Role Of Dimensionality Research Articles

Charge and dimensionality effects on the properties of CaNiN

Results of first-principles, density-functional, full-potential calculations on crystalline CaNiN and on single chains of NiN and CaNiN are presented. For crystalline CaNiN and single NiN chains we optimized the structural parameters. The role of dimensionality and charge transfer on the electronic structure is investigated by considering various related hypothetical crystalline structures of CaNiN where we have systematically turned off different interactions. This is achieved by expanding the lattice in different directions and/or rotating the layers of the NiN chains as well as considering structures where the Ca atoms have been removed. This is an unusual study of the dimensionality and charge effects in a crystalline compound and, although it is particularly well suited for CaNiN, it could also be applied to other quasi-low-dimensional materials like high-${T}_{c}$ superconductors and quasi-one-dimensional spin-density materials. Finally, we explore the magnetic properties of pure CaNiN.

Ab initio Optical Absorption in Conjugated Polymers: the Role of Dimensionality

The optical behavior of poly(para-phenylene vinylene) is explored through an ab initio scheme based on the Bethe–Salpeter equation, where the electron–hole interaction is included on top of a density functional theory calculation. Results for different solid-state packings are reviewed, demonstrating that the details of crystalline arrangement dramatically alter the optical properties and lead to a rich excitonic structure, where also charge-transfer states appear (electron and hole on different chains). Moreover, for a typical herringbone packing the excitonic state of the isolated molecule splits in two direct components (with electron and hole on the same chain), one for each non-translationally-invariant chain in the unit cell, and the optical inactivity of the lowest component can crucially quench the luminescence efficiency. Besides the far-field absorption spectra and the description of the excitonic states, a formalism to simulate the near-field spectra is presented that allows one to detect also excitonic states that are dipole-forbidden in the far-field spectra.

Role of dimensionality in Axelrod's model for the dissemination of culture

We analyze a model of social interaction in one- and two-dimensional lattices for a moderate number of features. We introduce an order parameter as a function of the overlap between neighboring sites. In a one-dimensional chain, we observe that the dynamics is consistent with a second-order transition, where the order parameter changes continuously and the average domain diverges at the transition point. However, in a two-dimensional lattice the order parameter is discontinuous at the transition point characteristic of a first-order transition between an ordered and a disordered state.

Efficiency of encounter-controlled reaction between diffusing reactants in a finite lattice: topology and boundary effects

The role of dimensionality (Euclidean vs. fractal), spatial extent, boundary effects and system topology on the efficiency of diffusion-reaction processes involving two simultaneously diffusing reactants is analyzed. We present numerically exact values for the mean time to reaction, as gauged by the mean walklength before reactive encounter, obtained via application of the theory of finite Markov processes, and via Monte Carlo simulation. As a general rule, we conclude that for sufficiently large systems, the efficiency of diffusion-reaction processes involving two synchronously diffusing reactants (two-walker case) relative to processes in which one reactant of a pair is anchored at some point in the reaction space (one-walker plus trap case) is higher, and is enhanced the lower the dimensionality of the system. This differential efficiency becomes larger with increasing system size and, for periodic systems, its asymptotic value may depend on the parity of the lattice. Imposing confining boundaries on the system enhances the differential efficiency relative to the periodic case, while decreasing the absolute efficiencies of both two-walker and one-walker plus trap processes. Analytic arguments are presented to provide a rationale for the results obtained. The insights afforded by the analysis to the design of heterogeneous catalyst systems is also discussed.

Melting from one to two to three dimensions

The transformation of a crystalline solid into a liquid, seeming to have no precursor and no intermediate states, has challenged scientists for over a century. The search for the fundamental mechanism stimulated the development of quantum mechanics, concepts of the roles of dimensionality and topological order in condensed matter, and experimental techniques to test the theories. We now understand that the transition begins at lower temperatures than the melting point of the bulk. It starts at the edges of crystal planes, progresses across the surface, evolves into the successive melting of atomic layers, and ends in bulk phase coexistence. The memory of the process remains within a few molecular distances at the crystal-melt interface.

