Periodic Array Of Quantum Dots Research Articles

Magnetic Properties of A Cavity‐Embedded Square Lattice of Quantum Dots or Antidots

AbstractQuantum electrodynamical density functional theory is applied to obtain the electronic density, spin polarization, as well as orbital and spin magnetizations of square periodic arrays of quantum dots or antidots subjected to the influence of a far‐infrared cavity photon field. A gradient‐based exchange‐correlation functional adapted to a 2D electron gas in a transverse homogeneous magnetic field is used in the theoretical framework and calculations. The obtained results predict a non‐trivial effect of the cavity field on the electron distribution in the unit cell of the superlattice, as well as on the orbital and spin magnetizations. The number of electrons per unit cell of the superlattice is shown to play a crucial role in the modification of the magnetization via the electron–photon coupling. The calculations show that cavity photons strengthen the diamagnetic effect in the quantum dot structure, while they weaken the paramagnetic effect in the antidot structure. As the number of electrons per unit cell of the lattice increases, the electron–photon interaction reduces the exchange forces that will otherwise promote strong spin splitting for both the dot and the antidot arrays.

Hofstadter butterflies for square and honeycomb periodic arrays of quantum dots with Aharonov-Bohm solenoids

Periodic array of quantum dots in a magnetic field is considered. The magnetic field consists of two components: uniform and periodic. The periodic field is presented by the Aharonov-Bohm solenoids inserted in the quantum dots. The model based on the theory of self-adjoint extensions of symmetric operators is suggested. Two types of “flux-energy” diagrams (“Hofstadter butterflies”) are constructed and discussed. Diagrams of the first type show the spectrum of the system for different values of the uniform magnetic field (flux) and fixed AB flux. Diagrams of the second type show the spectrum of the system for different values of the AB magnetic field flux and fixed flux of the uniform magnetic field. “Flux-energy” diagrams for honeycomb lattice demonstrates splitting of bands in comparison with the case of square lattice. One can see one more peculiarity: butterflies for honeycomb case don't contain wide band except from zero.

Model of tunnelling through periodic array of quantum dots

Several explicitly solvable models of electron tunnelling in a system of single and double two-dimensional periodic arrays of quantum dots with two laterally coupled leads in a homogeneous magnetic field are constructed. First, a model of single layer formed by periodic array of zero-range potentials is described. The Landau operator (the Schrodinger operator with a magnetic field) with point-like interactions is the system Hamiltonian. We deal with two types of the layer lattices: square and honeycomb. The periodicity condition gives one an invariance property for the Hamiltonian in respect to magnetic translations group. The consideration of double quantum layer reduces to the replacement of the basic cell for the single layer by a cell including centers of different layers. Two variants of themodel for the double layer are suggested: with direct tunneling between the layers and with the connecting channels (segments in the model) between the layers. The theory of self-adjoint extensions of symmetric operators is a mathematical background of the model. The third stage of the construction is the description of leads connection. It is made by the operator extensions theory method too. Electron tunneling from input lead to the output lead through the double quantum layer is described. Energy ranges with extremely small (practically, zero) transmission were found. Dependencies of the transmission coefficient (particularly, “zero transmission bands” positions) on the magnetic field, the energy of electron and the distance between layers are investigated. The results are compared with the corresponding single-layer transmission.

Model of tunnelling through periodic array of quantum dots in a magnetic field

A two-dimensional periodic array of quantum dots with two laterally coupled leads in a magnetic field is considered. The model of electron transport through the system based on the theory of self-adjoint extensions of symmetric operators is suggested. We obtain the formula for the transmission coefficient and investigate its dependence on the magnetic field.

Extraordinary Electron Transmission through a Periodic Array of Quantum Dots

We study electron transmission through a periodic array of quantum dots (QD) sandwiched between doped semiconductor leads. When the Fermi wavelength of tunneling electron exceeds the array lattice constant, the off-resonant per QD conductance is enhanced by several orders of magnitude relative to the single-QD conductance. The physical mechanism of the enhancement is delocalization of a small fraction of system eigenstates caused by coherent coupling of QDs via the electron continuum in the leads.

Patterning of Quantum Dot Bioconjugates via Particle Lithography

We present a simple technique to fabricate hexagonally ordered quantum dot bioconjugate (QDBC) dot arrays on glass coverslips. We used particle lithography to create periodic holes in a layer of methoxy-poly(ethylene glycol)-silane and then adsorbed QDBCs into the holes. To demonstrate the versatility of this technique, we made separate periodic arrays of quantum dots (QDs) conjugated to three different biologically important molecules: biotin, streptavidin, and anti-mouse IgG. The diameters of the regions where the QDBCs adsorbed were 500-600 nm and independent of the QDBC patterned. The site density of the QDBCs in the patterned holes could be varied by simply adjusting the coating concentration of the QDBC solution. We demonstrate the applicability of these substrates by designing a QDBC-based binding assay with a working concentration range of several orders of magnitude and a sub-picomolar detection limit.

