Number Of Topologies Research Articles

Topological confinement in Skyrme holography

We study phase transitions in five-dimensional Einstein gravity with a negative cosmological constant, coupled to a Skyrme matter field. These transitions are topological generalizations of the Hawking–Page transition between thermal anti de Sitter (AdS) spacetime and an AdS black hole. Phases are characterized by a topological number associated with the Skyrme field configuration. Depending on that topological number and on the Skyrme coupling strength, there occur transitions between those phases at two, one, or no value(s) of the temperature. Through the holographic (AdS/CFT) correspondence, these solutions are dual to topologically non-trivial states in a conformal field theory with an SU(2)-symmetry, which support either confined or deconfined (quasi-)particles at strong coupling. We compare to similar known phase transitions, and discuss potential applications to confinement in topological phases of condensed matter and the quark–gluon plasma.

Higher Chern number states in curved periodic nanowires

The coupling between the spin and momentum degrees of freedom due to spin–orbit interactions (SOI) suggests that the strength of the latter can be modified by controlling the motion of the charge carriers. In this paper, we investigate how the effective SOI can be modulated by constraining the motion of charge carriers to curved waveguides thereby introducing real-space geometric curvature in their motion. The change in the SOI can in turn induce topological phase transitions in the system. Specifically, we study how the introduction of periodic sinusoidal curvature in nanowires with intrinsic SOC can induce the onset of mid-gap topologically protected edge states, which can be characterized by a topological invariant or Chern number. The Chern number corresponds to the number of discrete charges that would be pumped across the length of the nanowire when the phase of a sliding gate potential relative to that of the sinusoidal curvature is varied adiabatically over a complete period. In addition, coupling to an external magnetization can be utilized as an experimental knob to modify the Chern number by displacing the energies of the curvature-induced bands relative to one another. The magnetization can be tuned to achieve large discrete jumps in the number of pump charges per phase period.

Topological Characterization of Dynamic Chiral Magnetic Textures Using Machine Learning

Recently proposed spintronic devices use magnetic skyrmions as bits of information. The reliable detection of those chiral magnetic objects is an indispensable requirement. Yet, the high mobility of magnetic skyrmions leads to their stochastic motion at finite temperatures, which hinders the precise measurement of the topological numbers. Here, we demonstrate the successful training of artificial neural networks to reconstruct the skyrmion number in confined geometries from time-integrated, dimensionally reduced data. Our results prove the possibility to recover the topological charge from a time-averaged measurement and hence smeared dynamic skyrmion ensemble, which is of immediate relevance to the interpretation of experimental results, skyrmion-based computing, and memory concepts

Band inversion in Bi2Se3 from fat band analysis

Bi2Se3 is an established thermoelectric material and has been gaining recent popularity as a topological insulator. This study explores the topological property of Bi2Se3 by performing first principles calculation on Bi2Se3 bulk system and employing the technique of fat band analysis from the projected density of states to visualize the band inversion. Electronic band structures of Bi2Se3 are compared for two cases: before and after including spin–orbit coupling (SOC) and a slight increase in bandgap is observed. Density of states and projected density of states are calculated and compared for both the cases. Band parity analysis suggested by Fu and Kane is employed to establish the strong topological invariant number of Bi2Se3.Therefore this study is aimed at understanding the tell-tale signs of a topological insulator from first principles calculation.

Topological Quantum Phase Transitions of Anisotropic Antiferromagnetic Kitaev Model Driven by Magnetic Field

AbstractThe evolution of quantum spin liquid states (QSL) of the anisotropic antiferromagnetic (AFM) Kitaev model with the [001] magnetic field by utilizing the finite‐temperature Lanczos method (FTLM) is investigated. In this anisotropic Kitaev model with and (K is the energy unit), due to the competition between anisotropy and magnetic field, the system emerges four exotic quantum phase transitions (QPTs) when and , while only two QPTs when . At these magnetic‐field tuning quantum phase transition points, the low‐energy excitation spectrums appear level crossover, and the specific heat, magnetic susceptibility and Wilson ratio display anomalies; accordingly, the topological Chern number may also change. These results demonstrate that the anisotropic interacting Kitaev model with modulating magnetic field displays more rich phase diagrams, in comparison with the isotropic Kitaev model.

