Quantum dimer model on the kagome lattice: solvable dimer-liquid and ising gauge theory

We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices include the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases. Using geometrical properties of the lattice, several results are obtained exactly, including the full spectrum of a dimer liquid. These models offer a very natural-and maybe the simplest possible-framework to illustrate general concepts such as fractionalization, topological order, and relation to Z2 gauge theories.     

Arrays of Ni nanowires in alumina membranes: magnetic properties and spatial ordering

Magnetic characteristics of arrays of Ni nanowires embedded in porous alumina are reviewed as a function of their spatial ordering. The different steps for the controlled production of highly-ordered nanowires is firstly described. Nanopores are formed into an hexagonal symmetry arrangement by self-organized process during anodization of pure Al. Parameters of the anodization allow us to control their diameter, hexagonal lattice parameter and size of crystalline domains. Subsequently, Ni nanowires are grown inside the pores by electrodeposition. Control of the pores filling and of geometrical ordering characteristics has been performed by SEM, HRSEM, RBS and AFM techniques. The magnetic characterisation of the arrays has been achieved by SQUID and VSM magnetometers, while information on the magnetic state of individual nanowires is obtained by MFM. Experimental studies are presented, particularly coercivity and remanence, for arrays with different degree of ordering (crystalline domains up to around 1 m), and for ratio diameter to lattice parameter (diameter ranging between 20 and 180 nm, and distance between 35 and 500 nm). FMR studies have allows us to obtain complementary information of the anisotropy and magnetic characteristics. A modelling of multipolar interacting nanowires is introduced to account for the influence of short and long range ordering degree of the arrays.Received: 24 November 2003, Published online: 15 June 2004PACS: 75.60.Jk Magnetization reversal mechanisms - 81.15.Pq Electrodeposition, electroplating     

Ordering in Ising models of parabolic shape

The features of order in narrow systems are studied for isotropic square lattice Ising models with general parabolic boundaries. Using Monte Carlo methods, magnetization profiles are calculated which agree very well with the conformal results and scale properly with the geometrical length parameter. The variation of the tip magnetization with temperature is obtained and the predicted stretched exponential form in the critical region is confirmed.     

Multi-vortex versus interstitial vortices scenario in superconducting antidot arrays

In superconducting thin films, engineered lattice of antidots (holes) act as an array of columnar pinning sites for the vortices and thus lead to vortex matching phenomena at commensurate fields guided by the lattice spacing. The strength and nature of vortex pinning is determined by the geometrical characteristics of the antidot lattice (such as the lattice spacing a₀, antidot diameter d, lattice symmetry, and orientation) along with the characteristic length scales of the superconducting thin films, viz., the coherence length (ξ) and the penetration depth (λ). There are at least two competing scenarios: (i) multiple vortices sit on each of the antidots at a higher matching period and (ii) there is nucleation of vortices at the interstitial sites at higher matching periods. Furthermore, it is also possible for the nucleated interstitial vortices to reorder under suitable conditions. We present our experimental results on NbN antidot arrays in the light of the above scenarios.     

Electric potential distribution near nanocone arrays on metal substrates

Based on the nanostructured surface model,where conical nanoparticle arrays grow out symmetrically from a plane metal substrate,a theoretical model of the local electric potential near nanocones is built when a uniform external electric field is applied.In terms of this model,the electric potential distribution near the nanocone arrays is obtained and given by a curved surface using a numerical computation method.The computational results show that the electric potential distribution near the nanocone arrays exhibit an obvious geometrical symmetry.These results could serve as a basis for explaining many abnormal phenomena,such as the abnormal infrared effects(AIREs) which are found on nanostructured metal surfaces,as well as a reference for investigating the applications of nanomaterials,such as nanoelectrodes and nanosensors.     

Super lattice formation of an array of volatile wetting droplets

For an ordered array of critical volatile wetting droplets the formation of a super lattice by an Ostwald-ripening-like competition process is considered. The underlying diffusion problem is treated within a quasistatic approximation and to first order in the inverse droplets distance. The approach is rather general but a square lattice and a triangular lattice are studied explicitly. Dispersion relations for the super lattice growth of these arrays are calculated. Received 29 November 1999 and Received in final form 15 February 2000     

Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays

We demonstrate that both the linear (diffraction) and the nonlinear dynamics of two-dimensional waveguide arrays are considerably more complex and versatile than their one-dimensional counterparts. The discrete diffraction properties of these arrays can be effectively altered, depending on the propagation Bloch k-vector within the first Brillouin zone of the lattice. In general, this diffraction behavior is anisotropic and therefore permits the existence of a new class of discrete elliptic solitons in the nonlinear regime.     

