Two-dimensional Superlattice Research Articles

Interparticle Spacing Control in the Superlattices of Carboxylic Acid-Capped Gold Nanoparticles by Hydrogen-Bonding Mediation

We have demonstrated that carboxylic acid-capped gold nanoparticles were self-assembled to form two-dimensional (2D) and/or three-dimensional (3D) superlattices at an air/water interface in the presence of a bifunctional hydrogen-bonding mediator such as 4-pyridinecarboxylic acid (PyC) or trans-3-(3-pyridyl)acrylic acid (PyA). Transmission electron microscopy revealed a hexagonal close-packed arrangement of nanoparticles in the superlattice with an extension of interparticle spacing. In the 2D superlattices, larger particles produced a higher-quality assembly having long-range translational ordering. Attenuated total reflectance IR (ATR-IR) spectroscopy revealed the presence of hydrogen bonds between the mediator used and the capping agents of carboxylic acid on nanoparticle surfaces. Since the experimentally obtained interparticle separation distance agreed approximately with that obtained by the geometrical model calculations, we conclude that the hydrogen-bonding mediation controlled the interparticle spacing or structure by monomolecular incorporation between adjacent nanoparticles in the superlattices.

Dynamical Self-Assembly of Nanocrystal Superlattices during Colloidal Droplet Evaporation byin situSmall Angle X-Ray Scattering

The nucleation and growth kinetics of highly ordered gold nanocrystal superlattices during the evaporation of nanocrystal colloidal droplets was elucidated by in situ time-resolved small-angle x-ray scattering. We demonstrated for the first time that the evaporation rate can affect the dimensionality of the superlattices. The formation of two-dimensional nanocrystal superlattices at the liquid-air interface of the droplet has exponential growth kinetics that originates from interface crushing.

Systematic Research on Insertion Materials Based on Superlattice Models in a Phase Triangle of LiCoO2 ­ LiNiO2 ­ LiMnO2: I. First-Principles Calculation on Electronic and Crystal Structures, Phase Stability and New Material

The first-principles calculations on the lithium insertion materials have been done to give the rationale for materials research on advanced lithium-ion batteries. To apply the computational methods, the model crystals are constructed by assuming in-plane two-dimensional superlattices based on -type structure for three sides of a phase triangle of Model crystals consisting of a superlattice gives two transition metal elements in the ratio of 3 to 1 and a superlattice model gives 2 to 1. For the ratio of 1 to 1, two model crystals are assumed, i.e., so-called “straight” and “zigzag” models. The first-principles calculations for these model crystals indicate that (i) is a solid solution between and (ii) is not expected to be a solid solution between and (unstable, phase separation is expected), and (iii) is not a solid solution between and is expected to be a stable phase). Among these compounds calculated, having a layered structure may be a new compound consisting of and in their formal charges, which is neither a solid solution between and nor between NiO and From these theoretical results, materials design toward the implementation of novel lithium insertion materials for advanced lithium-ion batteries is discussed. © 2004 The Electrochemical Society. All rights reserved.

Colloidal crystal microarrays and two-dimensional superstructures: a versatile approach for patterned surface assembly.

A simple, fast, and robust approach to colloidal assembly on patterned surfaces was developed. The approach involves the rapid settling and dewetting of suspensions of spherical colloids on lithographically templated surfaces. Using this method, we can quickly and easily fabricate close-packed colloidal crystal microarrays of both silica and polystyrene spheres that range in size from 500 nm to 4.5 microm. The microarrays tend to induce the formation of monolayer colloidal crystals, which can be interconnected and removed from the templates as free-standing colloidal crystal slabs. The same approach can also be used to assemble two-dimensional colloidal crystal superlattices that can adopt a variety of structures. Graphite, kagome, body-centered cubic, open hexagonal, tetragonal, and linear chain structures can all be quickly accessed by adjusting the ratio of the sphere diameter to the template diameter.