Transport infrastructure modifications and accessibility to public parks in Greater Cairo

It is widely accepted that transport infrastructure policies have significant consequences on the environment, housing, business, and people’s everyday movement. With the use of space syntax geometric (sum of angular deviations) and topological (number of directional changes) measures and conventional network metric distance, this article analyses the change in transport infrastructure in Greater Cairo between 2011 and 2021 and quantifies its likely impact on access to 57 public parks. The study advocates for a better understanding of the streetscape changes produced by transport infrastructure policies and how they may impact access to urban green spaces (UGS), particularly parks. The results suggest that the accessibility of 40 parks was reduced at both neighborhood and city-wide scales. Moreover, more than one-quarter of the total study area, including both densely populated marginalized areas and upscale neighborhoods, was significantly negatively affected by streetscape changes. Furthermore, the average distance traveled to parks increased from 3566 (m) in 2011–3612 (m) in 2021. These distances are high compared to the few hundred meters recommended in pedestrian accessibility strategies. These findings are not only important for policy makers in Egypt but will also be helpful to other similar contexts around the world by understanding and forecasting the likely implications of design changes and suggesting targeted strategies for improving access to UGS and, in turn, maximizing UGS use rates. In particular, our findings contribute to the debate on the problems caused by inner-city elevated highways. Lastly, this study provides a general analytical framework that can be applied to other cities across the globe to assess the effects of transport infrastructure changes on access to UGS.

Correlated Hofstadter spectrum and flavour phase diagram in magic-angle twisted bilayer graphene

In magic angle twisted bilayer graphene (MATBG), the moir\'e superlattice potential gives rise to narrow electronic bands1 which support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moir\'e and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here, using a scanning single-electron transistor microscope to measure local electronic compressibility, we simultaneously unveil novel sequences of broken-symmetry Chern insulators (CIs) and resolve sharp phase transitions between competing states with different topological quantum numbers and spin/valley flavor occupations. Our measurements provide a complete experimental mapping of the energy spectrum and thermodynamic phase diagram of interacting Hofstadter subbands in MATBG. In addition, we observe full lifting of the degeneracy of the zeroth Landau levels (zLLs) together with level crossings, indicating moir\'e valley splitting. We propose a unified flavor polarization mechanism to understand the intricate interplay of topology, interactions, and symmetry breaking as a function of density and applied magnetic field in this system.

Nonlinear topological phase transitions in the dimerized sine-Gordon model

We investigate the topological physics and the nonlinearity-induced trap phenomenon in a coupled system of pendulums. It is described by the dimerized sine-Gordon model, which is a combination of the sine-Gordon model and the Su-Schrieffer-Heeger model. The initial swing angle of the left-end pendulum may be regarded as the nonlinearity parameter. The topological number is well defined as far as the pendulum is approximated by a harmonic oscillator. The emergence of the topological edge state is clearly observable in the topological phase by solving the quench dynamics starting from the left-end pendulum. A phase diagram is constructed in the space of the swing angle $\xi \pi $ with $|\xi |\leq 1$ and the dimerization parameter $\lambda $ with $|\lambda |\leq 1$. It is found that the topological phase boundary is rather insensitive to the swing angle for $% |\xi |\lesssim 1/2$. On the other hand, the nonlinearity effect becomes dominant for $|\xi |\gtrsim 1/2$, and eventually the system turns into the nonlinearity-induced trap phase. Furthermore, when the system is almost dimerized ($\lambda \simeq 1$), coupled standing waves appear and are trapped to a few pendulums at the left-end, forming the dimer phase. Its dynamical origin is the cooperation of the dimerization and the nonlinear term.

Collapse Dynamics of Vortex Beams in a Kerr Medium with Refractive Index Modulation and PT-Symmetric Lattices

Using the two-dimensional nonlinear Schrödinger equation, the collapse dynamics of vortex beams in a Kerr medium with refractive index modulation and parity–time (PT) symmetric lattices are explored. The critical power for the collapse of vortex beams in a Kerr medium with real optical lattices (i.e., refractive index modulation lattices) was obtained and discussed. Numerical calculations showed that the number of self-focusing points, the locations of the collapse, and the propagation distances for collapse are sensitively dependent on the modulation factors, topological charge numbers, and initial powers. When the vortex optical field propagates in a Kerr medium with real optical lattices, the optical field will collapse into a symmetrical shape. However, the shape of the vortex beam will be chaotically distorted and collapse in asymmetric patterns during propagation in a Kerr medium with PT-symmetric lattices because of the presence of the complex refraction index. Introducing PT-symmetric lattices into nonlinear Kerr materials may offer a new approach to controlling the collapse of vortex beams.

Non-Hermitian Floquet topological phases in one-dimensional system

Periodically driven non-Hermitian systems have attracted a lot of attention due to their intriguing topological phases. In this work, we propose a periodically driven non-Hermitian one-dimensional system, which features rich Floquet topological phases. The non-Hermitian Floquet topological phases are characterized by a pair of topological winding numbers, and the non-Hermitian system demonstrates a bulk-edge correspondence.

