Number Of Topologies Research Articles

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.

Topological classes of thermodynamics of black holes in perfect fluid dark matter background

In this paper we explore the topological classes of thermodynamics of a family of black holes. In particular we investigate the influence of distinct fields, including the electric field, non-linear magnetic field, along with the perfect fluid matter background that can mimic dark matter in large distances. In light of these considerations, we shall henceforth denote this fluid as perfect fluid dark matter (PFDM). Our analysis reveals that the winding and topological numbers for the Schwarzschild and Kerr black holes in PFDM background are the same as the Schwarzschild and Kerr black holes, however for the Kerr-AdS background in PFDM we obtain a different topological number compared to the Kerr black hole in PFDM. Furthermore, we explore in details the interplay of electric charge and nonlinear magnetic charge, impacting the topological classes of thermodynamics both in the absence and presence of PFDM. Interestingly, it is demonstrated that the topological numbers associated with the static Hayward black holes, both in the absence and presence of PFDM, deviate from those of the Schwarzschild black hole. This observation shows that the presence of a magnetic charge introduces an additional role and can alter the topological numbers. Finally, our study culminates with the comprehensive analysis of the topological numbers pertaining to the Hayward black hole, considering the combined effects of PFDM and rotation.

Efficient phase-space generation for hadron collider event simulation

We present a simple yet efficient algorithm for phase-space integration at hadron colliders. Individual mappings consist of a single t-channel combined with any number of s-channel decays, and are constructed using diagrammatic information. The factorial growth in the number of channels is tamed by providing an option to limit the number of s-channel topologies. We provide a publicly available, parallelized code in C++ and test its performance in typical LHC scenarios.

Topological classes of black holes in de-Sitter spacetime

In this paper, we investigate the topological number of de-Sitter black hole solutions with different charges (q) and rotational (a) parameters. By using generalized free energy and Duan’s ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document}-mapping topological current theory, we find that the topological numbers of black holes can still be classified into three types. In addition, we interestingly found the topological classes for de-Sitter (dS) spacetime with distinct horizons, i.e., black hole event horizon and cosmological horizon, will be different. Moreover, we also investigate topological classifications of dS black hole solutions in higher dimensions with or without the Gauss-Bonnet term.

Thermodynamics, Ruppeiner geometry, and topology of Born-Infeld black hole in asymptotic flat spacetime

In the extended phase space, Born-Infeld anti-de Sitter black holes exhibit diverse phase transitions including the van der Waals type and reentrant phase transitions. In this paper, we aim to investigate the potential thermodynamical features for Born-Infeld black holes when the cosmological constant vanishes. Quite differently, although there present the swallow tail behavior of the free energy and temperature-entropy criticality, no phase transition will occur when we consider the thermodynamical stability. Further, based on these findings, the phase structures are explicitly shown with the stable, unstable black hole, and non-black hole regions. After excluding the non-black hole region, we observe that the scalar curvature of the Ruppeiner geometry is always positive, indicating a dominant repulsive interaction for both the stable and unstable black holes. Particularly, we also establish the topology for the thermodynamical critical point. By calculating the topological number, we confirm that this critical point of the Born-Infeld black holes is a conventional one. Although it is not an indicator of the first small-large black hole phase transition, it does signify the emergence of stable intermediate black holes. All these results uncover the thermodynamical features of the Born-Infeld black holes in the absence of the cosmological constant.

Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry

Linear crossings of energy bands occur in a wide variety of materials. In this paper we address the question of the quantization of the Berry winding characterizing the topology of these crossings in dimension D=2D=2. Based on the historical example of 22-bands crossing occuring in graphene, we propose to relate these Berry windings to the topological Chern number within a D=3D=3 dimensional extension of these crossings. This dimensional embedding is obtained through a choice of a gap-opening potential. We show that the presence of an (emergent) \mathcal{PT}𝒫𝒯 symmetry, local in momentum and antiunitary, allows the quantization of the Berry windings as multiples of \piπ. We illustrate this quantization mechanism on a variety of three-band crossings.

