Dot Lattice Research Articles

Unifying sequential effects in perceptual grouping

Temporally-extended perception involves a delicate balance of constancy and change. 'This can be seen, for instance, when viewing bistable figures such as the Necker cube. A recent study by Gepshtein and Kubovy of sequential effects in multistable dot lattices demonstrates constancy and change within the same set of data. They propose that these opposing trends might be explained by the same single factor: a persistent random orientation bias that is intrinsic to brain activity. This proposal could form the basis for a new account of multistability.

Dot lattice regularity influences grouping by similarity

Dot lattice regularity influences grouping by similarity

Vortex states of a superconducting film from a magnetic dot array.

Using Ginzburg-Landau theory, we find novel configurations of vortices in superconducting thin films subject to the magnetic field of a magnetic dot array, with dipole moments oriented perpendicular to the film. Sufficiently strong magnets cause the formation of vortex-antivortex pairs. In most cases, the vortices are confined to dot regions, while the antivortices can form a rich variety of lattice states. We propose an experiment in which the perpendicular component of the dot dipole moments can be tuned using an in-plane magnetic field. We show that in such an experiment the vortex-antivortex pair density shows broad plateaus as a function of the dipole strength. Many of the plateaus correspond to vortex configurations that break dot lattice symmetries. In some of these states, the vortex cores are strongly distorted. Possible experimental consequences are mentioned.

Commensurate vortex configurations in thin superconducting films nanostructured by square lattice of magnetic dots

Within the phenomenological Ginzburg–Landau (GL) theory, we investigate the vortex structure of a thin superconducting film (SC) with a regular matrix of ferromagnetic dots (FD) deposited on top of it. The vortex pinning properties of such a magnetic lattice are studied, and the field polarity dependent votex pinning is observed. The exact vortex configuration depends on the size of the magnetic dots, their polarity, periodicity of the FD-rooster and the properties of the SC expressed through the effective Ginzburg–Landau parameter κ *.

3D hexagonal versus trigonal ordering in self-organized PbSe quantum dot superlattices

Self-organized vertical and lateral ordering in PbSe/PbEuTe quantum dot superlattices grown by molecular beam epitaxy is investigated by synchrotron X-ray diffraction and atomic force microscopy. For small PbEuTe spacer thicknesses, the dots are ordered hexagonally in the lateral direction and vertically aligned along the growth direction. This yields an overall 3D hexagonal lattice of dots. For larger spacer thicknesses an FCC-like dot stacking is formed, resulting in the formation of a 3D trigonal dot lattice. From the analysis of the X-ray diffraction spectra the ordering is significantly better for the trigonally ordered dot samples.

Nanoengineered magnetic-field-induced superconductivity.

The perpendicular critical fields of a superconducting film have been strongly enhanced by using a nanoengineered lattice of magnetic dots (dipoles) on top of the film. Magnetic-field-induced superconductivity is observed in these hybrid superconductor/ferromagnet systems due to the compensation of the applied field between the dots by the stray field of the dipole array. By switching between different magnetic states of the nanoengineered field compensator, the critical parameters of the superconductor can be effectively controlled.

Spontaneous magnetism of quantum dot lattices.

The magnetism of square lattices of quantum dots with up to 12 electrons per dot is studied using the spin-density functional formalism. At small values of the lattice constant, all lattices are nonmagnetic and gapless. When the lattice constant is increased, the shell structure of the single dots governs the magnetism of the lattice. At closed shells, the lattices are nonmagnetic and have a gap at the Fermi level. At the beginning and at the end of a shell, they become ferromagnetic and stay gapless up to large values of the lattice constant. Antiferromagnetism was observed only at midshell after a band gap was opened.

Tight-Binding Model for Spontaneous Magnetism of Quantum Dot Lattices

We use a simple tight-binding model to study the magnetism of two-dimensional quantum dot lattices with 1 to 12 electrons per dot. The results show that in the middle of an electron shell the lattice favours antiferromagnetism while with nearly empty or full shells ferromagnetism is favoured. The size of the antiferromagnetic region increases with the coordination number of the dot. A one-dimensional dot lattice shows a spin-Peierls transition. The results for a square lattice are in good agreement with density functional calculations of Koskinen et al.

