Opposite Numbers Research Articles

Polariton vortex Chern insulator [Invited

We propose a vortex Chern insulator, motivated by recent experimental demonstrations on programmable arrangements of cavity polariton vortices by [S. Alyatkin et al., arXiv, ArXiv:2207.01850 (2022)10.48550/arXiv.2207.01850 ] and [J. Wang et al, Natl. Sci. Rev. 10, Nwac096 (2022)10.1093/nsr/nwac096]. In the absence of any external fields, time-reversal symmetry is spontaneously broken through polariton condensation into structured arrangements of localized co-rotating vortices. We characterize the response of the rotating condensate lattice by calculating the spectrum of Bogoliubov elementary excitations and observe the crossing of edge-states, of opposite vorticity, connecting bands with opposite Chern numbers. The emergent topologically nontrivial energy gap stems from inherent vortex anisotropic polariton-polariton interactions and does not require any spin-orbit coupling, external magnetic fields, or elliptically polarized pump fields.

Phase transition in bilayer quantum Hall system with opposite magnetic field

We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers. For the C = ±1 case, the two Landau levels of the bilayer experience opposite magnetic fields. We consider a mapped bilayer quantum Hall system at total filling where the intralayer interaction is repulsive and the interlayer interaction is attractive. We take exact diagonalization (ED) calculations on a torus to study the phase transition when the separation distance d/lB is driven. The critical point at d c/lB = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/lB < d c/lB , the states of each level are highly degenerate. The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r = 0. We find an exciton stripe phase composed of bound pairs. The ferromagnetic ground state is destroyed by the strong effective attractive potential. An electron composite-Fermion (eCF) and a hole composite Fermion (hCF) are tightly bound. In the region d/lB > d c/lB , a crossover from the d → d c limit to the large d limit is observed. The electron and hole composite Fermion liquids (CFL) are realized by composite Fermions (CF) which attach opposite fluxes, respectively.

Tunable Topological Phases in Two-Dimensional Electrides

Electrides have been extensively investigated, which revealed many exotic properties. Here, we suggest two feasible two-dimensional (2D) ferromagnetic electrides HfBa4X8 (X = Cl, Br), whose ground state displays a quantum anomalous Hall effect (QAHE) state with an easy x-axis magnetization. Excess electrons in these materials are confined in the cavity channel created by Ba2+ cations and X– anions and considerably affect both the magnetic and topological properties. By rotating the magnetization counterclockwise starting from the x axis, the system can achieve two QAHE states with the opposite Chern number and a period change of the band gap, and a 2D Weyl half-semimetal state will act as a critical point with the magnetization along the y axis. Our findings provide a material family platform for studying magnetic topological phase transition in electrides, which may exhibit unique applications in spintronic devices.

Transport of a topologically protected photonic waveguide on-chip

We propose a design on integrated optical devices on-chip with an extra width degree of freedom by using a photonic crystal waveguide with Dirac points between two photonic crystals with opposite valley Chern numbers. With such an extra waveguide, we demonstrate numerically that the topologically protected photonic waveguide retains properties of valley-locking and immunity to defects. Due to the design flexibility of the width-tunable topologically protected photonic waveguide, many unique on-chip integrated devices have been proposed, such as energy concentrators with a concentration efficiency improvement of more than one order of magnitude, and a topological photonic power splitter with an arbitrary power splitting ratio. The topologically protected photonic waveguide with the width degree of freedom could be beneficial for scaling up photonic devices, and provides a flexible platform to implement integrated photonic networks on-chip.

Topological slow light waveguide in photonic valley-locked heterostructures

In this work, a photonic valley-locked heterostructure is proposed, which is composed of a Dirac photonic crystal (DPC) and two valley photonic crystals (VPC), with opposite valley Chern numbers. By modifying the size of rods nearest to the domain walls, the topological valley waveguide state (TVWS) with large group index (n g = 100) can be found, which is called topological slow-light waveguide mode (TSWM). The simulation results based on finite element method demonstrate that the TSWM supports high energy capacity in the proposed heterostructure waveguide, which is suitable for integrating with the existing waveguides. Besides, TSWM is also valley-locked and immune to backscattering. Our finding paves a way of topological slow light, enrich the research of VPCs, and has new applications in optical communication devices.