Topological classes of higher-dimensional black holes in massive gravity

In this paper, we study topological numbers for five-, six- and seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity. We find that when the black holes are charged, they have the same topological number. The topological numbers for the uncharged black holes are 0 or 1, and the specific values are determined by the values of the black holes’ parameters. Since k and c_ 0^2c_2 m^2 appear together in the generalized free energy in the form of k +c_ 0^2c_2 m^2 , where k characterizes the horizon curvature and c_2 m^2 is the coefficient of the second term of massive potential associated with the graviton mass, this result is applicable to the black holes with the spherical, Ricci flat or hyperbolic horizons. This work shows that the parameters of the ghost-free massive gravity play an important role in topological classes of black holes.

Fractional Topological Numbers at Photonic Edges and Corners

Fractional Topological Numbers at Photonic Edges and Corners

Focusing characteristics of chirped phase-modulated Lorentz-Gaussian vortex beams.

This work presents a thorough investigation of the focusing characteristic of chirped phase modulated Lorentz-Gaussian (LG) vortex beams based on the vector diffraction theory. The results show that changing the first-order chirp parameter c 1 can effectively adjust the size of the focusing spot, and the distance between focusing spots can also be controlled. The second-order chirp parameter c 2 can control the up-and-down movement of the optical chain in the focusing region. Simultaneously, the length of the focusing spots can be accurately changed by modulating the waist width ω. In addition, the influence of integer topological charge number m on controlling the size of an optical dark trap is discussed in detail. And fractional topological charge number m can control the rotation of focus peak and the number of optical dark traps. Potential applications of these findings include optical shape and capture, optical particle transmission, and contemporary medical care.

Topological nature of black hole solutions in dRGT massive gravity

We study the thermodynamic properties of black holes in dRGT massive gravity theory using Duan’s [Formula: see text] mapping topological current theory. The topological features and the corresponding thermodynamic stability conditions for neutral and charged cases are discussed. A neutral black hole in four dimensions has a topological number 0, sharing the same topological class of [Formula: see text] Gauss–Bonnet–AdS black hole. We show that the charged black hole in four-dimensional massive gravity has the same topological structure as the AdS-RN black hole. Further, we have extended the calculations to higher dimensions. Our calculations strengthen the conjecture that the addition of higher interaction terms to Einstein–Hilbert action does not alter the topological number of black holes in four space–time dimensions. However, in higher-dimensional massive gravity, the topological number indeed depends on the black hole parameters.

Dynamics of skyrmion bags driven by spin wave

Skyrmion bags are spin textures with arbitrary integer topological charge numbers, holding promise for utilization in high-density racetrack memory devices. In this study, we investigate the dynamics of skyrmion bags driven by propagating spin waves in a magnetic nanostrip, employing micromagnetic simulations. Our findings reveal that propagating spin waves can induce a stable movement of skyrmion bags, irrespective of their topological charge numbers. The amplitude and frequency of the spin wave, alongside material parameters such as damping constant and saturation magnetization, exhibit discernible effects on the behavior of skyrmion bags. These outcomes have the potential to advance the development of racetrack memory based on skyrmion bags.

ObNoCs : Protecting Network-on-Chip Fabrics Against Reverse-Engineering Attacks

Modern System-on-Chip designs typically use Network-on-Chip (NoC) fabrics to implement coordination among integrated hardware blocks. An important class of security vulnerabilities involves a rogue foundry reverse-engineering the NoC topology and routing logic. In this paper, we develop an infrastructure, ObNoCs , for protecting NoC fabrics against such attacks. ObNoCs systematically replaces router connections with switches that can be programmed after fabrication to induce the desired topology. Our approach provides provable redaction of NoC functionality: switch configurations induce a large number of legal topologies, only one of which corresponds to the intended topology. We implement the ObNoCs methodology on Intel Quartus™ Platform, and experimental results on realistic SoC designs show that the architecture incurs minimal overhead in power, resource utilization, and system latency.

