2D Rectangular Lattice Research Articles

Theory of the collective behavior of two-dimensional periodic ensembles of dipole-coupled magnetic nanoparticles

The magnetic behavior of two-dimensional (2D) periodic ensembles of dipole-coupled nanoparticles (NPs) is investigated theoretically by considering all possible structural organizations in 2D Bravais lattices, namely, square, triangular, rectangular, rhombic, and oblique lattices. The different interaction-energy landscapes (ELs) are characterized by determining the local minima that define the stable and metastable magnetic configurations as well as the transition states connecting them. The topology of the resulting ergodic ensemble of stationary states is analyzed from both local and energy perspectives by calculating the corresponding kinetic networks and disconnectivity graphs. For all lattices, the magnetic orders of the ground-state and low-lying metastable configurations are identified, including the elementary relaxation processes between them. A remarkable profound dependence of the collective magnetic behavior on the structural arrangement of the NPs is revealed. Square and triangular nanostructures are extremely good structure seekers, showing starlike kinetic networks and disconnectivity graphs with palm-tree form. Their continuously degenerate ground states are throughout-reaching hubs connected to nearly all excited magnetic configurations over a single first-order saddle point. Rhombic ensembles have double-funnel ELs in which the time-inversion-related ground states play the role of hubs with exceedingly high connectivity densities. These systems need to undergo very few elementary transitions with small downward energy barriers to relax from any configuration towards one of the ground states. However, the energy barriers between the two funnels are quite large and, furthermore, they increase as the number of particles in the unit cell is increased. Therefore, ergodicity breaking is expected in the thermodynamic limit. Finally, the rectangular and oblique lattices show contrasting ground-state orders, the former consists of an antiferromagnetic alternation of head-to-tail chains of spins while the latter is ferromagnetic. Nevertheless, the ELs of these nanostructures are qualitatively very similar. In both cases, all excited magnetic configurations consist of independent flipping of the chains of spins that are formed along the direction of the shorter Bravais vector. The whole energy spectrum of metastable magnetic configurations can thus be mapped to a one-dimensional Ising model. As a result, the kinetic network of stationary points is latticelike and the disconnectivity graphs have a willow-tree form. In conclusion, the collective magnetic behaviors of nanostructures having different point-group symmetries are contrasted and related by varying the parameters of the lattices that interpolate between them.

Electro-Elastic Modeling of Thermal Spin Transition in Diluted Spin-Crossover Single Crystals.

Spin-crossover solids have been studied for many years for their promising applications as optical switches and reversible high-density memories for information storage. This study reports the effect of random metal dilution on the thermal and structural properties of a spin-crossover single crystal. The analysis is performed on a 2D rectangular lattice using an electro-elastic model. The lattice is made of sites that can switch thermally between the low-spin and high-spin states, accompanied by local volume changes. The model is solved by Monte Carlo simulations, running on the spin states and atomic positions of this compressible 2D lattice. A detailed analysis of metal dilution on the magneto-structural properties allows us to address the following issues: (i) at low dilution rates, the transition is of the first order; (ii) increasing the concentration of dopant results in a decrease in cooperativity and leads to gradual transformations above a threshold concentration, while incomplete spin transitions are obtained for big dopant sizes. The effects of the metal dilution on the spatiotemporal aspects of the spin transition along the thermal transition and on the low-temperature relaxation of the photo-induced metastable high-spin states are also studied. Significant changes in the organization of the spin states are observed for the thermal transition, where the single-domain nucleation caused by the long-range elastic interactions is replaced by a multi-droplet nucleation. As to the issue of the relaxation curves: their shape transforms from a sigmoidal shape, characteristic of strong cooperative systems, into stretched exponentials for high dilution rates, which is the signature of a disordered system.

Clamping of spin-crossover solid inducing crystal bending and spatial spin organization

The present work investigates the effect of mechanical clamping on thermally induced spin transition in a deformable spin-crossover single crystal. We performed the analysis, which combined Monte Carlo and molecular dynamics simulations, on a 2D rectangular lattice using an electro-elastic model, taking into account for the change of spin states and volume along the transition process. The molecules (the sites) of the crystal can be either in the low-spin (LS) or in the high-spin (HS) states which are respectively characterized with small and bigger molecular volumes. We found that straining the system edge along the thermal spin transition not only influences the nature of the phase transition which changes from first-order to continuous but also causes the appearance of significant macroscopic bending effects. Furthermore, the spatiotemporal investigations of the strained spin transition networks revealed the formation of spatially modulated HS/LS patterns resulting from the system's bending which promotes spatially organized tensile and compressive regions. These results demonstrate the interplay/competition between the stretching effects favored by temperature and the macroscopic bending triggered by the external constraints imposed to the lattice, lead to the emergence of complex self-organized spin structures and shape deformation in the strained SCO solids.

