Two-dimensional Square Lattice Research Articles

Magnetic Order Transition of a Two-Dimensional Square-Lattice Electrocatalyst Assembled by Fe-N4 Units: Crucial Role on Oxygen Reduction.

Herein, we theoretically investigate the effect of magnetic orders on electrocatalytic oxygen reduction reaction (ORR) properties on the Fe-N4 site-embedded two-dimensional (2D) covalent organic framework (Fe-N4@COF-C3N2) under realistic environments. The Fe-N4@COF-C3N2 shows a 2D square-lattice (sql) topology with three magnetic order states: one ferromagnetic state (FM) and two antiferromagnetic states (AFM1 and AFM2). Specially, the electrocatalyst in the AFM2 state shows a remarkable onset potential of 0.80 V/reversible hydrogen electrode (RHE) at pH 1, superior to the existing most excellent noble-metal catalysts. Thermodynamically, the onset potential for the 4e- ORR is 0.64 V/RHE at pH 1, with a magnetic state transition process of FM → AFM1 → FM → FM → FM, while at pH 13, the onset potential for the 4e- ORR is 0.54 V/RHE, with the magnetic transition process of FM → FM → AFM1 → FM → FM. Generally, this finding will provide new avenues to rationally design the Fe-N4 electrocatalyst.

The Fulde-Ferrell-Larkin-Ovchinnikov states in s and d-wave superconductor with spin-dependent bandwidth imbalance on square lattice

We study numerically the phase diagram for s and d-wave fermionic superfluidity/superconductivity with spin-dependent bandwidth imbalance on a two-dimensional square-lattice. We also investigate the spontaneous space symmetry breaking states at low temperatures by solving the Bogoliubov-de Gennes equations. It is found that, the spatial configuration of the order parameter, both the uni-directional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states and the two-dimensional FFLO state may show up in the presence of finite spin-dependent bandwidth imbalance. Moreover, we calculate the spectra of local density of states, and the experimental proposals of observing such FFLO states are therefore suggested.

Photonic band gaps of two-dimensional square-lattice photonic crystals based on 8-shaped scatters

A novel photonic crystals (PhC) based on 8-shaped scatters with two-dimensional (2-D) square-lattice is presented. By employing the MIT photonic bands (MPB), the relationship between the structural parameters of the PhC and the properties of photonic band gaps (PBG) are investigated. The calculation results of 8-shaped scatters with 2-D square-lattice demonstrate that the reduction of scatters’ symmetry can produce larger number of PBG and broaden the width of PBG only for TM mode, and reversely for TE mode. The peculiarity would meet the distinguish employment of different mode. By optimizing the structural parameters, the maximum absolute PBG 0.1028(ωa/2πc) at R=0.3, ɛr=11.56, θ=45° is obtained and six absolute PBGs is got at R=0.3, θ=115°, ɛr∈[32.3, 33.5].

A Two-Dimensional Square-Lattice Photonic Crystal with Rotated Square Cylinders and Cross Thin Plates Exhibiting Wide Photonic Bandgap

A new type of two-dimensional square-lattice photonic crystal structure made of rotated square cylinders and cross thin plates is presented and numerically investigated using the plane-wave expansion method. The largest absolute photonic bandgap (APBG) reaches 14.3%. The proposed structure can have promising application for its large APBG and convenience in designing optical circuits.

Band Gaps of Two-Dimensional Square-Lattice Photonic Crystal with Button-Shaped Dielectric Rods

In this paper, a new structure of two-dimensional (2D) square-lattice photonic crystal (SLPC) with button-shaped dielectric rods (BSDRs) is designed, and the properties of band gaps are analyzed by Plane Wave Expansion Method (PWM). The optimal samples that possess the width of absolute band gap are obtained by scanning the three parameters: the radius of large circular R in button mark, the ratio of the radius of small circular to the radius of large circular r/R, and the rotating angle of button mark Ө. It is shown that when r/R=0.485, R=0.406um, and Ө =750, the largest absolute band gap of 0.0406 (ωa/2πc) exists for normalized frequencies in the range 0.7501 to 0.7910 (ωa/2πc). Besides，we can get at most five absolute band gaps when r/R=0.485, R=0.406um, and Ө =600.

Evaluation of the two-particle propagator for the Hubbard model with the help of theHubbard-I approximation

The Hubbard-I approximation is generalized to allow for direct evaluation of the equal-timeanomalous two-electron propagator for the Hubbard model on a two-dimensional squarelattice. This propagator is compared against the quantum Monte Carlo data obtainedby Aimi and Imada (2007 J. Phys. Soc. Japan 76 113708) in the limit of strongelectron–electron interaction. The Hubbard-I predictions are in good qualitativeagreement with the Monte Carlo results. In particular, d-wave correlations decay ascr − 3 (‘free-electron’ behaviour)if the separation r exceeds 2–3 lattice constants. However, the Hubbard-I approximation underestimates the coefficientc by a factor of about 3. We conclude that the Hubbard-I approximation,despite its simplicity and artefacts, captures the qualitative behaviour of thetwo-particle propagator for the Hubbard model, at least for moderate values ofr.

Surface plasmon polaritons on square-lattice arrays of three-fold symmetric nanostructures

The influence of the geometry of three-fold symmetric rotor shaped nanostructures arranged as a two-dimensional square-lattice on the excitation of surface plasmon polaritons (SPPs) is studied numerically. We consider SPP-related extrema of the far-field reflectivity R ( α ) as a function of the polarization angle α of the incident light. In agreement with recent experimental work, it is observed that these extrema shift away from α = 0 ° and α = 90 ° , where they are found for rotationally invariant nanostructures. The polarization angle corresponding to the most efficient SPP excitation is found to be independent of the shape of the individual nanostructures. We further investigate the influence of the shape and size of the nanostructures and discuss consequences for optical near- and far-field properties.