Twisted-bilayer FeSe and the Fe-based superlattices

We derive BM-like continuum models for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: (I) a single monolayer experiencing an external periodic potential, and (II) twisted bilayers with long-range moire tunneling. A symmetry derivation for the inter-layer moire tunnelling is provided for both the \GammaΓ and MM high-symmetry points. In this paper, we focus on moire bands formed from hole-band maxima centered on \GammaΓ, and show the possibility of moire bands with C=0C=0 or ±1±1 topological quantum numbers without breaking time-reversal symmetry. In the C=0C=0 region for \theta→0θ→0 (and similarly in the limit of large superlattice period for I), the system becomes a square lattice of 2D harmonic oscillators. We fit our model to FeSe and argue that it is a viable platform for the simulation of the square Hubbard model with tunable interaction strength.

Polarization characteristics of partially coherent radially and azimuthally polarized beams with vortex phase propagating through atmospheric turbulence

Analytical formulas for the normalized spectral Stokes parameters of the partially coherent radially and azimuthally polarized beams with vortex phase (i.e., PCRPV and PCAPV beams) propagating through the turbulent atmosphere are derived. The polarization properties of PCRPV and PCAPV beams in atmospheric turbulence have been studied in detail. Our findings show that different correlation lengths induce nonuniform distribution to degree of polarization (DOP) and the normalized spectral Stokes parameters. And different correlation lengths also cause the polarization singularity splitting. Besides, we find also that the vortex phase will lead to the rotation of distributions of orientation angles and the normalized spectral Stokes parameters of PCRPV and PCAPV beams in turbulence, and the rotation degree will become obvious with increasing topological charge number. It can be found also that larger topological charge number can reduce the speed of polarization singularities destroyed by atmospheric turbulence, meaning that PCRPV and PCAPV beams with a larger topological charge has a stronger ability to resist atmospheric turbulence. Our studies could be important for free-space optical communications and polarization lidar system.

Dynamics of magnetic skyrmionium driven by voltage-controlled strain gradients

A magnetic skyrmionium with zero topological number has no skyrmion Hall effect during motion; hence, it has excellent application prospects in racetrack memory. Here, we investigate dynamics of magnetic skyrmionium driven by voltage-controlled in-plane strain gradients via both electromechanical and micromagnetic simulations. It is found that the skyrmionium can be efficiently driven along the direction of the in-plane strain gradients without deflection, that is, the skyrmion Hall angle is zero, and the velocity of skyrmionium can be effectively increased by reducing the magnetic damping constant and increasing the intensity of the strain gradient. Moreover, the driving force and velocity of the skyrmionium increase correspondingly with the increase in size. Most importantly, we demonstrate that the skyrmionium can be efficiently driven by strain gradients under realistic conditions with thermal noise and material inhomogeneity in the ferromagnetic film. The results presented in this study are promising for applications in skyrmionium-based information memory devices.

Experimental study of the transport characteristics of fractional-order vortex beams in a turbulent atmosphere simulator

Fractional vortex beams have attracted increasing attention due to their complex yet intriguing physical properties, such as radial notch intensity distribution and higher degrees of modulation in orbital angular momentum. In this study, we experimentally investigated and compared the beam spread and beam wander characteristics of fractional-order vortex beams with those of integer-order vortex beams after passing through a turbulent atmosphere simulator with varying turbulence intensities. Our results revealed that the beam spread of both fractional-order and integer-order vortex beams increased in a stepwise manner with the topological charge number, indicating that a larger topological charge number resulted in more severe beam spread. Interestingly, we observed that the beam radius of fractional-order vortex beams between two adjacent integer orders initially grew slowly and then rapidly before finally stabilizing into a curvilinear growth trend. This is in contrast to the linear growth trend exhibited by the beam radius of integer-order vortex beams. Furthermore, we found that the growth of the beam radius of half-integer-order vortex beams followed the linear growth trend of the beam radius of integer-order vortex beams. When the integer part of the topological charge was fixed, we observed that stronger turbulence resulted in more severe beam wander for both integer-order and fractional-order vortex beams, with the variance of the center-of-mass drift following the same growth curve. However, when the turbulence intensity is constant, both integer-order and fractional-order vortex beams exhibit a weaker beam wander effect with increasing topological charge. Our findings may provide valuable insights for applications such as optical communication and optical measurement using fractional-order vortex beams.

