Two-dimensional Triangular Lattice Research Articles

Tuning of Magnetic Ordering by Y Substitution in Ca3Co2O6

We have studied the magnetic and thermal properties of Y substituted Ca 3 Co 2 O 6 . Ca 3 Co 2 O 6 exhibits the ferrimagnetic ground state due to ferromagnetic intrachain coupling and antiferromagnetic interchain coupling. As Y substitution increases, which results in variation of the interaction strength of both interchain and intrachain coupling, gradual but unique changes of ground state from ferrimagnetic to nonmagnetic state have been observed in dc susceptibility, isothermal magnetization, heat capacity, and ac susceptibility. Y substitution induces site percolation on Co–O one-dimensional (1D) chain as well as Co two-dimensional (2D) triangular lattice, and site percolation as well as frustration explains experimental results of doped Co–O 1D chain system. The spin configuration of the Y substituted Ca 3 Co 2 O 6 can be understood by using crystal field splitting model.

Tunable band gap in a photonic crystal modulated by a nematic liquid crystal

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the tunable band gap in a photonic crystal modulated by a nematic liquid crystal. Numerical simulations show that the band gaps can be continuously tuned in two-dimensional square and triangular lattices of cylinders by infiltrating nematic liquid crystals. Then we can control the band gap in a PC structure. We also analyzed the gap maps of tunable band gap by considering various indices modulation of liquid crystals. These results can be used as tunable field-sensitive polarizer in photonic integrated circuits.

Slanted-pore photonic band-gap materials

We present a detailed analysis of three-dimensional photonic band-gap materials consisting of lattices of slanted pores with n = 2 , 3, and 4 pores per unit cell. These slanted pores emanate from one or two masks consisting of a two-dimensional square or triangular lattice of holes placed on the top surface of the crystal. We also consider the case in which the top surface is "polished" at an angle after the first set of slanted pores is generated from the first mask. A second set of slanted pores is then generated from a second mask placed on the new angled surface. Using these architectures, we demonstrate photonic band gaps of up to 25% of the gap center frequency when the crystal is made from materials with a dielectric constant ratio of 11.9:1 (silicon with air pores). The proposed structures are amenable to microfabrication using established techniques such as x-ray lithography or two-photon direct writing in a polymer template, followed by inversion and replication of the template with polycrystalline silicon. They can also be microfabricated by direct plasma etching in single crystal semiconductors. An alternative fabrication protocol consists of photoelectrochemical etching of deep pores in a single crystal semiconductor followed by focused ion beam or reactive ion etching of the second lattice of directed pores.

Electron correlation in the two-dimensional triangular lattice of [formula omitted] with [formula omitted

Magnetism of layered cobaltites Na x CoO 2 with x = 0.6 and 0.9 has been investigated by a positive muon spin rotation and relaxation ( μ + SR) spectroscopy together with magnetic susceptibility and specific heat measurements, using single-crystal samples in the temperature range between 250 and 1.8 K. Zero-field μ + SR measurements on Na 0.9 CoO 2 indicate a transition to an incommensurate spin density wave state at 19 K ( = T SDW ) . Since Na 0.6 CoO 2 is paramagnetic down to 1.8 K, the magnitude of T SDW is found to strongly depend on x . This behavior is explained using the Hubbard model within a mean field approximation on two-dimensional triangle lattice in the CoO 2 plane. Also, both the appearance of the IC-SDW state by the change in x and the magnitude of the electronic specific heat parameter of Na 0.6 CoO 2 indicate that Na x CoO 2 is unlikely to be a typical strongly correlated electron system.

The Influence of Cation and Vacancy Distributions on the Ionic Conductivity of Acceptor Doped Oxygen Ion Conductors

Abstract We present a simple model for the ionic conductivity of an acceptor doped oxygen ion conductor, (A1− x BB x B)O2− x B/2, which can be applied to yttria doped zirconia (YSZ). The model considers repulsive interaction between the dopant cations and interactions between oxygen vacancies and dopant cations, which may be zero, attractive or repulsive. For simplicity, we consider a two-dimensional triangular lattice, where the oxygen ions occupy triangles formed by the cations. At first we calculate the fractions of B-clusters consisting of B-pairs, B-triplets and B-quartets and then the fractions of AAA-, AAB-, ABB- and BBB-triangles. The vacancies are distributed to the triangles using quasi-chemical reactions for the exchange between the different sites. The resulting vacancy distribution is used in a simplified model for the oxygen ion conductivity which considers jump rates between different oxygen sites that depend on their local neighbourhood and the nature of the cation–cation edge which has to be crossed during a jump. Strongly reduced jump rates through A–B and B–B edges are necessary to obtain a maximum of the conductivity as a function of the dopant fraction. The most beneficial effect of the acceptor dopant is obtained for repulsive interaction between vacancies and dopant ions, such as Y, Gd or Sm, which are known to cause high oxygen ion conductivities. For dopants with attractive V–B interaction our model predicts only small oxygen ion conductivities.