Photonic crystal-based biosensor for detection of human red blood cells parasitized by plasmodium falciparum

In this paper, a biosensors based on a two-dimensional photonic crystal (2D PhC) waveguide including a ring resonator is designed and simulated based on refractive index changes of red blood cells. The proposed biosensor structure consists of an elliptical photonic crystal ring resonator and two linear waveguides containing silicon nitride rods in a 2D rectangular lattice with circular rods. The biosensor is utilized to detect the stages of the Plasmodium falciparum cycle in red blood cells and to diagnose malaria disease. The proposed design distinguishes with high sensitivity between normal red blood cells and cells infected with Plasmodium falciparum. This biosensor is very compact, consists of gold rods in the air background and works very well at two input central wavelengths of 0.514 and 1.55 μm. The finite-difference time-domain (FDTD) method is used to simulate and investigate the device. The biosensor is extremely compact which is very suitable for lab-on-chip applications and exhibits higher sensitivity at both input central wavelengths compared with that of previously reported sensors.

Effects of alkyl-substituent length on photovoltaic performance of bulk heterojunction solar cells utilizing non-peripherally octaalkyltetrabenzotriazaporphyrins

We report alkyl-substituent length dependences of optical and electronic characteristics, crystal structures, and photovoltaic performances of bulk-heterojunction organic solar cells utilizing non-peripherally alkyl-substituted tetrabenzotriazaporphyrin (CnTBTAPH2). By extending the pentyl (n = 5) to octyl (n = 8) substituents, the molecular alignment was affected and the intercolumnar packing was probably modified from pseudo-hexagonal structure to 2D rectangular lattice. Furthermore, the devices utilizing the C5TBTAPH2 and C6TBTAPH2 discotic macrocycles with the short-alkyl-substituents exhibited a relatively high photovoltaic performance with a power conversion efficiency of around 4.7% in comparison with those utilizing the long-alkyl-substituted macrocycles. These differences in the device performance could be understood by taking the hole mobility and highest occupied molecular orbital energy level into consideration.

A two-state model for the modulated B7 liquid crystalline phase exhibited by bent-core molecules

Liquid crystals (LC) made of bent-core (BC) organic molecules have been intensively studied over the past two decades. The B7 LC consists of smectic layers in which tilted molecules have an in-plane polar packing, the polarization vector (P) having a splay distortion forming stripes of tens of nanometers in width, and undulated layers giving rise to 2D rectangular or oblique lattices. The prevailing phenomenological theory attributes this structure to a strong coupling between molecular tilt in the layers and divP. Based on our recent studies on other phases exhibited by BC molecules, we propose a new model in which the physical origin of the stripes arises from a minority (~10%) of the BC molecules having less bent excited state (ES) conformers which can freely rotate about their long axes, and aggregate to form smectic C type walls, in which the tilt angle is relatively small. The more bent ground state (GS) conformers with polar packing in turn form the splayed structure between such walls to lower the free energy. The mismatch in the layer spacing between the domains with ES and GS conformers generates the structures in the B7 phase described above. The model predicts a weak first order transition from B7 to the uniform B2 phase as the temperature is lowered, as experimentally observed in some compounds. We show that the observed slow increase of the stripe width in the LC to micrometer dimensions in free standing films can be attributed to changes in the physical parameters by chemical degradation and absorption of ions by the exposed polarized layers. We also describe different possible structures of the undulated layers, including a stacking of racemic pairs of SmCaPF layers within the stripes. Some possible methods of testing the model are also indicated.

Lattices of Hydrodynamically Interacting Flapping Swimmers

Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in modeling the temporally long-lived hydrodynamic interactions between many dynamic bodies. We address this through a novel discrete-time dynamical system (iterated map) that describes the hydrodynamic interactions between flapping swimmers arranged in one- and two-dimensional lattice formations. Our 1D results exhibit good agreement with previously published experimental data, in particular predicting the bistability of schooling states and new instabilities that can be probed in experimental settings. For 2D lattices, we determine the formations for which swimmers optimally benefit from hydrodynamic interactions. We thus obtain the following hierarchy: while a side-by-side single-row "phalanx" formation offers a small improvement over a solitary swimmer, 1D in-line and 2D rectangular lattice formations exhibit substantial improvements, with the 2D diamond lattice offering the largest hydrodynamic benefit. Generally, our self-consistent modeling framework may be broadly applicable to active systems in which the collective dynamics is primarily driven by a fluid-mediated memory.