Role of dimensionality on the two-photon absorption response of conjugated molecules: The case of octupolar compounds

A comparative study of the two-photon absorption (TPA) properties of octupolar compounds and their dipolar one-dimensional counterparts is presented on the basis of correlated quantum-chemical calculations. The roles of dimensionality and symmetry are first discussed on the basis of a simple exciton picture where the ground-state and excited-state wavefunctions of three-arm octupolar systems are built from a linear combination of the corresponding single-arm wavefunctions. This model predicts a factor of 3 increase in the TPA cross section in the limiting case of three independent charge-transfer pathways. When taking into account the full chemical structures of representative octupolar molecules, the results of the calculations indicate that a much larger enhancement associated with an increase in dimensionality and delocalization can be achieved when the core of the chromophore allows significant electronic coupling among the individual arms. These theoretical predictions are in agreement with the experimental determination of the TPA cross sections for crystal violet and the related compound, brilliant green, and suggest new strategies for the design of conjugated materials with large TPA cross sections.

Modeling self-assembly in molecular fluids

Equilibrium self-assembly in fluids is studied in the framework of the lattice density-functional theory (DFT). In particular, DFT is used to model the phase behavior of anisotropic monomers. Though anisotropic monomers are a highly idealized model system, the analysis presented here demonstrates a formalism that can be used to describe a wide variety of phase transitions, including processes referred to as self-assembly. In DFT, the free energy is represented as a functional of order parameters. Minimization of this functional allows modeling spontaneous nano-scale phase transitions and self-assembly of supramolecular structures. In particular, this theory predicts micellization, lamellization, fluid–glass phase transitions, crystallization, and more. A classification of phase transitions based on general differences in self-assembled structures is proposed. The roles of dimensionality and intermolecular interactions in different types of phase transitions are analyzed. The concept of primordial codes is discussed in terms of the structural variety of self-assembled systems.

Transport properties and charge density wave instabilities in the quasi-two-dimensional monophosphate tungsten bronzes (PO2)4(WO3)2m (m=5) and KxP4W8O32

The monophosphate tungsten bronzes (PO2)4(WO3)2m are quasi-two-dimensional conductors which show charge density wave (CDW) type electronic instabilities. These compounds can be viewed as model systems where the role of dimensionality, pressure and doping on the electronic instabilities can be investigated. Varying m leads to a change in the quasi-two-dimensional character while inserting an alkaline element in the tunnels of the crystal structure allows to study the role of band filling. On the other hand, the application of an hydrostatic pressure is a useful tool to study the role of intra- and inter-planes interactions. We report a study of classical and quantum transport properties of the recently synthesized m=5 compounds which exist under two structural varieties as well as transport properties of the doped compounds KxP4W8O32. In undoped compounds, Shubnikov–de Haas and angular dependent magnetoresistance oscillations bring new information on the Fermi surface (FS) topology in the CDW state. In KxP4W8O32, the transitions are not conventional Peierls instabilities in contrast with the parent undoped compound m=4. We discuss the origin of this anomaly.

Role of Dimensionality in Dimerized Two-Band Systems

We have studied the ground state properties of Pd(dmit)2 salts using an effective dimer model. This model describes low-energy excitations of the two-band Hubbard model and is derived by a strong coupling expansion. Dimensionality of the Fermi surface, density-of-states singularity, and magnetic frustration in the dimer model are simultaneously controlled by substituting the cation.

History of the search for continuous melting

The melting of crystals has resisted efforts to understand the microscopic process for more than a century. The course of the struggle has stimulated the development of quantum mechanics, concepts of long-range order, the role of dimensionality in condensed matter, surface physics, and more sensitive experimental techniques to test the theories. After years of probing the mechanism within the bulk material, we learn that the answer has been lying on the surface.

Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality

We study the energy spectra of small three-dimensional (3D) and two-dimensional (2D) semiconductor quantum dots through different theoretical approaches (single-site Hubbard and Hartree-Fock Hamiltonians); in the smallest dots we also compare with exact results. We find that purely 2D models often lead to an inadequate description of the Coulomb interaction existing in realistic structures, as a consequence of the overestimated carrier localization. We show that the dimensionality of the dots has a crucial impact on (i) the accuracy of the predicted addition spectra, and (ii) the range of validity of approximate theoretical schemes. When applied to realistic 3D geometries, the latter are found to be much more accurate than in the corresponding 2D cases for a large class of quantum dots; the single-site Hubbard Hamiltonian is shown to provide a very effective and accurate scheme to describe quantum dot spectra, leading to good agreement with experiments.