Modified dynamic opposite learning assisted TLBO for solving Time-Cost optimization in generalized construction projects

This study proposes an improved version of teaching learning-based optimization (TLBO) with a modified dynamic-opposition learning (MDOL) strategy, called modified dynamic oppositional learning TLBO (MDOLTLBO) to narrow the gap between research and practice for generalized time–cost optimization. Instead of opposite numbers, this study employs modified dynamic opposite points for the population initialization and generation jumping. This novel feature of the proposed algorithm is intended to diminish the randomness of the initial population and minimize the search effort required to achieve the optimal set of time–cost alternatives in the search space. An iterative-based varying weighting factor for MDOL is introduced to adjust the range of the search space with the aim of balancing the dynamicity and diversity of the algorithm. Hence, the MDOLTLBO algorithm can identify diversified and high-quality solutions based on non-dominated solutions. Four different case studies of real construction projects, ranging from 29 to 290 activities, were investigated to demonstrate the applicability of the proposed model. The experimental findings verify that the proposed algorithm is efficient, effective, and highly satisfying. Hence, the primary contribution of this study is MDOL approach that can successfully achieve high-quality solutions and good convergence speed for large-scale discrete time–cost optimization problems with generalized logical relationships.

Particle–hole symmetry protects spin-valley blockade in graphene quantum dots

Particle-hole symmetry plays an important role in the characterization of topological phases in solid-state systems1. It is found, for example, in free-fermion systems at half filling and it is closely related to the notion of antiparticles in relativistic field theories2. In the low-energy limit, graphene is a prime example of a gapless particle-hole symmetric system described by an effective Dirac equation3,4 in which topological phases can be understood by studying ways to open a gap by preserving (or breaking) symmetries5,6. An important example is the intrinsic Kane-Mele spin-orbit gap of graphene, which leads to a lifting of thespin-valley degeneracy and renders graphene a topological insulator in a quantumspin Hall phase7 while preserving particle-hole symmetry. Here we show that bilayer graphene allows the realization of electron-hole double quantum dots that exhibit near-perfect particle-hole symmetry, in which transport occurs via the creation and annihilation of single electron-hole pairs with opposite quantum numbers. Moreover, we show that particle-hole symmetric spin and valley textures lead to a protected single-particle spin-valley blockade. The latter will allow robust spin-to-charge and valley-to-charge conversion, which are essential for the operation of spin and valley qubits.

Extended terahertz valley-locked surface waves in designer surface plasmon crystals

Topological valley-locked edge states have been attracting much attention in terahertz (THz) and optical regimes due to their unique unidirectional backscattering-immune feature. However, these one-dimensional edge transports are essentially not compatible to traditional waveguides or devices. In this work, we propose a THz topological waveguide supporting two dimensional valley-locked surface waves based on designer surface plasmon crystals. The waveguide is implemented by designing a sandwich-like A|C|B heterostructure with three domains. The central domain C carrying a Dirac cone in the band structure is topologically trivial. The A and B domains consist of two distinct topological structures with opposite valley-Chern numbers. Unlike topological edge states existing only at the interface of conventional A|B domain wall structure, extended topological valley-locked surface states propagating along the whole B domain are observed in our proposed structure. This heterostructure with designable waveguide width is more flexible for interfacing with existing THz devices, and is quite suitable for high-throughput and high-power-capacity applications. Besides, the unique features of momentum-valley locking and immunity against sharp bends are reserved. This work may promote future topological and traditional integrated functional devices in THz and optical regimes.

A Novel Definition of Fuzzy Difference on Non-increasing Fuzzy Real Numbers

In this paper, firstly, a novel definition of a fuzzy difference based on non-increasing fuzzy real numbers is introduced, which is different from the previous definitions by using fuzzy interval-numbers and Zadeh’s extension principle. Then we give some important conclusions of fuzzy difference from the view of two cuts of fuzzy sets. Moreover, a definition of a opposite fuzzy real number is given so that we show the connection between the fuzzy difference and fuzzy addition on fuzzy real numbers. Finally, we provide several examples for the sake of illustrating the fuzzy difference on non-increasing fuzzy real numbers is reasonable generalization of classical difference. In addition, we give the prospect that we want to use this difference to research fuzzy derivatives.