Transmission of photonic crystal coupled-resonator waveguide (PhCCRW) structure enhanced via mode matching

A method for increasing the coupling efficiency between ridge optical waveguides and PhCCRWs is described. This increase is achieved via W1 channel waveguide sections, formed within a two-dimensional triangular lattice photonic crystal using mode-matching. The mode-matching is achieved by low quality-factor modified cavities added to both the input and output ports of the PhCCRW. A three dimensional finite-difference time-domain method has been used to simulate light propagation through the modified PhCCRW. We have fabricated PhCCRWs working at 1.5microm in silicon-on-insulator material. Measurements and simulations show that the overall transmission is improved by a factor of two.

Spin-resonance peak inNaxCoO2∙yH2Osuperconductors: A probe of the pairing symmetry

Spin dynamics in the superconducting state of the newly discovered ${\mathrm{Na}}_{x}\mathrm{Co}{\mathrm{O}}_{2}∙y{\mathrm{H}}_{2}\mathrm{O}$ superconductor with three possible pairing symmetries (${p}_{x}+i{p}_{y}$, $d+i{d}^{\ensuremath{'}}$, and $f$ wave) is studied theoretically on a two-dimensional triangular lattice. We find that a spin resonance peak, which is found to have a close relevance to the relative phase of the gap function and the geometry of the Fermi surface, appears in both the in-plane and the out-of-plane components of the spin susceptibility for the spin-singlet $(d+i{d}^{\ensuremath{'}})$-wave pairing, while only in the out-of-plane (in-plane) component for the spin-triplet $({p}_{x}+i{p}_{y})$-wave ($f$-wave) pairing. We also indicate that there is no spin resonance for an $s$-wave pairing. These distinct features may be used to probe or determine the pairing symmetry in this compound unambiguously.

Fast Tree Search for A Triangular Lattice Model of Protein Folding

Using a triangular lattice model to study the designability of protein folding, we overcame the parity problem of previous cubic lattice model and enumerated all the sequences and compact structures on a simple two-dimensional triangular lattice model of size 4+5+6+5+4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, and achieved 223+212 different sequences excluding the reverse symmetry sequences. The total string number of distinct compact structures was 219,093, excluding reflection symmetry in the self-avoiding path of length 24 triangular lattice model. Based on this model, we applied a fast search algorithm by constructing a cluster tree. The algorithm decreased the computation by computing the objective energy of non-leaf nodes. The parallel experiments proved that the fast tree search algorithm yielded an exponential speed-up in the model of size 4+5+6+5+4. Designability analysis was performed to understand the search result.

Properties of Abrikosov lattices as photonic crystals

The possibility of viewing the Abrikosov vortices arranged into two-dimensional triangular lattices in type-II superconductors in external magnetic fields, as photonic crystals for electromagnetic waves, has been investigated theoretically. Due to the Bragg diffraction on a periodic lattice, electromagnetic waves with wavelengths corresponding to lattice spacings cannot propagate in the Abrikosov lattices with different dielectric constants inside and outside the vortices. Conditions for obtaining effective properties of the Abrikosov lattices as photonic crystals by changing of Ginzburg-Landau parameters and applied magnetic fields are clarified.

Effects of symmetry reduction in two-dimensional square and triangular lattices

We investigate the absolute photonic band gap (PBG) formation in two-dimensional (2-D) photonic crystals designed using symmetry reduction approach. The lattice symmetry, shape and orientation of dielectric scatterers affect the photonic gap parameters. We use symmetry reduction, achieved either by including additional rods into the lattice unit cell or by reorienting noncircular scatterers to engineer the photonic band gaps in 2-D square and triangular structures. The case of air rods drilled into silicon background is considered. We show that for square structures symmetry reduction can be an effective way to enlarge the absolute PBG, but for triangular lattices any modification of the crystal structure considerably reduces the absolute PBG width. We also discuss the practical technological feasibility of the proposed structures.

Electron correlation in the two-dimensional triangle lattice ofNaxCoO2

Magnetism of layered cobaltites ${\text{Na}}_{x}{\text{CoO}}_{2}$ with $x=0.6$ and 0.9 has been investigated by a positive muon spin rotation and relaxation $({\ensuremath{\mu}}^{+}\text{SR})$ spectroscopy together with magnetic susceptibility and specific-heat measurements, using single-crystal samples in the temperature range between 250 and $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Zero-field-(ZF-) ${\ensuremath{\mu}}^{+}\text{SR}$ measurements on ${\text{Na}}_{0.9}{\text{CoO}}_{2}$ indicate a transition from a paramagnetic to an incommensurate spin-density wave state (IC-SDW) at $19\phantom{\rule{0.3em}{0ex}}\mathrm{K}(={T}_{\text{SDW}})$. The anisotropic ZF-${\ensuremath{\mu}}^{+}\text{SR}$ spectra suggest that the oscillating moments of the IC-SDW direct along the $c$ axis. Since ${\text{Na}}_{0.6}{\text{CoO}}_{2}$ is paramagnetic down to $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the magnitude of ${T}_{\text{SDW}}$ is found to strongly depend on $x$. This behavior is well explained using the Hubbard model within a mean-field approximation on two-dimensional triangular lattice in the ${\text{CoO}}_{2}$ plane. Also, both the appearance of the IC-SDW state by the change in $x$ and the magnitude of the electronic specific-heat parameter of ${\text{Na}}_{0.6}{\text{CoO}}_{2}$ indicate that ${\text{Na}}_{x}{\text{CoO}}_{2}$ is unlikely to be a typical strongly correlated electron system.

