Irreducible first Brillouin zone for two-dimensional magnonic crystals with asymmetric complex lattices

2021 ◽  
pp. 2150170
Author(s):  
Hui Yang ◽  
Guo-Hong Yun ◽  
Yong-Jun Cao
Keyword(s):  
Brillouin Zone ◽  
Unit Cell ◽  
Square Lattice ◽  
Two Dimensional ◽  
Area Formula ◽  
Irreducible Part ◽  
Full Band ◽  
Magnonic Crystals ◽  
Magnonic Crystal ◽  
Complex Basis

Two-dimensional (2D) magnonic crystal (MC) with an asymmetric complex basis is proposed in this paper, and its band structures are calculated in the whole area of the first Brillouin zone (BZ). This kind of MCs is composed of two different atoms in the unit cell, and the symmetry of the unit cell is broken due to changes in the position of the second atom, so the irreducible part of the BZ is no longer the small area [Formula: see text] for square lattice, and it must be expanded to the whole first BZ. Only by investigating the whole first BZ, can we get the true full band-gap for this kind of MCs.

Dispersion characteristics of periodic structural systems using higher order beam element dynamics

2019 ◽  
Vol 25 (2) ◽  
pp. 457-474
Author(s):  
M Ayad ◽  
N Karathanasopoulos ◽  
H Reda ◽  
JF Ganghoffer ◽  
H Lakiss
Keyword(s):  
Dynamic Equilibrium ◽  
Dimensional Space ◽  
Higher Order ◽  
Unit Cell ◽  
Square Lattice ◽  
Structural Systems ◽  
Discrete Dynamics ◽  
Two Dimensional ◽  
Dispersion Characteristics ◽  
Order Expansion

In the current work, we elaborate upon a beam mechanics-based discrete dynamics approach for the computation of the dispersion characteristics of periodic structures. Within that scope, we compute the higher order asymptotic expansion of the forces and moments developed within beam structural elements upon dynamic loads. Thereafter, we employ the obtained results to compute the dispersion characteristics of one- and two-dimensional periodic media. In the one-dimensional space, we demonstrate that single unit-cell equilibrium can provide the fundamental low-frequency band diagram structure, which can be approximated by non-dispersive Cauchy media formulations. However, we show that the discrete dynamics method can access the higher frequency modes by considering multiple unit-cell systems for the dynamic equilibrium, frequency ranges that cannot be accessed by simplified formulations. We extend the analysis into two-dimensional space computing with the dispersion attributes of square lattice structures. Thereupon, we demonstrate that the discrete dynamics dispersion results compare well with that obtained using Bloch theorem computations. We show that a high-order expansion of the inner element forces and moments of the structures is required for the higher wave propagation modes to be accurately represented, in contrast to the shear and the longitudinal mode, which can be captured using a lower, fourth-order expansion of its inner dynamic forces and moments. The provided results can serve as a reference analysis for the computation of the dispersion characteristics of periodic structural systems with the use of discrete element dynamics.

A Two-Dimensional Coordination Polymer Formed from Cobalt(II) and an Extended Dipyridyl Ligand

2020 ◽  
Vol 73 (6) ◽  
pp. 547 ◽  
Author(s):  
Hydar A. AL-Fayaad ◽  
Rashid G. Siddique ◽  
Kasun S. Athukorala Arachchige ◽  
Jack K. Clegg
Keyword(s):  
Coordination Polymer ◽  
Cell Volume ◽  
Crystal Structures ◽  
Unit Cell Volume ◽  
Suzuki Coupling ◽  
Unit Cell ◽  
Square Lattice ◽  
Two Dimensional ◽  
Cobalt Ions ◽  
One Dimensional