Molecular-beam epitaxial growth of GaAs and InGaAs/GaAs nanodot arrays using anodic Al2O3 nanohole array template masks

Highly ordered arrays of nanosized GaAs-based dots were successfully prepared on GaAs (001) substrates by molecular-beam epitaxy using selected area growth. Selected area growth employed alumina nanochannel array (NCA) templates formed by anodic oxidation, bonded to the GaAs substrates. Homogeneous GaAs dots, as well as compositionally modulated heterostructures within the nanosized dots, were demonstrated. In the latter case, multilayer InGaAs/GaAs heterostructured nanodot arrays were fabricated. Dot growth occurred only as defined by the template mask, resulting in a hexagonal lattice of dots with 100 nm period spacing, with dots retaining the circular lateral shape of the pores as determined by the NCA template pore size; dot diameters were adjustable from 45 to 85 nm for a lattice period of 100 nm. Cathodoluminescence spectra from an InGaAs/GaAs 10×10 dot array clearly showed an emission peak at 920 nm (5 K), confirming the formation of a high-quality InGaAs/GaAs quantum dot array.

Symmetry breaking in self-assembled monolayers on solid surfaces. II. Anisotropic substrate elasticity

On a solid surface a monolayer mixture may separate into two phases. The phases can self-assemble into a variety of patterns, with the feature size on the scale of 1‐100 nm. This paper studies how the elastic anisotropy of the substrate affects the patterns. The substrate is taken to be of cubic crystal symmetry, although the method developed can be readily extended to treat substrates of any other crystalline symmetry. The surface stress differs from one phase to the other, and the difference refines the phases to reduce the elastic energy. The phase boundary energy tends to coarsen the phases. The two competing effects set the phase sizes and the phase patterns. The anisotropy of the substrate elasticity breaks the symmetry of the system. We formulate a phase field model on the basis of this physical picture. The numerical simulation shows that stripes tend to orient along the two compliant directions of the substrate, forming a tweedlike pattern. A square lattice of dots can also be obtained when the anisotropy is weak and the average concentration sufficiently deviates from half filling. We interpret these findings in terms of free energy minimization.

Temperature-induced magnetization reorientation in arrays of magnetic dots on a magnetic substrate

We studied magnetic properties of regular arrays of magnetic dots on a magnetic layer. We took into account the exchange interaction, the dipolar interaction of amplitude D between spins, and the perpendicular anisotropy A. The spins are of the classical Heisenberg model. Due to the competition between D and A, the ground state (GS) can be perpendicular or parallel to the substrate. We have studied the body-centered-cubic and hexagonal-close-packed dot lattices. We have determined the GS magnetic structure as a function of A and D by a steepest descent method. The results show that below (above) a critical value of D/A, the GS spin configuration is perpendicular (parallel). We have studied finite-temperature properties of our system of dots in the vicinity of the critical D/A by Monte Carlo simulations. The obtained results show spectacular features, in particular on the spin reorientation. A phase diagram in the vinicity of the critical value of D/A is presented.

Configurational anisotropy in square lattices of interacting cobalt dots

Magnetostatic coupling effects are investigated in square lattices of polycrystalline circular Co dots as a function of dot diameter, spacing, and thickness. We observe a quadratic anisotropy for closely spaced dots when the dot thickness exceeds 15 nm, correlated to a change in the magnetization reversal process from coherent rotation to vortex nucleation/annihilation. To understand the observed anisotropy micromagnetic simulations have been performed which show that vortex nucleation is strongly dependent on the micromagnetic configurations.

Nonlinear magneto-optical diffraction by two-dimensional magnetic superstructures

Nonlinear (at the second-harmonic frequency of the incident light) optical reflection by two-dimensional magnetic superstructures is theoretically studied. A square lattice of magnetic dots and a hexagonal lattice of magnetic bubbles (cylindrical magnetic domains) are considered. Because the periods of these structures are comparable with the wavelengths of the fundamental and the second-harmonic radiation, it would be possible to observe diffraction at the second-harmonic frequency. A polarization analysis of nonlinearly diffracted radiation is performed and the numbers of observable diffraction orders for the above structures are estimated.