Many-body Aharonov-Bohm caging in a lattice of rings

We study a system of a few ultracold bosons loaded into the states with orbital angular momentum $l=1$ of a one-dimensional staggered lattice of rings. Local eigenstates with winding numbers $+l$ and $-l$ form a Creutz ladder with a real dimension and a synthetic one. States with opposite winding numbers in adjacent rings are coupled through complex tunnelings, which can be tuned by modifying the central angle $\phi$ of the lattice. We analyze both the single-particle case and the few boson bound-state subspaces for the regime of strong interactions using perturbation theory, showing how the geometry of the system can be engineered to produce an effective $\pi$-flux through the plaquettes. We find non-trivial topological band structures and many-body Aharonov-Bohm caging in the $N$-particle subspaces even in the presence of a dispersive single-particle spectrum. Additionally, we study the family of models where the angle $\phi$ is introduced at an arbitrary lattice periodicity $\Gamma$. For $\Gamma>2$, the $\pi$-flux becomes non-uniform, which enlarges the spatial extent of the Aharonov-Bohm caging as the number of flat bands in the spectrum increases. All the analytical results are benchmarked through exact diagonalization.

Dekonstruksi Dalam Cerpen Saksi Mata Karya Agus Noor

This research reveals the existence of a number of binary oppositions and dismantling of the order contained in the short story Saksi Mata by Agus Noor. Saksi Mata short stories were chosen because they reveal something unusual and even inversely proportional to what we find in people's lives factually. The analysis in the short story Saksi Mata was carried out using a deconstruction approach. This research is a qualitative study and is presented descriptively. The primary data in this study is in the form of a short story with the title Saksi Mata and secondary data in the form of a number of severences that support the arrangement and answer of problems in this study. Data obtained by conducting in-depth readings of primary data and recording identified narratives that can answer research problems. The results of the data analysis carried out were obtained by a number of binary oppositions, namely hope and reality, honor and humiliation, testimony and blindness, eyewitnesses and defendants, stupid and clever, madness and power, as well as losers and heroes. The demolition of the order was carried out by presenting a blind dog figure as an eyewitness in a murder case at a trial.

Topological Magnons in Kitaev Magnets with Finite Dzyaloshinskii-Moriya Interaction at High Field

There have been intensive studies on Kitaev materials for the sake of realization of exotic states such as quantum spin liquid and topological orders. In realistic materials, the Kitaev interaction may coexist with the Dzyaloshinskii–Moriya interaction, and it is of challenge to distinguish their magnitudes separately. Here, we study the topological magnon excitations and related thermal Hall conductivity of kagome magnet exhibiting Heisenberg, Kitaev and Dzyaloshinskii–Moriya interactions exposed to a magnetic field. In a strong magnetic field perpendicular to the plane of the lattice ([111] direction) that brings the system into a fully polarized paramagnetic phase, we find that the magnon bands carry nontrivial Chern numbers in the full region of the phase diagram. Furthermore, there are phase transitions related to two topological phases with opposite Chern numbers, which lead to the sign changes of the thermal Hall conductivity. In the phase with negative thermal conductivity, the Kitaev interaction is relatively large and the width of the phase increases with the strength of Dzyaloshinskii–Moriya interaction. Hence, the present study will contribute to the understanding of related compounds.

Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models

The Kitaev honeycomb model hosts a fascinating fractionalized state of matter featuring emergent Majorana fermions and a vison particle that carries the flux of an emergent gauge field. In the exactly solvable model these visons are static but certain perturbations can induce their motion. We show that the nature of the vison motion induced by a Zeeman field is sharply distinct in the ferromagnetic vs the antiferromagnetic Kitaev models. Namely, in the ferromagnetic model the vison has a trivial non-projective translational symmetry, whereas in the antiferromagnetic Kitaev model it has a projective translational symmetry with $\pi$-flux per unit cell. The vison band of the ferromagnetic case has zero Berry curvature, and no associated intrinsic contribution to the thermal Hall effect. In contrast, in the antiferromagnetic case there are two gapped vison bands with opposite Chern numbers and an associated intrinsic vison contribution to the thermal Hall effect. We discuss these findings in the light of the physics of the spin liquid candidate $\alpha$-RuCl$_3$.

On the feasibility of general meanings in prepositional semantics

ABSTRACT The paper investigates the status of general meanings in prepositional semantics. On the basis of a review of the strategies employed in different accounts of prepositions, the paper argues that strict adherence to the notion of general meanings is unfeasible in the field, partly because a purely deductive method of description breaks down as the number of possible oppositions increases. This failure points to the need for a theoretical reformulation of the notion. The paper suggests that there are three conservative ways to pursue such a reformulation: by rejecting the idea that general meanings are autonomous from thought, by rejecting the principle of oppositional constitution or by rejecting the requirement of monosemy. The merits and flaws of these strategies are discussed and some theoretical and methodological motives in choosing between them are considered.