The synthesis of the extended dipyridyl ligand 4,4′-(2,5-dimethyl-1,4-phenylene)dipyridine (L) in an improved yield via the palladium catalysed Suzuki coupling of 4-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)pyridine (1) and 1,4-dibromo-2,5-dimethylbenzene (2) is reported along with its use to form a two-dimensional coordination polymer [Co2L2(OAc)4(H2O)2]n. The coordination polymer consists of one-dimensional chains of octahedral cobalt ions bridged by acetate ligands which are connected to form two dimensional sheets with square lattice (sql) topology via the dipyridyl ligands (L). The structure contains small voids totalling ~6.6% of the unit cell volume. The crystal structures 1, L, L·2H2O, and L·2HNO3 are also reported.

scholarly journals Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 328
Author(s):  
A. Nietner ◽  
B. Vanhecke ◽  
F. Verstraete ◽  
J. Eisert ◽  
L. Vanderstraeten
Keyword(s):  
Variational Principles ◽  
Valence Bond ◽  
Computational Effort ◽  
Unit Cell ◽  
Square Lattice ◽  
Partition Functions ◽  
Matrix Product ◽  
Two Dimensional ◽  
Matrix Product State ◽  
Tensor Networks

Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the description of such complex many-body systems, close to optimal variational principles based on such states are less obvious to come by. In this work, we generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices in the thermodynamic limit, to the study of regular two-dimensional tensor networks with a non-trivial unit cell. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell. We demonstrate the performance of our approach on the computation of the classical partition functions of the antiferromagnetic Ising model and interacting dimers on the square lattice, as well as of a quantum doped resonating valence bond state.

PHOTONIC DIRAC CONES REALIZED BY ACCIDENTAL DEGENERACY ON THE BRILLOUIN-ZONE BOUNDARY

2013 ◽  
Vol 28 (02) ◽  
pp. 1441008 ◽  
Author(s):  
KAZUAKI SAKODA
Keyword(s):  
Perturbation Theory ◽  
Group Theory ◽  
Brillouin Zone ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zone Boundary ◽  
Brillouin Zone Boundary ◽  
Exact Agreement ◽  
Accidental Degeneracy ◽  
Degenerate Perturbation Theory

The condition for the formation of Dirac cones at arbitrary points in the Brillouin zone by the accidental degeneracy of two photonic bands was examined by the degenerate perturbation theory and group theory based on the spatial symmetry of two modes. The analysis was applied to a two-dimensional square-lattice photonic crystal with C4v symmetry and the dispersion relation in the vicinity of the M point was examined. Exact agreement between the analytical and numerical calculation was obtained.

Effects of Asymmetrical Rotated Rectangular Basis in Two-Dimensional Gyromagnetic Photonic Crystals

2013 ◽  
Vol 834-836 ◽  
pp. 885-888
Author(s):  
Hui Ling Sun ◽  
Qing Bo Li ◽  
Hua Bao Chen ◽  
Bao Ding Chen
Keyword(s):  
Photonic Crystals ◽  
Band Structure ◽  
Band Gap ◽  
Brillouin Zone ◽  
Square Lattice ◽  
High Symmetry ◽  
Two Dimensional ◽  
Symmetry Line

The twist effects of the bands during the rotation of rectangular bases are analysed in two-dimensional gyromagnetic photonic crystals with a square lattice. We find that extrema’s position have been dislocated from the high-symmetry line in the whole area of the first Brillouin zone (BZ), resulting in erroneous values for the band gap. These make us to calculate the whole first BZ to obtain the authentic band structure instead of boundary calculation.

Two‐Dimensional V‐VI Binary Nanosheets with Square Lattice: A Theoretical Investigation

2021 ◽  
Author(s):  
Xin Qiao ◽  
Xiaodong Lv ◽  
Yinan Dong ◽  
Yanping Yang ◽  
Fengyu Li
Keyword(s):  
Theoretical Investigation ◽  
Square Lattice ◽  
Two Dimensional

scholarly journals Structural Disorder and Collective Behavior of Two-Dimensional Magnetic Nanostructures