Adaptive size-independent control of uncertain leader following systems with only relative displacement information

The adaptive robust size-independent consensus problem of leader following multi-agent systems (MASs) with unknown dynamics based on only onboard relative displacement information is studied. It is assumed that all followers only can measure the relative displacement regarding their adjacent agents. Due to lack of communication tools, each follower must estimate its uncertain dynamics and the leader acceleration simultaneously. A decentralized adaptive robust consensus law is presented to achieve the global state consensus for uncertain second-order multi-agent systems by employing only relative displacement information. According to the Lyapunov theorem, it is proved that without any knowledge about the number of followers and communication graph, the global state consensus is attained. The control and adaptive gains are tuned independently of the number of followers and communication topology. Therefore, the controller is robust against size-changing and can be applied to large-scale uncertain MASs. Afterward, it is verified that if the basis vectors are persistently exciting (PE), the estimation errors of uncertain vectors tend to zero. Several numerical scenarios are prepared to confirm the efficiency of this method.

Galois conjugates of string-net model

We revisit a class of non-Hermitian topological models that are Galois conjugates of their Hermitian counter parts. Particularly, these are Galois conjugates of unitary string-net models. We demonstrate these models necessarily have real spectra, and that topological numbers are recovered as matrix elements of operators evaluated in appropriate bi-orthogonal basis, that we conveniently reformulate as a concomitant Hilbert space here. We also compute in the bi-orthogonal basis thetopological entanglement entropy, demonstrating that its real part is related to the quantum dimension of the topological order. While we focus mostly on the Yang-Lee model, the results in the paper apply generally to Galois conjugates.

Extrinsic topology of Floquet anomalous boundary states in quantum walks

Bulk-boundary correspondence is a fundamental principle for topological phases where bulk topology determines gapless boundary states. On the other hand, it has been known that corner or hinge modes in higher order topological insulators may appear due to "extrinsic" topology of the boundaries even when the bulk topological numbers are trivial. In this paper, we find that Floquet anomalous boundary states in quantum walks have similar extrinsic topological natures. In contrast to higher order topological insulators, the extrinsic topology in quantum walks is manifest even for first-order topological phases. We present the topological table for extrinsic topology in quantum walks and illustrate extrinsic natures of Floquet anomalous boundary states in concrete examples.

Pattern-tunable synthetic gauge fields in topological photonic graphene

Abstract We propose a straightforward and effective approach to design, by pattern-tunable strain-engineering, photonic topological insulators supporting high quality factors edge states. Chiral strain-engineering creates opposite synthetic gauge fields in two domains resulting in Landau levels with the same energy spacing but different topological numbers. The boundary of the two topological domains hosts robust time-reversal and spin-momentum-locked edge states, exhibiting high quality factors due to continuous strain modulation. By shaping the synthetic gauge field, we obtain remarkable field confinement and tunability, with the strain strongly affecting the degree of localization of the edge states. Notably, the two-domain design stabilizes the strain-induced topological edge state. The large potential bandwidth of the strain-engineering and the opportunity to induce the mechanical stress at the fabrication stage enables large scalability for many potential applications in photonics, such as tunable microcavities, new lasers, and information processing devices, including the quantum regime.

Response of quantum spin Hall insulators to Zeeman fields, and device design based on stanene

The nontrivial topology of materials has been one of the keys for breaking through to a new stage of electronics involving phenomena such as topologically protected quantum spin Hall (QSH) states and quantum anomalous Hall (QAH) states. In this work, we study the Kane-Mele model with next-nearest-neighbor Rashba spin-orbit coupling (SOC), which accurately describes the QSH effect of two-dimensional group IV A materials. By investigating electronic structures with different SOCs and Zeeman fields, we obtain various phase transitions and plot rich phase diagrams where a time-reversal-symmetry-broken QSH insulator and three types of QAH insulators are identified based on calculations of topological invariants, including total and spin Chern numbers and Wannier function centers. In addition, the edge modes and spin texture within the bulk gap are also nontrivial. Based on the results of the model, we also study a real QSH material, stanene, with a large bulk gap and propose a scheme based on its transport properties to design a spin-resolved filter.