Pore-scale network modeling of microporosity in low-resistivity pay zones of carbonate reservoir

Archie's law is commonly used for the estimation of brine saturation using electrical conductivity of sedimentary rock. For a formation with narrow pore size distribution (PSD), low resistivity could mean high water saturation and hence, high water production. This, however, is not the case for many formations with wide PSDs, for which Low Resistivity Pay (LRP) zones have been reported with very low or none water cut production. One of the main causes resulting in LRP zones, especially in carbonates, is the existence of wide PSDs. Due to their small sizes, micro-pores have much higher threshold capillary pressures during drainage in a water-wet sample. In these systems, oil as the non-wetting phase preferably occupies larger pores leaving micro-pores saturated with brine. The existence of connected pathways through micro-pores that are fully saturated with a conductive phase (i.e., brine) creates ‘shortcuts’ for the electrical current which causes a short circuit and, ultimately, lowers rock resistivity measured from logs. Here in this work, we investigate the impact of microporosity on the electrical properties of porous media under multiphase flow conditions. We develop a pore-scale network model for the simulation of displacement sequences during drainage and imbibition in the presence of micro-pore networks. To do so, we first construct ‘macro’ networks on 2D rectangular lattices which are later altered to include micro-pores. A comprehensive set of sensitivity analyses is performed to assess the impact of various parameters including the tortuosity, geometry, and location of the microporosity (i.e., parallel or in series, continuous or non-continuous). Also, 3D networks for two different rock samples are used to investigate the effect of PSD on the electrical resistivity curves. This work helps to examine the use of Archie's equation for field applications, specifically, for evaluating formations with wide PSDs.

Hourglass Fermion in Two-Dimensional Material.

The hourglass fermion, as an exotic quasiparticle protected by nonsymmorphic symmetry, has excited great research interest recently. However, its bulk counterpart in two-dimensional (2D) solid-state materials has seldom been studied. In this Letter, we propose a 2D rectangular lattice made of p_{x} and p_{y} orbitals with glide mirror symmetry but without inversion symmetry to realize the hourglass fermion. The glide mirror symmetry guarantees a Dirac nodal line, while the Rashba spin-orbital coupling splits it into two Weyl nodal lines and generates two pairs of hourglass fermion located at the glide mirror plane. Furthermore, based on first principles calculations, we predict a surface-supported 2D material Bi/Cl-SiC(111) to realize our proposal, making a huge-bandwidth hourglass cone. Moreover, the hourglass fermion exhibits a spin-momentum locking spin texture and also sustains a giant spin Hall conductivity. Our results demonstrate a general routine for designing an hourglass fermion in 2D materials, which will be easily extended to other surfaces with different adatoms and lattice symmetries.

Dynamical Hamiltonian engineering of 2D rectangular lattices in a one-dimensional ion chain

Controlling the interaction graph between spins or qubits in a quantum simulator allows user-controlled tailoring of native interactions to achieve a target Hamiltonian. Engineering long-ranged phonon-mediated spin–spin interactions in a trapped ion quantum simulator offers such a possibility. Trapped ions, a leading candidate for quantum simulation, are most readily trapped in a linear 1D chain, limiting their utility for readily simulating higher dimensional spin models. In this work, we introduce a hybrid method of analog-digital simulation for simulating 2D spin models which allows for the dynamic changing of interactions to achieve a new graph using a linear 1D chain. We focus this numerical work on engineering 2D rectangular nearest-neighbor spin lattices, demonstrating that the required control parameters scale linearly with ion number. This hybrid approach offers compelling possibilities for the use of 1D chains in the study of Hamiltonian quenches, dynamical phase transitions, and quantum transport in 2D and 3D.

