Two-dimensional Triangular Lattice Research Articles

Colloidal particles in a drying suspension: A phase field crystal approach

Using a phase field crystal model we study the structure and dynamics of a drop of colloidal suspension during evaporation of the solvent. We model an experimental system where contact line pinning of the drop on the substrate is non-existent. Under such carefully controlled conditions, evaporation of the drop produces an ordered or disordered arrangement of the colloidal residue depending only on the initial average density of solute and the drying rate. We obtain a non-equilibrium phase boundary showing amorphous and crystalline phases of single component and binary mixtures of colloidal particles in the density-drying rate plane. While single-component colloids order in the two-dimensional triangular lattice, a symmetric binary mixture of mutually repulsive particles can be ordered into three triangular sub-lattices in two dimensions. Two of them are occupied by the two species of particles with the third sub-lattice vacant.

A possibility of high spin hole states in doped CoO2 layered systems

We introduce and investigate an effective five-band model for t2g and eg electrons to describe doped cobalt oxides with Co3+ and Co4+ ions in two-dimensional CoO2 triangular lattice layers, as in Na1−xCoO2. The effective Hamiltonian includes anisotropic kinetic energy (due to both direct Co–Co and indirect Co–O–Co hoppings), on-site Coulomb interactions parameterized by intraorbital Hubbard repulsion U and full Hund’s exchange tensor, crystal field terms and Jahn–Teller static distortions. We study it using correlated wave functions on 6 × 6 clusters with periodic boundary conditions. The computations indicate a low S = 0 spin to high S = 2 spin abrupt transition in the undoped systems when increasing strength of the crystal field, while intermediate S = 1 spins are not found. Surprisingly, for the investigated realistic Hamiltonian parameters describing low-spin states in CoO2 planes, doping generates high spins at Co4+ ions that are pairwise bound into singlets, seen here as pairs of up and down spins. It is found that such singlet pairs self-organize at higher doping into lines of magnetic ions with coexisting antiferromagnetic and ferromagnetic bonds between them, forming stripe-like structures. The ground states are insulating within the investigated range of doping because computed HOMO–LUMO gaps are never small enough.

Quantum phases of strongly interacting Rydberg atoms in triangular lattices

We present a theoretical study on the system of laser-driven strongly interacting Rydberg atoms trapped in a two-dimensional triangular lattice, in which the dipole-dipole interactions between Rydberg states result in exotic quantum phases. By using the mean-field theory, we investigate the steady state solutions and analyze their dynamical stabilities. We find that in the strong-interaction limit, the dynamics of the system is chaotic and exhibits random oscillations under appropriate laser detunings. Lyapunov exponent criterion is introduced to confirm the existence of this chaotic behavior. In addition, we present a full quantum calculation based on a six-atom model, and find that the system exhibits some bi-antiferromagnetic properties in every triangular cell when the one-photon detuning is exactly resonant or blue-shifted.

Diamond lattice photonic crystals from rolled-up membranes

A method is suggested for the fabrication of three-dimensional photonic crystals operating in the visible by rolling patterned prestressed membranes. A variety of architectures accessible using this fabrication scheme, including $\ensuremath{\langle}111\ensuremath{\rangle}$ and $\ensuremath{\langle}100\ensuremath{\rangle}$ diamond structures, were theoretically examined and optimized using photonic-band and density-of-optical-states calculations. The influence that finite size and bending have on a band gap was explored using a finite-element analysis of a two-dimensional triangular lattice of air holes.

Superlens realized by the two dimensional graded photonic crystal

In this paper, superlens realized by a two-dimensional (2D) triangular lattices graded photonic crystal (GPC) was studied. The graded photonic crystal (GPC) was obtained by varying the radius in each row so that its effective refractive index changes along the transverse direction. Plane wave expansion (PWE) method and finite-difference time-domain (FDTD) were adopted to show that negative refraction and superlens can be realized in the designed graded photonic crystal.