Two-dimensional lattice-fluid model with waterlike anomalies.

We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed.

Structural determination of iodine localization in single-walled carbon nanotube bundles by diffraction methods

X-ray- and neutron-diffraction investigations of iodine intercalated single-walled carbon nanotubes are reported. Charge transfer between nanotubes and iodine leads to the formation of ${\mathrm{I}}_{n}^{\ensuremath{-}}$ species (mainly ${\mathrm{I}}_{3}^{\ensuremath{-}}$ and ${\mathrm{I}}_{5}^{\ensuremath{-}})$ as shown by Raman spectroscopy. By combining x-ray and neutron experiments, we show that the ${\mathrm{I}}_{n}^{\ensuremath{-}}$ species are mainly localized inside the tubes. By comparing the experimental diagrams to our calculations, we show that some ${\mathrm{I}}_{n}^{\ensuremath{-}}$ species are also present in the channels in between three tubes inside the bundles. The intercalation process also increases the disorder of the two-dimensional triangular lattice leading to a broad distribution of the iodine-carbon distances. Well ordered single-walled nanotube bundles are recovered after dedoping.

Dome‐Shaped Magnetic Phase Diagram of Thermoelectric Layered Cobaltites

AbstractFor Abstract see ChemInform Abstract in Full Text.

Kinetic phase transition in A2 + B2 -->2AB reaction system.

Three lattice gas models for A2 + B2 -->2AB reaction system are studied by Monte Carlo simulation in two-dimensional triangular lattice surface. When both A2 and B2 adsorb and dissociate on the catalytic surface in the random dimer-filling mechanism or in the end-on dimer-filling mechanism, there is no reactive window in the reaction system and just a discontinuous phase transition appears from a "B+vacancy" poisoned state to an "A+vacancy" poisoned state. However, a reactive window appears when one of the two dimers, A2, dissociates in the random dimer-filling mechanism but another dimer, B2, is in the end-on dimer-filling mechanism and the system exhibits a discontinuous phase transition from the active reaction state to a B+ vacancy poisoned state and a continuous phase transition to an "A+vacancy" poisoned state. Furthermore, we show that the critical behavior of the continuous phase transition with infinitely many absorbing states belongs to the robust directed percolation universality class.

Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs

We present a channel drop filter by using channel drop tunneling processes in a two-dimensional triangular lattice photonic crystal slab. The channel drop filter is composed of two waveguides and two donor-type three-missing-holes cavities. At resonance, the power transferred to the drop waveguide and the power remaining in the bus are found to be about 61% and 5%, respectively. In order to improve the filter response, the out-of-plane quality factor must be much higher than the in-plane quality factor.

Dome‐Shaped Magnetic Phase Diagram of Thermoelectric Layered Cobaltites

AbstractFor Abstract see ChemInform Abstract in Full Text.

Group theoretical classification of the electronic structure of LiNiO2

Abstract I choose and discuss the electronic structure proper to two-dimensional triangular lattice among states classified group theoretically. Those are spin triangle arrangements, orbital ones and novel states whose wave function is expressed by a linear combination of magnetic octupole wave function.

Dome-shaped magnetic phase diagram of thermoelectric layered cobaltites.

Using muon spin spectroscopy we have found that, for both NaxCoO(2) (0.6<or=x<or=0.9) and three- and four-layer cobaltites, a common low temperature magnetic state (which in some cases is manifest as an incommensurate spin density wave) forms in the CoO(2) planes. Here we summarize those results and report an almost dome-shaped relation between the transition temperature into the low-T magnetic state and the composition x for NaxCoO(2) and/or the high-temperature asymptotic limit of thermopower in the more complex three- and four-layer cobaltites. This behavior is explained using the Hubbard model on a two-dimensional triangular lattice in the CoO(2) plane.

Group-theoretical description of the triangular air-silica photonic crystal - out-of-plane propagation

The method of assigning irreducible representations to modes in three-dimensional photonic structures is applied to the two-dimensional triangular air-silica lattice with out-of-plane wave propagation. In particular prediction of spatial symmetries of the crystal modes is addressed. We show how the photonic bands are affected by different rod radii and out-of-plane components from a group-theoretical point of view. One particular defect mode is analyzed and the structure which is optimal for air-guidance is found.