Transport in weakly and strongly modulated two‐dimensional electron systems realized by Cleaved‐Edge‐Overgrowth

Periodic modulation of a free two-dimensional electron system changes the bandstructure in which the electrons move. A weak modulation opens up small energy gaps in the free electron bandstructure while a strong, short-period modulation leads to the formation of well separated cosine-like minibands. We study transport in both cases using structures grown with the Cleaved-Edge-Overgrowth method. It allows to fabricate high quality two-dimensional electron systems with arbitrary modulation periods which are precise on an atomic scale. Perturbing the system only weakly with a long-period superlattice that is located some distance away from the electron layer leads to magneto-transport characteristics which exhibit each a number of different 1/B-periodic oscillations. These can be very well explained by semiclassical theory and allow the extraction of the Fermi surface of the system. The strong modulation with a short-period superlattice leads to the two-dimensional equivalent of a conventional superlattice. One very important difference lies in the stability of the expected negative differential conductance regime with respect to electric field instabilities. Geometrical considerations show that the observation of stable Bloch oscillations is possible in these systems. We will show that density dependent transport studies confirm the formation of a two-dimensional superlattice. Although negative diffential conductance, also observed in those samples, must be attributed to an inhomogeneous density distribution.

Probing the ladder spectrum arising from motion in a two-dimensional lattice driven by in-plane constant forces

The coherent interband dynamics of optically excited two-dimensional lateral surface superlattices (quantum-dot arrays), driven by an in-plane static electric field, has been investigated. Linear absorption and a spectrally resolved four-wave mixing signals are obtained. When the rational condition ${E}_{x}{/E}_{y}=p/q,$ with p and q prime to each other, is fulfilled, it is found that p peaks appear within the frequency interval ${\ensuremath{\omega}}_{\mathrm{Bx}}{=eE}_{x}a/\ensuremath{\Elzxh}$ in both linear absorption and degenerate four-wave mixing signals with different time delays. These findings are consistent with the recent spectral results [Phys. Rev. Lett. 86, 3116 $(2001)]$, hence providing a method for probing the coherent dynamics of quantum particles in two-dimensional lattices.

Inverse flux quantum periodicity in the amplitudes of commensurability oscillations in two-dimensional lateral surface superlattices

We report strong, amplitude modulated, commensurability oscillations in the magnetoresistance of short period, square, two-dimensional, lateral surface superlattices with symmetric potentials. The amplitude of the oscillations is strongly enhanced when one magnetic-flux quantum (h/e) passes through an integral number of cells of the superlattice. The temperature dependence of the strong oscillations agrees with the theory for commensurability oscillations in one-dimensional superlattices, but the smaller oscillations between these are more rapidly attenuated by increasing temperature. Although the structure we observe has the same flux periodicity as expected for the Landau-level substructure known as the Hofstadter butterfly, such substructure will not be resolved at the temperatures of measurement (1-10 K). We compare our data instead to a recent theoretical model which treats exactly this case, and find significant points of agreement.

Inverse flux quantum periodicity of magnetoresistance oscillations in two-dimensional short-period surface superlattices

Transport properties of the two-dimensional electron gas (2DEG) are considered in the presence of a perpendicular magnetic field B and of a weak two-dimensional (2D) periodic potential modulation in the 2DEG plane. The symmetry of the latter is rectangular or hexagonal. The well-known solution of the corresponding tight-binding equation shows that each Landau level splits into several subbands when a rational number of flux quanta $h/e$ pierces the unit cell and that the corresponding gaps are exponentially small. Assuming the latter are closed due to disorder gives analytical wave functions and simplifies considerably the evaluation of the magnetoresistivity tensor ${\ensuremath{\rho}}_{\ensuremath{\mu}\ensuremath{\nu}}.$ The relative phase of the oscillations in ${\ensuremath{\rho}}_{\mathrm{xx}}$ and ${\ensuremath{\rho}}_{\mathrm{yy}}$ depends on the modulation periods involved. For a 2D modulation with a short period $<~100\mathrm{nm},$ in addition to the Weiss oscillations the collisional contribution to the conductivity and consequently the tensor ${\ensuremath{\rho}}_{\ensuremath{\mu}\ensuremath{\nu}}$ show prominent peaks when one flux quantum$h/e$ passes through an integral number of unit cells in good agreement with recent experiments. For periods 300--400 nm long used in early experiments, these peaks occur at fields 10 to 25 times smaller than those of the Weiss oscillations and are not resolved.

Nanometric superlattices: non-lithographic fabrication, materials, and prospects

A non-lithographic technique that utilizes the self-organized, highly ordered anodized aluminum oxide (AAO) porous membrane as a template is employed as a general fabrication means for the formation of vastly different two-dimensional lateral nanometric superlattices. The fact that material systems as different as metals, semiconductors, and carbon nanotubes (CNT) can be treated with the same ease attests to the generality of this nano-fabrication approach. The original alumina nanopore membranes determine the uniformity, packing density, and size of the nanostructures. The flexibility of using a variety of materials, the accurate control over fabrication process, and the command over the alumina template attributes give us the freedom of engineering various physical properties determined by the shape, size, composition, and doping of the nanostructures. The novel nanomaterial platform realized by this unique technique is powerfully enabling for a broad range of applications as well as for uncovering new physical phenomena such as the collective behavior of arrays of nano-elements that may not be intrinsic to individual nano-elements.