Potential Energy Landscape for Hot Electrons in Periodically Nanostructured Graphene

We explore the spatial variations of the unoccupied electronic states of graphene epitaxially grown on Ru(0001) and observed three unexpected features: the first graphene image state is split in energy; unlike all other image states, the split state does not follow the local work function modulation, and a new interfacial state at +3 eV appears on some areas of the surface. First-principles calculations explain the observations and permit us to conclude that the system behaves as a self-organized periodic array of quantum dots.

Trapping of an electron in coupled quantum dots in graphene

Due to Klein's tunneling the electronic states of a quantum dot in graphene have finite widths and an electron in quantum dot has a finite trapping time. This property introduces a special type of interdot coupling in a system of many quantum dots in graphene. The interdot coupling is realized not as a direct tunneling between quantum dots but as coupling through the continuum states of graphene. As a result the interdot coupling modifies both the positions and the widths of the energy levels of the quantum dot system. We study the system of quantum dots in graphene theoretically by analyzing the complex energy spectra of the quantum dot system. We show that in a double-dot system some energy levels become strongly localized with an infinite trapping time. Such strongly localized states are achieved only at one value of the interdot separation. We also study a periodic array of quantum dots in graphene within a tight-binding mode for a quantum dot system. The values of the hopping integrals in the tight-binding model are found from the expression for the energy spectra of the double quantum dot system. In the array of quantum dots the states with infinitely large trapping time are realized at all values of interdot separation smaller than some critical value. Such states have nonzero wave vectors.

Surface-plasmon-enhanced fluorescence from periodic quantum dot arrays through distancecontrol using biomolecular linkers

We have developed a protein-enabled strategy to fabricate quantum dot (QD) nanoarrayswhere up to a 15-fold increase in surface-plasmon-enhanced fluorescence has been achieved.This approach permits a comprehensive control both laterally (via lithographically definedgold nanoarrays) and vertically (via the QD–metal distance) of the collectively behavingassemblies of QDs and gold nanoarrays by way of biomolecular recognition. Specifically, wedemonstrated the spectral tuning of plasmon resonant metal nanoarrays and self-assemblyof protein-functionalized QDs in a stepwise fashion with a concomitant incrementalincrease in separation from the metal surface through biotin–streptavidin spacer units.

X-ray scattering from periodic arrays of quantum dots

Three-dimensional periodic arrays of self-organized quantum dots in semiconductormultilayers are investigated by high-resolution x-ray scattering. We demonstratethat the statistical parameters of the dot array can be determined directly fromthe scattering data without performing a numerical simulation of the scatteredintensity.

Using magnetic fields and band gap engineering to achieve robust spin filtering in finite quantum dot arrays

In periodic quantum dot arrays, conductance can be modulated by exploiting band gap effects. Since the backscattering effects that produce some of the band gaps are comparatively strong, an open array with as little as three dots can be utilized to achieve zero transmission. Utilizing Zeeman-splitting, one can create a situation where, by the shifting the gaps for the individual spins, one can achieve nearly 100% spin polarization. The energy scales over which this polarization is achieved depends on the size of the band gaps. Thus, the effect can be enhanced further by band gap engineering, picking the structure that maximizes the size of the gaps for a given Fermi energy and field.

Quantum transport in semiconductor quantum dot superlattices: Electron-phonon resonances and polaron effects

Electron transport in periodic quantum dot arrays in the presence of interactions with phonons was investigated using the formalism of nonequilibrium Green's functions. The self-consistent Born approximation was used to model the self-energies. Its validity was checked by comparison with the results obtained by direct diagonalization of the Hamiltonian of interacting electrons and longitudinal optical phonons. The nature of charge transport at electron-phonon resonances was investigated in detail and contributions from scattering and coherent tunneling to the current were identified. It was found that at larger values of the structure period, the main peak in the current-field characteristics exhibits a doublet structure which was shown to be a transport signature of polaron effects. At smaller values of the period, electron-phonon resonances cause multiple peaks in the characteristics. A phenomenological model for treatment of nonuniformities of a realistic quantum dot ensemble was also introduced to estimate the influence of nonuniformities on current-field characteristics.

Energy bands of quantum dot arrays

The energy bands are derived for a simple model of quantum dot arrays. The periodic array of quantum dots is linked by conducting atoms. The electrons in the conducting linkers are described by a tight-binding model. The electrons in the quantum dots are strong correlated, and the correlation is described by a Hubbard term. The electrons on the quantum dots are allowed to fluctuate through hopping to and from the conducting atoms. We solve the energy band for conducting electrons with perturbation method for the case that the quantum dots are in a spin singlet state.