Double exchange model on triangular lattice: Non-coplanar spin configuration and phase transition near quarter filling

Unconventional anomalous Hall effect in frustrated pyrochlore oxides is originated from spin chirality of non-coplanar localized spins, which can also be induced by the competition between ferromagnetic (FM) double exchange interaction JH and antiferromagnetic superexchange interaction JAF. Here truncated polynomial expansion method and Monte Carlo simulation are adopted to investigate the above model on two-dimensional triangular lattice. We discuss the influence of the range of FM-type spin–spin correlation and strong electron–spin correlation on the truncation error of spin–spin correlation near quarter filling. Two peaks of the probability distribution of spin–spin correlation in non-coplanar spin configuration clearly show that non-coplanar spin configuration is an intermediate phase between FM and 120° spin phase. Near quarter filling, there is a phase transition from FM into non-coplanar and further into 120° spin phase when JAF continually increases. Finally the effect of temperature on the magnetic structure is discussed.

Synthesis and magnetic properties of a new series of triangular-lattice magnets, Na2BaMV2O8 (M = Ni, Co, and Mn)

A new series of triangular-lattice magnets, Na2BaMV2O8 (M = Ni, Co, and Mn), are reported. These three compounds crystallize with the Ag2BaMnV2O8 type structure, where the magnetic M2+ ions form a two-dimensional triangular lattice. The magnitude of the exchange interactions in these compounds is moderate because the nonmagnetic VO4 tetrahedra interrupt direct connections between MO6 octahedra. The magnetic susceptibilities of Na2BaNiV2O8 and Na2BaCoV2O8 reveal ferromagnetic transitions at 8.4 and 3.9 K, respectively. In contrast, the magnetic susceptibility of Na2BaMnV2O8 exhibits a broad maximum at around 2.3 K, which suggests antiferromagnetic nearest-neighbour interactions and a significant effect of geometric frustration. The specific heat and magnetization curve of Na2BaMnV2O8 indicate that magnetic long-range ordering appears below 1.5 K.

Dynamical behavior of disordered spring networks

We study the dynamical rheology of spring networks with a percolation model constructed by bond dilution in a two-dimensional triangular lattice. Hydrodynamic interactions are implemented by a Stokesian viscous coupling between the network nodes and a uniformly deforming liquid. Our simulations show that in a critical connectivity regime, these systems display weak power law rheology in which the complex shear modulus scales with frequency as G^* ~ (i * omega)^Delta where Delta = 0.41, in discord with a mean field prediction of Delta = 1/2. The weak power law rheology in the critical regime can be understood from a simple scaling relation between the macroscopic rheology and the nonaffine strain fluctuations, which diverge with vanishing frequency for isostatic networks. We expand on a dynamic effective medium theory, showing that it quantitatively describes the rheology of a diluted triangular lattice far from isostaticity; although the EMT correctly predicts the scaling form for the rheology of near-isostatic networks, there remains a quantitative disparity due to the mean-field nature of the EMT. Surprisingly, by connecting this critical scaling of the rheology with that of the strain fluctuations, we find that the dynamical behavior of disordered spring networks is fully determined by the critical exponents that govern the behavior of elastic network in the absence of viscous interactions.

Superconductivity in an Inhomogeneous Bundle of Metallic and Semiconducting Nanotubes

Using Bogoliubov-de Gennes formalism for inhomogeneous systems, we have studied superconducting properties of a bundle of packed carbon nanotubes, making a triangular lattice in the bundle's transverse cross-section. The bundle consists of a mixture of metallic and doped semiconducting nanotubes, which have different critical transition temperatures. We investigate how a spatially averaged superconducting order parameter and the critical transition temperature depend on the fraction of the doped semiconducting carbon nanotubes in the bundle. Our simulations suggest that the superconductivity in the bundle will be suppressed when the fraction of the doped semiconducting carbon nanotubes will be less than 0.5, which is the percolation threshold for a two-dimensional triangular lattice.

Crystal Growth, Structure, and Magnetic Properties of a Two‐dimensional Triangular Lattice Magnet, Cu2(OH)3HCO2

We prepared single crystals of basic copper formate Cu(2)(OH)(3)HCO(2) (1) by hydrolysis of formate anions in an aqueous solution of copper formate. X-ray structure analysis showed that this material has a two-dimensional triangular lattice network with S = 1/2. The temperature dependence of magnetic susceptibility revealed antiferromagnetic ordering at 5.4 K. A spin-flop transition was observed at about 20 kOe at 2 K, thereby indicating metamagnetic-like behavior. The saturation magnetization was almost one-half of the theoretical value at 2 K under 70 kOe. The magnetic behaviors of 1 were also discussed with regard to its crystal structure. The preparation method presented herein is convenient and available for single crystal growth of metal hydroxide derivatives with various anions.