Nonequilibrium stationary states and phase transitions in directed Ising models

We study the nonequilibrium properties of directed Ising models with non-conserveddynamics, in which each spin is influenced by only a subset of its nearest neighbours. Wetreat the following models: (i) the one-dimensional chain; (ii) the two-dimensional squarelattice; (iii) the two-dimensional triangular lattice and (iv) the three-dimensionalcubic lattice. We raise and answer the question: (a) under what conditions is thestationary state described by the equilibrium Boltzmann–Gibbs distribution? Weshow that, for models (i), (ii) and (iii), in which each spin ‘sees’ only half of itsneighbours, there is a unique set of transition rates, namely with exponentialdependence in the local field, for which this is the case. For model (iv), we find thatany rates satisfying the constraints required for the stationary measure to beGibbsian should satisfy detailed balance, ruling out the possibility of directeddynamics. We finally show that directed models on lattices of coordination numberz≥8 with exponential rates cannot accommodate a Gibbsian stationary state. We conjecturethat this property extends to any form of the rates. We are thus led to the conclusion thatdirected models with Gibbsian stationary states only exist in dimensions one and two.We then raise the question: (b) do directed Ising models, augmented by Glauberdynamics, exhibit a phase transition to a ferromagnetic state? For the modelsconsidered above, the answers are open problems, with the exception of the simplecases (i) and (ii). For Cayley trees, where each spin sees only the spins further fromthe root, we show that there is a phase transition provided the branching ratio,q, satisfiesq≥3.

Symmetry Classes of Spin and Orbital Ordered States in a t2g Hubbard Model on a Two-Dimensional Square Lattice

Masanori Hamada,1 Akira Nakanishi,2 Akira Goto3 and Masa-aki Ozaki4 1Graduate School of Materials Science, Nara Institute of Science and Technology, Ikoma 630-0192, Japan 2Department of General Education, Osaka Institute of Technology, Osaka 535-8585, Japan 3Department of General Education, Kochi National College of Technology, Nangoku 599-8531, Japan 419-21 Kohata Kumakouji, Uji, Kyoto 611-0002, Japan

二维正方晶格光子晶体平板的近场成像特性

二维正方晶格光子晶体平板的近场成像特性

Density of States in Two-DimensionalSquare Lattices Around Half Filling with Strong Impurities

We calculate the lowest-order quantum-interference correction tothe density of states (DOS) of weakly-disordered two-dimensional(2D) tight-binding square lattices around half filling. Theimpurities are assumed to be randomly distributed on smallfractions of the sites, and have a strong potential yielding aunitary-limit scattering. In addition to the usual diffusive modesin the retarded-advanced channel, there appear diffusive πmodes in the retarded-retarded (or advanced-advanced) channel dueto the existence of particle-hole symmetry. It is found that theπ-mode diffuson gives rise to a logarithmic suppression to theDOS near the band center, which prevails over the positivecorrection contributed by π-mode cooperon. As a result, theDOS is subject to a negative total correction. This result isqualitatively different from the divergent behavior of the DOS atthe band center predicted previously for disordered 2Dtwo-sublattice models with the particle-hole symmetry.

Resonating-Valence-Bond Ground State ofCaV4O9Studied by the Gutzwiller-Projected Schwinger-Boson Method

An antiferromagnetic Heisenberg model on a 1/5-depleted two-dimensional square-lattice, a model of CaV$_4$O$_9$, is investigated by variational Monte Carlo simulation. A prototype of a trial wave function is made by projecting out the doubly occupied states from the Schwinger-boson mean-field solution. Then variational Monte Carlo simulation is performed up to $40 \times 40 $ sites(including $320$ vacant sites). The optimized state has the lowest energy, $-0.5510J$, ever reported. For this state energies of a dimer bond and a plaquette bond, staggered magnetization, static structure factor, and excitation spectrum are calculated. It is shown that the N\'eel order survives and there is no gap at isotropic coupling.

Surface magnetic anisotropy in amorphous alloys

The total in-plane magnetic anisotropy and the in-plane surface magnetic anisotropy constants have been measured in nearly-zero magnetostrictive amorphous ribbons in as-quenched state. The magnetostatic energy of a two-dimensional square-lattice of parallelepipeds or ellipsoids, whose dimensions are determined by the parameters characterizing the roughness, is evaluated. From the results obtained, it is concluded that the in-plane surface anisotropy can be magnetostatic in origin but it has little influence on the total in-plane magnetic anisotropy of the ribbon. >

Structure of large two-dimensional square-lattice diffusion-limited aggregates: Approach to asymptotic behavior

Efficient algorithms have been used to grow large (4×106 site) diffusion-limited aggregation (DLA) clusters on two-dimensional (2D) square lattices. As the clusters grow larger, their envelope grows, from a more or less round shape characteristic of small clusters, through a diamond shape characteristic of clusters containing about 105 sites, into a cross shape. Results from about 25 clusters indicate that the exponents describing the length l and width w of the four major arms vary continuously with M (the cluster mass) over the range 103<M<4×106. We find that the effective exponent ν?=dln(l)/dln(M) increases systematically from 0.585 to 0.61 at the highest mass. This may be consistent with a limiting value of (2/3) (as found for uniaxially biased DLA in two dimensions) but only with large corrections to scaling in our range of M. The exponent ν⊥=dln(w)/dln(M) decreases systematically, to about 0.48 at M=4×106. Our results are consistent with an asymptotic (scaling) fractal geometry for square-lattice DLA but suggest that these fractals are neither self-similar nor homogeneous.

A collision model on the two-dimensional square-lattice

A collision model on the two-dimensional square-lattice