A quantum dot image processor

A two-dimensional (2-D) periodic array of quantum dots, where each dot is coupled with its nearest neighbors and interfaced with an underlying material exhibiting a negative differential resistance, is theoretically investigated as a dynamical system for image processing. A circuit level study of such a system is performed and the circuit parameters for this paper are extracted by experimentally measuring them in an electrochemically self-assembled quasi-periodic quantum dot array. Large 2-D dot arrays with 4-neighborhood rectangular lattice structure are then simulated and it is shown that if image data are introduced as initial conditions to these arrays, the steady-state response of the system realizes an image processing task similar to edge detection-enhancement. In addition, the quantum dot architecture is capable of horizontal-vertical line detection with a simple arrangement of the coupling resistances between the dots. These applications are demonstrated via numerical experiments.

Kinetic Monte Carlo Simulations of Strain-Induced Nanopatterning on Hexagonal Surfaces

AbstractGuided self assembly of periodic arrays of quantum dots has recently emerged as an important research field not only to reduce component size and manufacturing cost but also to explore and apply quantum mechanical effects in novel nanodevices. The intention of this kinetic Monte Carlo (KMC) simulation study is to investigate self-organized nanopatterning on hexagonal surfaces for relaxed periodic surface strain fields applied to Pt(111) epitaxy. The KMC model is a full diffusion bond-counting model including nearest neighbor as well as second-nearest neighbor interactions with an event catalogue consisting of 8989 events modeling the effect of the biaxial surface strain field. The strain dependence of the fcc site and the saddle point for a Pt adatom migrating on top of the Pt(111) surface is calculated using the embedded atom method. Both the valley and the saddle point energies show an excellent linear dependence on the strain. These results are applied in the KMC model. The surface strain in this study is caused by a hexagonal network of dislocations at the interface between the substrate and a mismatched epitaxial layer. How the selforganization of deposited atoms is influenced by the surface strain will be addressed.

Eigenvalues imbedded in the band spectrum for a periodic array of quantum dots

A solvable model for a periodic array of quantum dots in a uniform magnetic field is proposed having eigenvalues imbedded in a continuous spectrum. The continuous spectrum of the array may be absolutely continuous as well as singular continuous. The model is based on the operator extension theory.

Operator extension theory models for periodic array of quantum dots and double quantum layer in a magnetic field

Solvable models for periodic array of quantum dots and for double quantum electron layer in a magnetic field based on the theory of self-adjoint extensions of symmetric operators is suggested. The spectral problem reduces to finite-dimensional one by using harmonic analysis on magnetic translations group. The dispersion equations are obtained. Properties of a gap between symmetric and antisymmetric states are discussed.

Periodic array of quantum dots in a magnetic field: Irrational flux; honeycomb lattice

The solvable model of a periodic array of quantum dots in a magnetic field is investigated. It is shown that in the case of square lattice and irrational flux the energy spectrum of a charged particle in the array has a fractal structure. In the case of honeycomb lattice the existence of an additional splitting of magnetic bands related with lattice geometry. The position of the Van Hove singularities is determined.

Edge states, band structure, and the Hall effect in two-dimensional lattice structures: quantum dot arrays and the tight-binding model

Using a model that is based on a transfer matrix formalism, we study the electronic structure and transport in two dimensional periodic arrays of quantum dots in magnetic fields. The quantum dots in our model are connected to each other via ballistic constrictions. The spectrum for this system has much in common with that with the tight-binding model. In particular, q bulk bands arise if the normalized magnetic flux per unit cell is p/q, where p and q are coprime integers. Working within an edge-state picture, we investigate if these similarities translate to a correspondence in the transport properties of the two systems. As we shall show, the answer to this question depends very much on the transmission probability of the constrictions. Our analysis also shows that, under certain circumstances, the Hall conductance within the context of the tight-binding model may take on fractional values.

Structural Characterization of Reactive Ion Etched Semiconductor Nanostructures Using X-Ray Reciprocal Space Mapping

AbstractWe have studied GaAs/AlAs periodic quantum dot arrays using high resolution x-ray diffraction (reciprocal space mapping) around the (004) and (113) reciprocal lattice points. From the distribution of the diffracted intensities we deduced the average strain status of the dots. From the numerical simulations it is evident that random elastic strain fields are present, which extend through almost the entire volume of the quantum dot. The simulations of the x-ray measurements revealed that the crystalline part of the dots is considerably smaller as scanning electron micrographs would indicate.