Proximity-effect induced density limitations for electron-beam patterned planar photonic nanomaterials

Patterning of deeply subwavelength artificial nanomaterials, e.g. photonic crystals or plasmonic metamaterials, for the visible or near-infrared optical spectrum is a challenging task. Electron-beam lithography is often the method of choice thanks to its combination of flexibility, accuracy and availability in many research laboratories. In this article an analytical model for large and dense arrays of photonic nanostructures is presented which allows to predict the maximum fill ratio (radius divided by nearest neighbor distance) before the onset of resist loss between the individual elements. The model includes geometrical parameters of the design (lattice constant, lattice symmetry), the resist contrast and proximity parameters (beam broadening, backscatter range, backscatter efficiency). It is shown that the resist contrast has a significant impact on the achievable maximum fill ratio even for large nearest neighbor distances and that the beam broadening is of paramount importance. The background energy level which is determined by the backscatter efficiency and the lattice symmetry is shown to have a weaker influence on the maximum fill ratio. The derived model can be used as a guideline in the project planning stage to predict achievable fill ratios at a planned lattice constant and consequently an assessment whether a desired functionality at a certain wavelength is possible or not.     

The collapse transition of branched polymers on a fractal lattice

Using the exact renormalization group equations we study the asymptotic behaviour of branched polymers on the modified rectangular lattice. We find a critical value of the temperature above which the polymer has the geometry of a random lattice animal, while below it the polymer collapses into a compact phase. The exact values of various geometrical and thermal critical exponents are obtained.     

Nanoporous alumina membrane prepared by nanoindentation and anodic oxidation

The fabrication of nanopatterned surfaces at large scale attracts the interest of research groups from a wide range of areas as biotechnology, nanoelectronics and nanomagnetism. An extended method to pattern the surface in the nanoscale is the fabrication of ordered arrays of nanoelements based on porous templates as Nanoporous Anodic Aluminium Oxide (NAAO). One of the challenges of the NAAO fabrication, based on self-organized methods, is the control of the symmetry and lattice parameter of the ordered nanoporous films. In this work, we present a combined method based on Atomic Force Microscopy (AFM) nanoimprint and anodic oxidation of Al surface. AFM nanoindentations substitute the first anodization process and even more important, allow us to control the symmetry and the lattice parameter of the ordered arrays. In addition, by using AFM nanoimprint method it is possible to select the region were the ordered alumina grows. We demonstrate that square nanoporous arrays of alumina with lattice parameter of 105 nm can be obtained by this method.     

Geometrical effects on the charge/discharge properties of quantum dot flash memories

We investigate the addition spectra of arrays of quantum dots (QDs) under different geometrical distributions. We use a Hubbard Hamiltonian where we include intra- and inter-dot interactions. Exact diagonalisation is used to calculate the eigenstates of arrays containing several QDs and the conductance addition spectrum is calculated using the Beenakker Approach for a single-dot generalised to an array of QDs. The charging/discharging process of the QDs is theoretically studied when a bias is applied to a metallic gate on top of the structure. The occupancy and conductance as a function of the gate bias is obtained, a crucial feature to understanding the memory charging process for non-volatile memories that are based on MOS devices with embedded semiconductor QDs.     

银纳米粒子阵列中衍射诱导高品质因子的四偶极晶格等离子体模式

金属纳米颗粒阵列中形成的四偶极晶格共振模式具有低辐射损耗、高品质因子的特性,因此广泛应用于纳米激光、传感、固态照明等领域.基于时域有限差分法在均匀环境下研究了银纳米圆柱阵列的光谱与近场特性.研究结果表明,在x偏振光直入射下,通过调节阵列x方向的周期,共振强度先增加后降低,当两个方向上的周期相等时,提出的阵列结构能够产生一个线宽约0.4 nm、品质因子高达1815的四偶极晶格共振模式,这种共振模式呈现出Fano线型的透射谷;调控y方向的周期能够实现从Fano线型的透射峰到透射谷的转变.本文说明了粒子大小、晶格周期对四偶极晶格共振模式的重要性,同时为银纳米颗粒在可见光波段设计高品质因子共振提供了优化策略.     