Weyl nodal lines, Weyl points and the tunable quantum anomalous Hall effect in two-dimensional multiferroic metal oxynitride: Tl2NO2.

The investigation of two-dimensional (2D) multiferroic and topological quantum phases is a significant topic in current condensed matter physics. In this study, we discover quantum topological phases in the multiferroic material Tl2NO2. We observe that its ferroelectric (FE) phase displays a ferromagnetic ground state with magnetization favoring in-plane orientation. In the absence of spin-orbit coupling (SOC), a Weyl nodal loop around the Fermi level is evident, representing a 1D band crossing between spin-up and spin-down states. When spin-orbit coupling is taken into account, setting the magnetization in-plane, the Weyl nodal loop becomes gapped. Additionally, a pair of 2D Weyl nodes appear on the high-symmetry path, protected by a vertical mirror symmetry allowed by the magnetization. Remarkably, we prove that the Weyl nodes are situated at the topological phase transition between two quantum anomalous Hall (QAH) phases with opposite Chern numbers. Therefore, by adjusting the magnetization, it is possible to switch the propagation direction of chiral edge states. Furthermore, from its ferroelectric state to a paraelectric state, the time-reversal symmetry breaking nodal line is transformed into a Weyl point, achieving 100% spin polarization. Particularly, the Weyl points remain robust against SOC when the vertical mirror symmetry is preserved. Importantly, we also demonstrate that the Weyl point also represents the transition point where the QAH phase changes the sign of its Chern number. Overall, our study provides new insights into the study of multiferroic and topological phenomena in 2D materials and offers a potential avenue for controlling QAH phases.

Crystal and molecular structure of Michler’s ketone as a pure phase

The pure phase crystals of Michler’s ketone, [4-(CH3)2NC6H4]2CO, are reported herein as monoclinic in the space group P21/c with Z’ = 2 by single-crystal X-ray diffraction. The data collection of the title compound proved quite difficult, which could explain why the structure has not been reported previously. The crystallographically independent molecules in the asymmetric unit differ by dihedral angles of 24.60/30.34° and 25.25/27.20° between the essentially planar 4-dimethylaminophenyl (DMAP) rings and the central C2C=O plane of the ketone and dihedral angles of 52.14 and 47.41°, respectively, between the DMAP planes. A DMAP ring of each molecule overlaps in the lattice with a methyl ring that overlays the ring centroid of the opposite number (CMe-Cg distances of 3.452 and 3.505 Å), describing sets of trifurcated CAr-acceptor hydrogen bond interactions (HBIs). The trifurcated HBIs possess H∙∙∙CAr distances of 2.90, 2.75, and 2.86 Å; CMe∙∙∙Car distances of 3.554(5), 3.798(5) and 3.881(5) Å; and ÐCMe-H∙∙∙CAr of 115.0, 121.3 and 167.7°, respectively. Stabilization of the asymmetric unit in the title compound is further achieved by supramolecular synthons such as CMe-H∙∙∙CAr (2.831 Å), CAr-H∙∙∙O (2.561 Å) and CAr-H∙∙∙H-CAr (2.290 Å) and coulombic CMe-Ocontact (3.209 Å). The structures of the two independent molecules in the asymmetric unit of the title compound were compared with the same molecule as found in the following co-crystals, adducts or salts: a halogen-bonded adduct with 1,4-diiodotetrafluorobenzene; a hydrogen-bonded adduct with a fluorinated phenol; a coordination complex between the ketone and a trimeric mercury acceptor; and two salts from protonation or methylation at one of the amino nitrogen atoms.

Thermal Hall conductivity with sign change in the Heisenberg–Kitaev kagome magnet

The Heisenberg–Kitaev (HK) model on various lattices has attracted a lot of attention because it may lead to exotic states such as quantum spin liquid and topological orders. The rare-earth-based kagome lattice (KL) compounds and have q = 0, 120° order and canted ferromagnetic (CFM) order, respectively. Interestingly, the HK model on the KL has the same ground state long-range orders. In the theoretical phase diagram, the CFM phase resides in a continuous parameter region and there is no phase change across special parameter points, such as the Kitaev ferromagnetic (KFM) point, the ferromagnetic (FM) point and its dual FM point. However, a ground state property cannot distinguish a system with or without topological nontrivial excitations and related phase transitions. Here, we study the topological magnon excitations and related thermal Hall conductivity in the HK model on the KL with CFM order. The CFM phase can be divided into two regions related by the Klein duality, with the self dual KFM point as their boundary. We find that the scalar spin chirality, which is intrinsic in the CFM order, changes sign across the KFM point. This leads to the opposite Chern numbers of corresponding magnon bands in the two regions, and also the sign change of the magnon thermal Hall conductivity.