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1392
Author(s):  
David Gallina ◽  
G. M. Pastor
Keyword(s):  
Interaction Energy ◽  
Time Evolution ◽  
Magnetic Nanostructures ◽  
Thermal Quenching ◽  
Structural Disorder ◽  
Square Lattice ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Two Dimensional ◽  
Energy Landscapes

Structural disorder has been shown to be responsible for profound changes of the interaction-energy landscapes and collective dynamics of two-dimensional (2D) magnetic nanostructures. Weakly-disordered 2D ensembles have a few particularly stable magnetic configurations with large basins of attraction from which the higher-energy metastable configurations are separated by only small downward barriers. In contrast, strongly-disordered ensembles have rough energy landscapes with a large number of low-energy local minima separated by relatively large energy barriers. Consequently, the former show good-structure-seeker behavior with an unhindered relaxation dynamics that is funnelled towards the global minimum, whereas the latter show a time evolution involving multiple time scales and trapping which is reminiscent of glasses. Although these general trends have been clearly established, a detailed assessment of the extent of these effects in specific nanostructure realizations remains elusive. The present study quantifies the disorder-induced changes in the interaction-energy landscape of two-dimensional dipole-coupled magnetic nanoparticles as a function of the magnetic configuration of the ensembles. Representative examples of weakly-disordered square-lattice arrangements, showing good structure-seeker behavior, and of strongly-disordered arrangements, showing spin-glass-like behavior, are considered. The topology of the kinetic networks of metastable magnetic configurations is analyzed. The consequences of disorder on the morphology of the interaction-energy landscapes are revealed by contrasting the corresponding disconnectivity graphs. The correlations between the characteristics of the energy landscapes and the Markovian dynamics of the various magnetic nanostructures are quantified by calculating the field-free relaxation time evolution after either magnetic saturation or thermal quenching and by comparing them with the corresponding averages over a large number of structural arrangements. Common trends and system-specific features are identified and discussed.

Spin-Singlet Ground State in Two-Dimensional S=1/2 Frustrated Square Lattice: (CuCl)LaNb2O7

2005 ◽  
Vol 74 (6) ◽  
pp. 1702-1705 ◽  
Author(s):  
H. Kageyama ◽  
T. Kitano ◽  
N. Oba ◽  
M. Nishi ◽  
S. Nagai ◽  
...  
Keyword(s):  
Ground State ◽  
Square Lattice ◽  
Singlet Ground State ◽  
Two Dimensional ◽  
Spin Singlet

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

Molecular Dynamics Simulations of Shock-Defect Interactions in Two-Dimensional Nonreactive Crystals

1992 ◽  
Vol 296 ◽  
Author(s):  
Robert S. Sinkovits ◽  
Lee Phillips ◽  
Elaine S. Oran ◽  
Jay P. Boris
Keyword(s):  
Molecular Dynamics ◽  
Hexagonal Lattice ◽  
Square Lattice ◽  
Two Dimensional ◽  
Connection Machine ◽  
Defect Sites ◽  
Principal Axes ◽  
Shock Motion ◽  
Defect Interactions ◽  
Dynamics Simulations

AbstractThe interactions of shocks with defects in two-dimensional square and hexagonal lattices of particles interacting through Lennard-Jones potentials are studied using molecular dynamics. In perfect lattices at zero temperature, shocks directed along one of the principal axes propagate through the crystal causing no permanent disruption. Vacancies, interstitials, and to a lesser degree, massive defects are all effective at converting directed shock motion into thermalized two-dimensional motion. Measures of lattice disruption quantitatively describe the effects of the different defects. The square lattice is unstable at nonzero temperatures, as shown by its tendency upon impact to reorganize into the lower-energy hexagonal state. This transition also occurs in the disordered region associated with the shock-defect interaction. The hexagonal lattice can be made arbitrarily stable even for shock-vacancy interactions through appropriate choice of potential parameters. In reactive crystals, these defect sites may be responsible for the onset of detonation. All calculations are performed using a program optimized for the massively parallel Connection Machine.

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