Spatially site-controlled InAs quantum dot lattices

A spatial site-control method for InAs quantum dots (QDs) is proposed and demonstrated using ultrahigh vacuum in situ processing. Regular InAs QD arrays are initially prepared as strain templates on GaAs surfaces by the scanning tunneling microscope (STM) probe-assisted site-control technique. Multiple layers of InAs Stranski–Krastanov QDs are then grown with GaAs spacers for strain-induced vertical alignment above the regular QD arrays, resulting in three-dimensional QD lattices. Step-by-step STM observations reveal the growth mode of QDs in the vertical alignment process.

Magnetic-field effects on a two-dimensional Kagomé lattice of quantum dots

Magnetic field effects on single-particle energy bands (Hofstadter butterfly), Hall conductance, flat-band ferromagnetism, and magnetoresistance of two-dimensional Kagome lattices are studied. The flat-band ferromagnetism is shown to be broken as the flat-band has finite dispersion in the magnetic field. A metal-insulator transition induced by the magnetic field (giant negative magnetoresistance) is predicted. In the half-filled flat band, the ferromagnetic-paramagnetic transition and the metal-insulator one occur simultaneously at a magnetic field for strongly interacting electrons. All of the important magnetic fields effects should be observable in mesoscopic systems such as quantum dot superlattices.

Time-resolved photoluminescence near Fermi level in a field-induced quantum dot lattice

Time-resolved photoluminescence (PL) near Fermi level is measured in a bias-voltage-induced quantum dot lattice, where the PL peak has been widely known to be originated from Fermi-edge singularity (FES). It is suggested from the dependencies of lifetimes on temperatures, applied magnetic fields, and bias voltage, that the peak is mainly due to radiative relaxation process of a hole.

Self-assembling quantum dot lattices through nucleation site engineering

The long range ordering of epitaxial semiconductor quantum dots is investigated using several crystal growth techniques on prepatterned substrates. We have developed two nucleation site control techniques: one which uses localized surface chemical potential engineering and one which uses localized surface strain engineering. We present experimental results that demonstrate the ability to create ordered quantum dot lattices and discuss the different mechanisms involved in the long range ordering of quantum dots.

Symmetry breaking in self-assembled monolayers on solid surfaces: Anisotropic surface stress

This paper models the self-assembly dynamics of a two-phase monolayer on an elastic substrate. The two phases coarsen to reduce the phase boundary energy and refine to reduce the elastic energy. To minimize the total free energy, the two phases can order into nanoscale patterns. We combine the continuum phase field model of spinodal decomposition and the anisotropic surface stress. The numerical simulation shows various patterns, such as interwoven stripes, parallel stripes, triangular lattice of dots, and herringbone structures. The surface stress anisotropy causes a transition from the parallel stripes to the herringbone structures. We show that this symmetry breaking mesophase transition obeys the classical theory of Landau.

An Instructional Two-Dimensional Diffraction Laboratory Using Patterns Created with Electron-Beam Lithography

ABSTRACTAn instructional laboratory in two-dimensional diffraction is discussed. The experiment is appropriate for undergraduate students in materials science, solid-state physics (as was the case with our group), modern physics, or optics. The experiment is performed using visible light from a laser incident on a 2D lattice of gold dots deposited with electron beam lithography on a glass substrate. The pattern is microscopic with a lattice constant on the same order of magnitude as the wavelength of light used. Students observe the diffraction pattern, and then quantitatively determine the positions of maxima. These data are used by the students to reconstruct the (real space) microscopic lattice. The students can simulate the experiment with software that computes reciprocal lattice and diffraction patterns for an arbitrary 2D lattice.

Three-Dimensional Quantum Dot ?Crystal? Formation in CdTe/ZnTe Superlattices

The observation of both vertical and lateral ordering of quantum dots in CdTe/ZnTe superlattices with different thickness of ZnTe spacer is reported. The simultaneous presence of both types of ordering in the studied structures is evidenced by transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) studies. The TEM results show that when the spacer thickness is smaller than 25 monolayers, the islands are vertically correlated along the axis tilted by 40° with respect to the growth direction. On the other hand, the SAXS spectra exhibit four intensity maxima of scattering at q = 0.2 Å—1 along [100], [], [010] and [] crystallographic directions. We interpret them as originating from a locally formed square quantum dot lattice.