Multiple nonlinear Bragg diffraction of femtosecond laser pulses in a photonic lattice with hexagonal domains

The frequency doubling of femtosecond laser pulses in a two-dimensional (2D) rectangular nonlinear photonic lattice with hexagonal domains is studied experimentally and theoretically. The broad fundamental spectrum enables frequency conversion under nonlinear Bragg diffraction for a series of transverse orders at a fixed longitudinal quasi-phase-matching order. The consistent nonstationary theory of the frequency doubling of femtosecond laser pulses is developed using the representation based on the reciprocal lattice of the structure. The calculated spatial distribution of the second-harmonic spectral intensity agrees well with the experimental data. The condition for multiple nonlinear Bragg diffraction in a 2D nonlinear photonic lattice is offered. The hexagonal shape of the domains contributes to multibeam second harmonic excitation. The maximum conversion efficiency for a series of transverse orders in the range 0.01%–0.03% is obtained.

Systematic study of the completeness of two-dimensional classical ϕ4 theory

The completeness of some classical statistical mechanical (SM) models is a recent result that has been developed by quantum formalism for the partition functions. In this paper, we consider a 2D classical [Formula: see text] filed theory whose completeness has been proved in [V. Karimipour and M. H. Zarei, Phys. Rev. A 85 (2012) 032316]. We give a new and general systematic proof for the completeness of such a model where, by a few simple steps, we show how the partition function of an arbitrary classical field theory can be derived from a 2D classical [Formula: see text] model. To this end, we start from various classical field theories containing models on arbitrary lattices and also [Formula: see text] lattice gauge theories. Then we convert them to a new classical field model on a nonplanar bipartite graph with imaginary kinetic terms. After that, we show that any polynomial function of the field in the corresponding Hamiltonian can approximately be converted to a [Formula: see text] term by adding enough numbers of vertices to the bipartite graph. In the next step, we give a few graphical transformations to convert the final nonplanar graph to a 2D rectangular lattice. We also show that the number of vertices which should be added grows polynomially with the number of vertices in the original model.

Relativistic energy-dispersion relations of 2D rectangular lattices

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters [Formula: see text], core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

Algorithm for Identification of Infinite Clusters Based on Minimal Finite Automaton

We propose a finite automaton based algorithm for identification of infinite clusters in a 2D rectangular lattice with L=X×Y cells. The algorithm counts infinite clusters and finds one path per infinite cluster in a single pass of the finite automaton. The finite automaton is minimal according to the number of states among all the automata that perform such task. The correctness and efficiency of the algorithm are demonstrated on a planar percolation problem. The algorithm has a computational complexity of O(L) and could be appropriate for efficient data flow implementation.

A design principle of polymers processable into 2D homeotropic order.

How to orient polymers homeotropically in thin films has been a long-standing issue in polymer science because polymers intrinsically prefer to lie down. Here we provide a design principle for polymers that are processable into a 2D homeotropic order. The key to this achievement was a recognition that cylindrical polymers can be designed to possess oppositely directed local dipoles in their cross-section, which possibly force polymers to tightly connect bilaterally, affording a 2D rectangular assembly. With a physical assistance of the surface grooves on Teflon sheets that sandwich polymer samples, homeotropic ordering is likely nucleated and gradually propagates upon hot-pressing towards the interior of the film. Consequently, the 2D rectangular lattice is constructed such that its b axis (side chains) aligns along the surface grooves, while its c axis (polymer backbone) aligns homeotropically on a Teflon sheet. This finding paves the way to molecularly engineered 2D polymers with anomalous functions.

Interfacial self-assembly of a bacterial hydrophobin

The majority of bacteria in the natural environment live within the confines of a biofilm. The Gram-positive bacterium Bacillus subtilis forms biofilms that exhibit a characteristic wrinkled morphology and a highly hydrophobic surface. A critical component in generating these properties is the protein BslA, which forms a coat across the surface of the sessile community. We recently reported the structure of BslA, and noted the presence of a large surface-exposed hydrophobic patch. Such surface patches are also observed in the class of surface-active proteins known as hydrophobins, and are thought to mediate their interfacial activity. However, although functionally related to the hydrophobins, BslA shares no sequence nor structural similarity, and here we show that the mechanism of action is also distinct. Specifically, our results suggest that the amino acids making up the large, surface-exposed hydrophobic cap in the crystal structure are shielded in aqueous solution by adopting a random coil conformation, enabling the protein to be soluble and monomeric. At an interface, these cap residues refold, inserting the hydrophobic side chains into the air or oil phase and forming a three-stranded β-sheet. This form then self-assembles into a well-ordered 2D rectangular lattice that stabilizes the interface. By replacing a hydrophobic leucine in the center of the cap with a positively charged lysine, we changed the energetics of adsorption and disrupted the formation of the 2D lattice. This limited structural metamorphosis represents a previously unidentified environmentally responsive mechanism for interfacial stabilization by proteins.