Performance analysis of different transformer-less inverter topologies for grid-connected PV systems

Transformerless Photovoltaic (PV) inverters are gaining popularity compared to their transformer-based counterparts. They are more efficient, cost-effective, and smaller in volume. Despite this, parasitic capacitance causes the common mode current to flow between the PV array and the grid. In addition to losses, leakage current increases electromagnetic interference (EMI) and poses issues to the protection system. Transformerless inverters should therefore be so designed that the leakage current is minimized. Common mode voltage changes (VCM) causes the leakage current. There are a number of PV inverter topologies that have been designed to minimize these variations. This paper discusses H4, H5 and HERIC single-phase PV inverter topologies. Circuit simulations have been used for analysis. HERIC Topology is best one of these since it reduces the leakage current with lowest power loss due to ac bypass instead of usual dc side decoupling. It is a type of resonant converter that operates at high frequencies to achieve efficient power conversion. In this work comparison has been made between topologies for their effectiveness in reducing leakage current. Moreover, its variation with load has been studied, a perspective missed in other studies.

Magnetic resonance-based imaging biopsy with signatures including topological Betti number features for prediction of primary brain metastatic sites.

This study incorporated topology Betti number (BN) features into the prediction of primary sites of brain metastases and the construction of magnetic resonance-based imaging biopsy (MRB) models. The significant features of the MRB model were selected from those obtained from gray-scale and three-dimensional wavelet-filtered images, BN and inverted BN (iBN) maps, and clinical variables (age and gender). The primary sites were predicted as either lung cancer or other cancers using MRB models, which were built using seven machine learning methods with significant features chosen by three feature selection methods followed by a combination strategy. Our study dealt with a dataset with relatively smaller brain metastases, which included effective diameters greater than 2mm, with metastases ranging from 2 to 9mm accounting for 17% of the dataset. The MRB models were trained by T1-weighted contrast-enhanced images of 494 metastases chosen from 247 patients and applied to 115 metastases from 62 test patients. The most feasible model attained an area under the receiver operating characteristic curve (AUC) of 0.763 for the test patients when using a signature including features of BN and iBN maps, gray-scale and wavelet-filtered images, and clinical variables. The AUCs of the model were 0.744 for non-small cell lung cancer and 0.861 for small cell lung cancer. The results suggest that the BN signature boosted the performance of MRB for the identification of primary sites of brain metastases including small tumors.

Self-assembly morphology and solid state of four organic-polyoxometalate hybrids based on Berberine

Four organic-polyoxometalate hybrids were fabricated by the polyoxoanions and berberine cations from active ingredients of traditional Chinese medicine. Four hybrids were constructed with different topological kernels and number of cations on the surface. The structures of hybrids were characterized and confirmed by elemental analysis, thermogravimetric (TG) analysis, infrared spectra and 1HNMR. The TG results indicate that hybrids have higher thermal stability than BR. The sites of interaction between BR caitons and POMs based on electrostatic attraction were near the nitrogen atom of isoquinoline skeleton. Self-assembly behaviors and aggregates morphology of four hybrids were obtained by fluorescence microscope, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction (XRD). Hybrids dispersed in methanol show multilayered vesicle structure. Especially, the two hybrids containing Eu show fluorescence property. Relatively, XRD results imply that BR-SiW appears as specially ordered layered structure with cubic symmetry in solid state resulting from aggregates accumulation.