Electrongfactor in one- and zero-dimensional semiconductor nanostructures

We investigate theoretically the Zeeman effect on the lowest confined electron in quantum wires and quantum dots. A general relation is established between the symmetry of a low-dimensional system and properties of the electron g factor tensor, ${g}_{\ensuremath{\alpha}\ensuremath{\beta}}.$ The powerful method used earlier to calculate the transverse g factor in quantum wells is extended to one-dimensional (1D) and 0D zinc-blende-based nanostructures and analytical expressions are derived in the frame of Kane's model for the g factors in quantum wells, cylindrical wires, and spherical dots. The role of dimensionality is illustrated on two particular heteropairs, ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ and ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}\mathrm{P}.$ The efficiency of the developed theoretical concept is demonstrated by calculating the three principal values of the g factor tensor in rectangular quantum wires in dependence on the wire width to establish also the connection with the 2D case.

The Role of Dimensionality in the Stability of a Confined Condensed Bose Gas

We study analytically the ground-state stability of a Bose–Einstein condensate (BEC) confined in an harmonic trap with repulsive or attractive zero-range interaction by minimizing the energy functional of the system. In the case of repulsive interaction the BEC mean radius grows by increasing the number of bosons, instead in the case of attractive interaction the BEC mean radius decreases by increasing the number of bosons: to zero if the system is one-dimensional and to a constant minimum radius, with a maximum number of bosons, if the system is three-dimensional.

Free electron model for optical polarizabilities: Role of dimensionality

The free electron model proposed by Rustagi and Ducuing to explain the enhancement of the second-order hyperpolarizabilities of π-con-jugated linear molecules with increasing conjugation length has been extended to two and three dimensions. The sign and magnitude for the linear (α) and third order (γ) polarizabilities as a function of the size and electron density of the systems have been obtained. Some simple general conclusions on the role of dimensionality in the nonlinear response have been obtained.

Free electron model for optical polarizabilities: Role of dimensionality

Free electron model for optical polarizabilities: Role of dimensionality

From one- to two-dimensional complexes for quadratic nonlinear optics: the influence of ligand and complexing metal atoms

Metal complexes display interesting properties in terms of molecular optimization of quadratic nonlinear properties, combined with a good thermal stability and a large flexibility of geometrical and electronic properties. The role of dimensionality and intramolecular charge transfer of the pure ligand is investigated here, in particular for Schiff base derivatives. Also, the influence of metal electronic configurations on the quadratic hyperpolarizability is investigated in the series of Ni II, Co II and Cu II atoms, showing the interest of open-shell structures as compared to closed-shell complexes in the case of a weakly nonlinear ligand. Finally, strongly octupolar two-dimensional systems, subphthalocyanines, are shown to present very large second-order nonlinear polarizabilities, with static values as high as measured on a trinitro-substituted SubPc by the harmonic light scattering technique.

Phase transitions on surfaces

Abstract One of the principal motivations for modern studies of adsorbed films, surfaces and interfaces is an abiding interest in the roles of dimensionality in condensed matter. While research during the last two decades has shown that physisorbed monolayers can be good experimental representations of two dimensional matter, more recent studies have demonstrated that surface transitions of semi infinite crystals are different from those of bulk materials (1,2).

The role of dimensionality in a threshold-controlled neural network

The role of dimensionality in a threshold-controlled neural network

The role of dimensionality in a threshold-controlled neural network

When a network is not fully interconnected, the topology of the interconnection scheme becomes potentially important. I have investigated the effect of the dimensionality of the interconnection in a Hopfield-type network on the storage capacity of the network. The capacity was found to be independent of the dimensionality of the interconnections for 1,2,3 and 4-dimensional geometries and to depend only on the total number of interconnections available in a given network. In addition, no evidence of any instabilities was observed, in contrast to physical systems of reduced dimensionality.

The role of dimensionality in the kinetic Ising model of spinodal decomposition: Evidence from zero-temperature quenches

We study a three-dimensional Ising lattice gas model with spin-exchange dynamics quenched from infinite to zero temperature. We consider a wide range of values of the binary composition (i.e., magnetization) and annealed vacancy concentration. We find that, as in two dimensions, the system freezes in a configuration very far from equilibrium, and that the interface energy per bond in the frozen state, which is very large, in all cases takes very nearly the same values as in two dimensions. We discuss the implications of these results regarding the irrelevance of dimensionality in this problem.