Entropy Production from the Master Equation for Driven Lattice Gases

Entropy production was calculated for the driven lattice gas on small two-dimensional square, hexagonal and triangular lattices. Steady-state and time-dependent properties were calculated with the master equation, using the complete transition matrix for all configurations. Entropy production from dissipated work or from probability current was the same for transition rates that preserved local detailed balance. Entropy production was calculated along several relaxation paths. Steady states, on all three lattices, were not states of either maximum or minimum entropy production.

Spin Hall conductivity on the anisotropic triangular lattice

We present a detailed study of the spin Hall conductivity on a two-dimensional triangular lattice in the presence of Rashba spin-orbit coupling. In particular, we focus part of our attention on the effect of the anisotropy of the nearest neighbor hopping amplitude. It is found that the presence of anisotropy has drastic effects on the spin Hall conductivity, especially in the hole doped regime where a significant increase or/and reversed sign of the spin Hall conductivity has been obtained. We also provide a systematic analysis of the numerical results in terms of Berry phases. The changes of signs observed at particular density of carriers appear to be a consequence of both Fermi surface topology and change of sign of electron velocity. In addition, in contrast to the two-dimensional square lattice, it is shown that the tight binding spin-orbit Hamiltonian should be derived carefully from the continuous model on the triangular lattice.

Spin-wave dynamics for the high-magnetic-field phases of the frustrated CuFeO2antiferromagnet: Predictions for inelastic neutron scattering

We evaluate the spin-wave spectra for the high-field phases of the frustrated triangular lattice antiferromagnet with a focus on the observed high-magnetic-field phases of CuFeO${}_{2}$. After determining the appropriate magnetic ground state using a combination of Monte Carlo simulations and variational methods for a two-dimensional triangular lattice, we evaluate the spin excitation frequencies and intensities using a rotational Holstein-Primakoff expansion for both the collinear and noncollinear states. These predictions should help experimentalists to identify the magnetic ground states of CuFeO${}_{2}$ and other triangular-lattice antiferromagnets using inelastic neutron scattering.

1 × 2 Beam splitter with high efficiency based on nonreciprocal photonic crystal waveguide

This paper presents a new method for designing efficient 1 × 2 beam splitter in two-dimensional triangular lattice photonic crystals (PhCs). The proposed splitter is based on the one-way edge mode of gyromagnetic PhC, thus can prevent scattering losses even when there are defects or obstacles in its channels. The incident electromagnetic wave can be evenly split into two output channels as long as structural symmetry is kept in a small area around the -junction. The loss effect of gyromagnetic material on the splitting behavior is examined. Moreover, power ratio between the two outputs can be tuned by introducing a defect at a proper position in the splitter. The advantages of the proposed splitter have been validated through numerical simulations.

New design of channel drop filters based on photonic crystal ring resonators

In this paper, a new design of channel drop filters (CDFs) based on photonic crystals ring resonators (PCRRs) is presented. The filter characteristics for single-ring and dual-ring configurations based on two-dimensional (2D) triangular lattice photonic crystal (PC) silicon rods have been investigated by using the two-dimensional (2D) finite-difference time-domain (FDTD) method. Backward dropping efficiency of 96% and forward dropping efficiency up to 98% can be achieved in third communication window. Moreover, we investigate the dependence of resonant frequency on dielectric constant of whole rods of the structure as well as radius of the coupling rods. This device can be used as an optical channel drop filter (OCDF) in future communication applications.