Effect of a magnetic field on the long-range magnetic order in insulatingNd2CuO4and nonsuperconducting and superconductingNd1.85Ce0.15CuO4

We have measured the effect of a c-axis aligned magnetic field on the long-range magnetic order of insulating Nd2CuO4, as-grown nonsuperconducting and superconducting Nd1.85Ce0.15CuO4. On cooling from room temperature, Nd2CuO4 goes through a series of antiferromagnetic (AF) phase transitions with different noncollinear spin structures. In all phases of Nd2CuO4, we find that the applied c-axis field induces a canting of the AF order but does not alter the basic zero-field noncollinear spin structures. Similar behavior is also found in as-grown nonsuperconducting Nd1.85Ce0.15CuO4. These results contrast dramatically with those of superconducting Nd1.85Ce0.15CuO4, where a c-axis aligned magnetic field induces a static, anomalously conducting, long-range ordered AF state. We confirm that the annealing process necessary to make superconducting Nd1.85Ce0.15CuO4 also induces epitaxial, three-dimensional long-range ordered cubic (Nd,Ce)2O3 as an impurity phase. In addition, the annealing process makes a series of quasi two-dimensional superlattice reflections associated with lattice distortions of Nd1.85Ce0.15CuO4 in the CuO2 plane. While the application of a magnetic field will induce a net moment in the impurity phase, we determine its magnitude and eliminate this as a possibility for the observed magnetic field-induced effect in superconducting Nd1.85Ce0.15CuO4.

Synthesis of Well-Defined and Low Size Distribution Cobalt Nanocrystals: The Limited Influence of Reverse Micelles

Cobalt nanocrystals are produced in cobalt(II) bis(2-ethylhexyl)sulfosuccinate (Co(AOT)2) reverse micelles. It is found that their size distribution is related to the volume of reducing agent added to the micellar system. At a low volume of reducing agent, the micelles play the role of nanoreactors in which take place the nucleation and growth of cobalt. In the supersaturate regime, that is, at a high volume of reducing agent, micelles are destroyed. In the first case, the nanocrystal size polydispersity is about 29%, while in the latter case, it can decrease to 8%. This low size polydispersity has to be related on one hand to the excess of the reducing agent that modifies the nucleation and growth processes and on the other hand to the structural and chemical evolutions of the micellar system. To obtain well-defined two-dimensional superlattices, the size distribution needs to be less than 13%.

Kubo conductivity in two-dimensional Fibonacci lattices

The electronic transport at zero degrees in quasiperiodic systems is investigated by using the Kubo–Greenwood formula and a novel renormalization method, which allows an evaluation in an exact way of the products of the Green’s function in macroscopic Fibonacci chains. The analysis of transport properties in two-dimensional Fibonacci superlattices and in double quasiperiodic lattices is carried out by means of the convolution technique. The spectrally averaged conductance shows a linear dependence with the width of the system and a power-law decay as its length increases along the applied electric field.

Permissible symmetries of multi-domain configurations in perovskite ferroelectric crystals

Permissible symmetries of multi-domain structures are analyzed in the m3̄m→3m, m3̄m→4mm and m3̄m→mm2 ferroelectric species. Domain structures produced by the application of external electric and/or mechanical fields that allow for the formation of two-dimensional domain superlattice are described in terms of effective group symmetry. Based on our analysis, the most perspective directions for properties enhancement through domain engineering are specified for perovskite ferroelectric crystals having tetragonal, rhombohedral, and orthorhombic symmetries.

Construction of 2D Superlattices of Gold Nanoparticles at an Air/Water Interface Based on Hydrogen-Bonding Networks

Abstract Two-dimensional (2D) superlattices of mercaptosuccinic acid-modified gold nanoparticles were constructed at an air/water interface in the presence of 4-pyridinecarboxylic acid (PyC). Hydrogen-bonding interaction caused the incorporation of PyC into the surface-functionalized gold nanoparticles, suggesting that the interparticle spacing in the superlattices is controllable with an intercalating molecule.