Quantum anomalous Hall effect and electric-field-induced topological phase transition in AB-stacked MoTe2/WSe2 moiré heterobilayers

We propose a mechanism to explain the quantum anomalous Hall (QAH) effect and the electric-field-induced topological phase transition in AB-stacked $\mathrm{MoTe}{}_{2}/\mathrm{WSe}{}_{2}$ moir\'e heterobilayers at $\ensuremath{\nu}=1$ hole filling. We suggest that the Chern band of the QAH state is generated from an intrinsic band inversion composed of the highest two moir\'e hole bands with opposite valley numbers and a gap opening induced by two Coulomb-interaction-driven magnetic orders. These magnetic orders, including an in-plane ${120}^{\ensuremath{\circ}}$-N\'eel order and an in-plane ferromagnetic order, interact with moir\'e bands via corresponding in-plane exchange fields. The N\'eel order ensures the insulating gap, the ferromagnetic order induces the nonzero Chern number, and both orders contribute to time-reversal symmetry breaking. The N\'eel order is acquired from the Hartree-Fock exchange interaction and the formation of ferromagnetic order is attributed to interlayer-exciton condensation and exciton ferromagnetism. The exciton ferromagnetism can be demonstrated by excitonic Bose-Hubbard physics and Berezinskii-Kosterlitz-Thouless transition. In low electric fields, the equilibrium state is a Mott-insulator state. At a certain electric field, a correlated insulating state composed of the hole-occupied band and the exciton condensate becomes the thermodynamically stable phase and the topological phase transition occurs as the ferromagnetic order emerges. The consistency between the present theory and experimental observations is discussed. Experimental observations, including the spin-polarized/valley-coherent nature of the QAH state, the absence of charge gap closure at the topological phase transition, the canted spin texture, and the insulator-to-metal transition are interpreted by the mechanism.

Acoustic Valley-Locked Waveguides in Heterostructures of a Square Lattice

The transport behaviors of topological guiding modes for classical waves in heterostructures with width degree of freedom have attracted much attention recently. With the width degree of freedom, topological waveguides are endowed with increased capacity in energy transport and improved flexibility in interfacing existing devices. However, to date, such topological waveguides are only realized in hexagonal lattices, by virtue of the known valleys existing at the Brillouin zone corners. Here, we report on the implementation of topological waveguides in heterostructures of a square lattice, consisting of three domains of acoustic crystals: the middle domain has Dirac points and the two side domains have valleys of opposite valley Chern numbers. A pair of counterpropagating topological waveguide modes, with amplitudes that are uniform in the central domain and attenuated sidewards in the two side domains, are supported in the heterostructure. We experimentally verify that the topological waveguide modes are valley locked and backscattering immune, and they have a high capacity for energy transport. We also demonstrate experimentally the conversion between the valley waveguide states and the usual valley edge states. More interestingly, when the central domain of the Dirac points is applied with a transverse structural gradient mirror symmetrically, a different kind of topological waveguide mode emerges. We verify that the waveguide modes possess the same topological properties.

Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases

Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of four-dimensional Z_{2} topological insulator (TI) protected by CP symmetry, whose 3D boundary supports an odd number of Dirac cones. A specific perturbation splits each bulk massive Dirac cone into two valleys separated in energy-momentum space with opposite second Chern numbers, in which the 3D boundary modes become a nodal sphere or a Weyl semimetallic phase. By introducing the electromagnetic (EM) and pseudo-EM fields, exotic topological responses of our 4D system are revealed, which are found to be described by the (4+1)D mixed Chern-Simons theories in the low-energy regime. Notably, several topological phase transitions occur from a CP-broken Z_{2} TI to a Z TI when the bulk gap closes by giving rise to exotic double-nodal-line or nodal-hyper-torus gapless phases. Finally, we propose to probe experimentally these topological effects in cold atoms.