Dipolar Bose–Einstein condensate soliton on a two-dimensional optical lattice

Using a three-dimensional mean-field model we study one-dimensional dipolar Bose–Einstein condensate (BEC) solitons on a weak two-dimensional (2D) square and triangular optical lattice (OL) potentials placed perpendicular to the polarization direction. The stabilization against collapse and expansion of these solitons for a fixed dipolar interaction and a fixed number of atoms is possible for short-range atomic interaction lying between two critical limits. The solitons collapse below the lower limit and escapes to infinity above the upper limit. One can also stabilize identical tiny BEC solitons arranged on the 2D square OL sites forming a stable 2D array of interacting droplets when the OL sites are filled with a filling factor of 1/2 or less. Such an array is unstable when the filling factor is made more than 1/2 by occupying two adjacent sites of OL. These stable 2D arrays of dipolar superfluid BEC solitons are quite similar to the recently studied dipolar Mott insulator states on 2D lattice in the Bose–Hubbard model by Capogrosso-Sansone et al. [B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo, Phys. Rev. Lett. 104 (2010) 125301].

Surface vortex solitons near boundaries of photonic lattices

We report on the existence and properties of vortex solitons at the edge and in the corner of two-dimensional triangular photonic lattices. We describe novel types of discrete vortex solitons, as well as the ring surface vortex solitons, localized in the lattice corners or at its edges. We observe that stable surface vortex solitons exist only in the form of a discrete six-lobe solution at the edge of the photonic lattice. Oscillations and irregular dynamics are observed for the ring vortex solutions and discrete two- and three-lobe solutions.

Tuning entanglement and ergodicity in two-dimensional spin systems using impurities and anisotropy

We consider the entanglement in a two-dimensional $XY$ model in an external magnetic field $h$. The model consists of a set of seven localized spin-$\frac{1}{2}$ particles in a two-dimensional triangular lattice coupled through nearest-neighbor exchange interaction $J$. We examine the effect of single and double impurities in the system as well as the degree of anisotropy on the nearest-neighbor entanglement and ergodicity of the system. We have found that the entanglement of the system at the different degrees of anisotropy mimics that of the one-dimensional spin systems at the extremely small and large values of the parameter $\ensuremath{\lambda}=h/J$. The entanglement of the Ising and partially anisotropic systems shows phase transition in the vicinity of $\ensuremath{\lambda}=2$, whereas, the entanglement of the isotropic system suddenly vanishes there. Also, we investigate the dynamic response of the system containing single and double impurities to an external exponential magnetic field at different degrees of anisotropy. We have demonstrated that the ergodicity of the system can be controlled by varying the strength and location of the impurities as well as the degree of anisotropy of the coupling.

Photonic band gap in Ge-based two-dimensional triangular lattice photonic crystals

The relationship between the filling factor and the circumcircle radius of the regular polygon scatter is deduced in a two-dimensional triangular lattice photonic crystal.The photonic band gaps(PBGs) are calculated with the plane wave expansion method in Ge-based two-dimensional triangular lattice photonic crystals.When Ge cylinder is placed in air background,the TM band gaps and TE band gaps appear with the TM band gaps dominating.As Ge filling factor increases,the width of the photonic band gaps increase initially but then decrease and the center frequency decrease.The width of the first band gap of the TM band gaps reaches the maximum at the radius of 0.14a.On the contrary,when air cylinder is placed in Ge background,the TM band gaps and TE band gaps as well as the complete band gaps appear with the TE band gaps dominating.With the air filling factor increasing,the width of the photonic band gaps also increase initially then decrease,whereas the center frequency increase.The width of the first band gap of TE band gaps and the largest complete band gap reaches the maximum at the radius of 0.46a and 0.49a,respectively.

Comparative study of photonic band gaps of germanium-based two-dimensional triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals

Photonic band gaps (PBGs) of germanium-based two-dimensional (2D) triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals (PCs) with the scatterer radius in the range of [0,0.3a] and within two cases of the construction (germanium cylinders being placed in air, air cylinders being placed in germanium) have been calculated by using the plane wave expansion (PWE) method. Germanium-based 2D triangular-lattice PC and 2D decagonal quasi-periodic PC are more easily to generate PBG than 2D square-lattice PC. 2D decagonal quasi-periodic PC is more easily to generate complete band gap than the other two kinds of PCs. The PBG properties of the three PCs are similar to the properties of silicon-based system as the radius of the scatterer cylinder increases. Nevertheless, the germanium-based system is more likely to generate PBG than silicon-based system. These findings will guide the design of PBG-type microstructure devices.