Resonance reflection of light from two-dimensional superlattice structures

The exciton Bloch states in a quantum well with a two-dimensional periodic potential are studied theoretically. Expressions are derived for the light reflection coefficient and the exciton oscillator strength for a structure with this type of lateral superlattice. The redistribution of the oscillator strength between exciton states with varying period and depth of the potential is analyzed. The limiting cases where the nearly free exciton and tight-binding approximations are applicable are considered.

Atomistic simulations of strain distributions in quantum dot nanostructures

Strain distributions around a Ge quantum dot (QD) buried in a Si spacer layerare investigated theoretically by means of classical molecular dynamicssimulations using the Tersoff potential. Applying periodic boundary conditionslaterally, two-dimensional superlattices of QDs are obtained. Strain distributionsin systems of different sizes and lattice misorientations are computed in order toexplain possible vertical correlations in self-organized three-dimensional QDsuperstructures. Generally, the strain of relaxed systems displays an oscillatorybehaviour as a function of the distance from the QD. For QD systems with growthdirection [001], a simple fitting function is used to describe the strain along avertical path above the QD by an oscillation and a decay according to a powerlaw. For QDs with the shape of a truncated pyramid, the planar straindecays by a power of approximately −3. The period of the oscillation isnearly proportional to the QD superlattice constant and decreases withincreasing coordination number of the QD superlattice. In misoriented systemswith a small tilt angle about the [110] axis, the region of tensile planarstrain above the QD is bent in the direction opposite to the misorientationcausing a vertical correlation with lateral shift. For a tilt angle ≈55°, nostrain oscillation is found which implies a perfect vertical correlation.

Synthesis and self-assembly of colloidal nanoparticles.

We describe recent developments in the synthesis of semiconductor nanoparticles, which lead to a substantial improvement of the luminescence quantum efficiency. Concerning a theoretical model for the growth of an ensemble of nanoparticles, the highest quantum efficiencies are achieved in particles that grow under conditions of a rapid exchange of monomers at the particle surface, leading to a smooth surface structure. Selective etching, core-shell formation and doping of nanoparticles are also discussed as fluorescence-enhancing preparative techniques. Examples of self-assembly of almost-uniformly-sized nanoparticles are given, which result in two-dimensional and three-dimensional superlattices, colloidal crystals and crystalline structures built-up from particles of different sizes. Finally, the self-assembled oriented attachment of quasi-spherical ZnO nanoparticles onto single-crystalline nanorods is presented.

Probing wave functions at step superlattices: confined versus propagating electrons

Electron wave functions at lateral nanostructures can be readily explored using photoemission with tunable synchrotron radiation. Such systems are ideal for applications in nanotechnology because they are easily accessed by read–write devices that scan across a surface. As model system here we use vicinal Au(111) surfaces, with an array of terraces separated by straight, monatomic steps, which exhibit atomically accurate periodicity due to an intrinsic surface reconstruction. We analyze two extreme cases where electrons are either localized into lateral quantum-well states or propagating across the step superlattice. We are able to probe the electron probability density at the lateral quantum-wells as well as the Fourier spectrum of the two-dimensional (2D) superlattice states.

Energy level engineering in InAs quantum dot nanostructures

We present an advanced method to tailor the optical and electrical properties of semiconductor quantum dot structures. By embedding vertically stacked quantum dots in a two-dimensional superlattice, the advantages of self-organized growth and of band structure engineering can be combined. The transition energies between the dot levels and the extended states of the superlattice can be adjusted by the period of the superlattice. We apply this scheme for photodetectors made of InAs quantum dots embedded in an AlAs/GaAs superlattice. The dark current of these devices is reduced by more than one order of magnitude compared to the devices without a superlattice.

Nonlithographic fabrication of lateral superlattices for nanometric electromagnetic-optic applications

A nonlithographic technique that utilizes highly ordered anodized aluminum oxide (AAO) porous membrane as a template is employed as a general fabrication means for the formation of an array of vastly different two-dimensional lateral superlattice nanostructures. The fact that material systems as different as metals, semiconductors, and carbon nanotubes can be treated with the same ease attest to the generality of this nanofabrication approach. The original AAO membranes determine the uniformity, packing density, and size of the nanostructures. The flexibility of using a variety of materials, the accurate control over fabrication process, and the command over AAO template attributes, gives us the freedom of engineering various physical properties determined by the shape, size, composition, and doping of the nanostructures. The novel nanomaterial platform realized by this unique technique is powerfully enabling for a broad range of applications.