Rates of diffusion-limited reaction in periodic systems

The pseudopotential and perturbation theory are used to derive the first three terms in the expansion of the smallest eigenvalue of the Helmholtz equation both for infinite two-dimensional systems with an array of perfectly absorbing circles centered on (1) a square lattice and (2) a triangular lattice, and also for infinite three-dimensional systems both with arrays of perfectly absorbing interspersed cylinders and with an array of perfectly absorbing spheres centered on (1), a simple cubic lattice, (2) a body-centered cubic lattice, and (3) a facecentered cubic lattice. In all cases, the perturbation parameter involves the ratio of the radius of the absorber to the lattice spacing. These eigenvalues and the corresponding eigenfunctions are used to compute the first three terms of expansions of the first passage time of a diffusing point particle randomly placed outside the absorbers. Expressing the perturbation parameter as a function of the area or volume fraction occupied by the absorbers reveals a remarkable similarity among the rates of diffusion-limited reaction for arrays of absorbers and the corresponding radially symmetric system containing one central absorber.     

增强光子晶体谐振腔模式选择性的方法分析

在分析计算金属光子晶体的正三角形晶格TE模式的色散特性、全局带隙分布图的基础上,针对TE04模光子晶体谐振腔中仍有较多的模式竞争且金属柱半径较小的问题,结合模式分布特点图,通过优化和选择工作点的位置,将TE04中的竞争模从5种减少为2种,大幅度降低了TE04工作模式中的模式竞争,并且增加了晶格常数和金属柱半径,使之能够承受更大的热损耗,有利于提高腔体功率容量。仿真验证了数值计算的正确性并得出了完整的TE04场分布。     

Geometry and symmetries in lattice spinor gravity

Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space and time is not put in a priori, and the euclidean and the Minkowski quantum field theory are unified in one functional integral. The metric and its signature arise as a result of the dynamics, corresponding to a given ground state or cosmological solution. Geometrical objects as the vierbein, spin connection or the metric are expectation values of collective fields built from an even number of fermions. The quantum effective action for the metric is invariant under general coordinate transformations in the continuum limit. The action of our model is found to be also invariant under gauge transformations. We observe a “geometrical entanglement” of gauge- and Lorentz-transformations due to geometrical objects transforming non-trivially under both types of symmetry transformations.     

Regular packings on periodic lattices

We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction φ(d)(X). It is proved to be continuous with an infinite number of singular points X(ν)(min), X(ν)(max), ν = 0, ±1, ±2,…. In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of φ(d)(X) is discussed in the context of geometrical frustration effects, transitions in the contact numbers, and number-theoretical properties. Implications and generalizations for more general packing problems are outlined.     

Fabrication of gold nano-particle arrays using two-dimensional templates from holographic lithography

We report a simple and cost effective method to fabricate regular metallic particle arrays over large areas with good regularity by using holographic lithography interference for the study of localized surface plasmon. Samples of disk-shaped gold nano-particles arranged in square arrays with lattice spacing ranging from 300 nm to 600 nm were successfully fabricated on glass substrates first by sputtering a thin gold layer onto two-dimensional photoresist templates of hole arrays in square lattice obtained by the holographic method and then removing the photoresist by a lift-off procedure. The plasmonic resonance of the gold nano-particle arrays due to the change of morphology by thermal annealing was studied. The disk-shaped gold nano-particles were found to become more round shaped upon heating and blue shift of the extinction plasmonic band was observed. The results were explained with model calculations using spheroidal particles.     

Incidence of element distribution on the ultrasonic field of segmented annular arrays

Segmented annular arrays are sometimes used for 3D ultrasonic imaging. However, owing to their geometrical complexity, the acoustic field generated by this type of aperture has not been adequately described. In this work, a method based on the array factor approach is used to describe the field radiated by sector annular arrays. This approach allows one to analyse the influence on the field of several aperture parameters, such as the number of elements per annulus, size and spatial distribution of elements, etc. In addition, strategies to reduce grating lobes are presented.