Wide-range and tunable diffraction management using 2D rectangular lattice photonic crystals

We propose that 2D rectangular lattice photonic crystals composed of dielectric rods can be utilized for wide-range and tunable diffraction management. The control of diffraction for a normally incident beam is achieved by either properly choosing the operating frequency or changing the refractive index of the dielectric rods. The convergent, collimated, and divergent beam behaviors corresponding to a wide range of diffraction are clearly illustrated using FDTD simulations. The tunability of diffraction around the frequency of super-collimation is also analyzed and demonstrated.

Chromonic‐Like Physical Luminescent Gels Formed by Ionic Octahedral Iridium(III) Complexes in Diluted Water Solutions

The first example of spontaneous self‐assembly of ionic octahedral Ir(III) complexes containing carboxylates counterions into luminescent ordered aqueous gel phases is reported. The gel phases formed at 2.5% w/w (“Ir‐Ci”:H20) are investigated by POM, 1H and 2H NMR and UV–vis spectroscopies, whereas a detailed structural analysis by WAXS, SAXS, and SANS experiments is performed for the acetate complex, in both anisotropic gel and isotropic phases. This comprehensive investigation shows that the complex with the shortest carboxylate self‐assembles into double string polyelectrolyte‐type supramolecular columns surrounded by the counterions, at low concentrations in the isotropic solution (1.0% w/w). Upon increasing concentration, these supramolecular columns grow one‐dimensionally, and eventually gelation occurs and birefringent textures begin to be observed by POM, resembling the textures developed by chromonic systems. The gelation occurs with the close packing of the supramolecular columns sheathed in their solvation shell into a 2D rectangular lattice. Furthermore, a significant enhancement of the luminescence quantum yield is observed for all the complexes in the gel phases with respect to the isolated molecule.

Sr2FeO3 with Stacked Infinite Chains of FeO4 Square Planes

The synthesis of Sr2FeO3 through a hydride reduction of the Ruddlesden-Popper layered perovskite Sr2FeO4 is reported. Rietveld refinements using synchrotron and neutron powder diffraction data revealed that the structure contains corner-shared FeO4 square-planar chains running along the [010] axis, being isostructural with Sr2CuO3 (Immm space group). Fairly strong Fe-O-Fe and Fe-Fe interactions along [010] and [100], respectively, make it an S = 2 quasi two-dimensional (2D) rectangular lattice antiferromagnet. This compound represents the end-member (n = 1) of the serial system Sr(n+1)FenO(2n+1), together with previously reported Sr3Fe2O5 (n = 2) and SrFeO2 (n = ∞), thus giving an opportunity to study the 2D-to-3D dimensional crossover. Neutron diffraction and Mössbauer spectroscopy show the occurrence of G-type antiferromagnetic order below 179 K, which is, because of dimensional reduction, significantly lower than those of the other members, 296 K in Sr3Fe2O5 and 468 K in SrFeO2. However, the temperature dependence of magnetic moment shows a universal behavior.

Optical simulation of three-dimensional x-ray diffraction using two-dimensional lattices and a Fabry–Perot etalon

The basic experimental setup of a Fabry–Perot etalon between a collimating and a focusing lens is modified by introducing 2D rectangular lattices between the etalon and the collimating lens. Consequently, the irradiance of the interference fringes on a screen in the focal plane of the focusing lens changes and is modified by the diffraction pattern of the 2D lattice. The constructive interference directions resulting from both the etalon and the diffraction by the 2D lattice have to correlate in order to obtain maximum irradiance. Considering this experiment in a didactical context and analysing how a 2D rectangular lattice is seen through the etalon, the investigation provides us with the concept of an optical space containing a row of virtual 2D lattices. Due to the partially reflecting plane surfaces of the etalon, different virtual images of the 2D lattice form a 3D lattice with a tetragonal or orthorhombic structure. As an optical interface, the simple setup with a 2D lattice and an etalon models a 3D lattice. Using a laser, the diffraction pattern of a 2D lattice and etalon can be used to optically simulate 3D x-ray diffraction. The experiments can be included wherever undergraduate or graduate students have to follow up Laue's formulation of x-ray diffraction.