Topological phases and collective modes in U(1) and SU(2) sectors of spin-orbit-coupled two-dimensional superfluid Fermi gases

We study the emergence of finite-temperature topological phase transitions of the Berezinskii-Kosterlitz-Thouless type and the collective mode spectrum of two-dimensional Fermi gases in the presence of attractive $s$-wave interactions, spin-orbit coupling, and Zeeman fields. We show that neglecting the spin-dependent phase shift on the fermionic wave function misses an important point. Including this spin-dependent shift, we derive the effective low-energy and long-wavelength quantum action for independent (unlocked) phase fluctuations in the U(1) (charge) and SU(2) (spin) sectors and show that at least two phase transitions occur because charge and spin degrees of freedom are coupled due to the presence of spin-orbit and Zeeman fields. Furthermore, we demonstrate that vortex and antivortex excitations are characterized by two topological quantum numbers, corresponding to the quantized circulation of charge and spin velocities. Finally, we show that there are two collective modes in the superfluid phase at low temperatures which arise due to the coupling between sound and transverse-spin waves.

Global and local topological quantized responses from geometry, light, and time

To describe a spin-$\frac{1}{2}$ particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space, we introduce $C$ square (${C}^{2}$) as a local formulation of the global topological invariant. For the Haldane model on the honeycomb lattice, this ${C}^{2}$ can be measured from the Dirac points through circularly polarized light related to the high-symmetry $M$ point(s). For the quantum spin Hall effect and the Kane-Mele model, the ${\mathbb{Z}}_{2}$ topological number robust to interactions can be measured locally from a correspondence between the Pfaffian and light. We address a relation with a spin pump and the quantum spin Hall conductance. The analogy between light and magnetic nuclear resonance may be applied for imaging, among other applications.

UAVs assisted Network Partition Detection and Connectivity Restoration in Wireless Sensor and Actor Networks

Wireless sensor networks have been extensively employed in different data collection and monitoring applications because of their serviceability in harsh environments. The interconnected network is a fundamental requirement for these applications. The simultaneous failure of multiple nodes causes connectivity loss and can partition the network into various segments. It is crucial to identify the partitions in the partitioned network and reconnect them to achieve application-related goals. This paper provides a new Unmanned Aerial Vehicles (UAVs) assisted Network Partition Detection and Connectivity Restoration (UAV-NetRest) solution encompassing all phases from failure detection to network partition recovery. The proposed algorithm is tested according to detection and recovery time, distance traveled by UAVs in detection and recovery phases, the number of messages transmitted, and the number of deployed relay nodes. The performance of the UAV-NetRest's recovery algorithm is compared with the existing recovery techniques proposed in the literature. The simulation results demonstrate that the UAV-NetRest recovers the network with significantly less recovery time and minimum distance traveled by UAVs. The algorithm deploys minimum relay nodes as compared to other techniques. Network partitioning is an unpredictable incident, and simulation results entirely depend on the number of failed nodes, proximity and topology of network partitions, and the number of UAVs employed. The paper provides a new framework that covers all the aspects required for network partition recovery. This proposed work can be a seed source for future researchers to further optimize the detection and recovery phases.

Phase shift, ellipticity, angle, and topological number in skyrmion lattices

We theoretically study skyrmion lattices realized in a Kondo lattice model on a triangular lattice, focusing on the phase, ellipticity, and angle of the constituent multiple-Q waves. Analyzing the numerical data obtained in the previous study [Ozawa R, Hayami S and Motome Y 2017 Phys. Rev. Lett. 118 147205], we extract these parameters for the two types of skyrmion lattices with the skyrmion number of 1 and 2. We show that the topological transition between the two skyrmion lattices driven by an external magnetic field is accompanied by significant modulations of all three parameters.

A general topology identification framework for distribution systems using smart meter and μ-PMU measurements

To enhance topology observability of the power distribution network (PDN), a general topology identification framework using multiple measurement data records of nodal voltages and currents is constructed in this paper. The framework includes three topology identification approaches to handle different situations. The first approach describes a modified three-stage heuristic procedure for the single topology identification while leveraging the sparsity feature of the nodal admittance matrix, which can lead to more accurate identification results than the base model in the literature; The second approach presents a multi-topology identification model to process the measurement data set with a given number of topologies, which classifies records into a fixed number of topology categories and then determines the nodal admittance matrix for each topology category; The third approach designs a two-stage procedure for the measurement data set containing an unknown number of topologies, which determines the number of topologies, the record classification, and the nodal admittance matrices of individual topologies. Effectiveness of the proposed models in efficiently identifying the PDN’s topologies is illustrated via several cases, with measurement data sets containing a given or an unknown number of topologies. In addition, the sensitivity analysis quantifies the influence of the number of records, the standard deviation of measurement errors, and the pre-specified maximum number of nonzero elements in each column of the nodal admittance matrix on the accuracy of the identification results.