. Topological edge states and Chern numbers

Superconductivity in monolayer and few-layer graphene. II. Topological edge states and Chern numbers

Single-celled metasurface for labeled vortex beam generator

Vortex light is a unique beam characterized by a spiral phase as it propagates. A fundamental parameter of vortex light is the topological charge, which determines the amount of angular momentum and plays a crucial role in tailoring its behavior. However, conventional measurement methods for determining the topological charge, such as those based on interference and phase modulation, tend to be intricate and complex. In this regard, a labeled vortex beam generator is proposed, composed of a metasurface with a single-celled configuration. When the metasurface is illuminated by light of the designed wavelength, the outgoing light exhibits a vortex structure. Furthermore, the topological charge numbers can be directly observed with distinct labeled patterns when the metasurface is placed in an orthogonal-polarized optical path. With advantages such as ultra-compactness, high robustness, and exceptional precision, the proposed metasurface exhibits significant potential for applications in optical communication, light manipulation, optical sensing, etc.