One-dimensional Quantum Dot Research Articles

Theoretical investigation of electron-phonon interaction in one-dimensional silicon quantum dot array interconnected with silicon oxide layers

Electronic and phononic states and their interactions in one-dimensional arrays of Si quantum dots interconnected with thin oxide layers is theoretically investigated. Electronic states under low electric field condition are obtained in the Kronig-Penny potential. Approximate expression for phonon wave functions is developed and numerically calculated using the linear atomic chain model. Simulated dispersion relation shows acoustic phonon modes, phonon band gaps, and confined optical phonon modes. Electron-phonon scattering rate is written using a one-dimensional expression. Intraminiband scattering rates and energy relaxation rates are simulated both for absorption and emission processes. The scattering rate varies from 10 12 to 10 14 , depending on the initial electron energy. The scattering rate for absorption/emission processes rapidly decreases at near the top/bottom of minibands due to limited number of phonon branches that can mediate the scattering processes. Negative energy relaxation rate is observed near the bottom of minibands, which is due to larger scattering rate for absorption process and smaller phonon energy mediating the scatterings for emission process. The scattering rate for absorption decreases rapidly with decreasing temperature. Once the temperature drops down to 100 K, the energy relaxation rate for emission process dominates the absorption process.

Reduction of acoustic-phonon deformation potential in one-dimensional array of Si quantum dot interconnected with tunnel oxides

The scattering potential for the acoustic deformation potential scattering in a one-dimensional silicon quantum dot array interconnected by thin oxide layers is theoretically investigated. One-dimensional phonon normal modes are numerically obtained using the linear atomic chain model. The strain caused by an acoustic-phonon vibration is absorbed by the oxide layers, resulting in the reduction of the strain in the Si dots. This effect eventually leads to ∼40% reduction of the scattering potential all over the structure. The amount of the reduction does not depend on the phonon energy, but rather on the ratio of the Si dot size to the oxide thickness.

Exciton effects on the nonlinear optical rectification in one-dimensional quantum dots

Exciton effects on the nonlinear optical rectification in one-dimensional quantum dots are studied. The numerical results are presented for GaAs/AlGaAs quantum dots. The results show that the optical rectification coefficient is greatly enhanced because of the quantum confinement of exciton. It is over two times bigger than that obtained by without considering exciton effects. In addition, the optical rectification coefficient is related to the relaxation time T 2 .

Negative differential conductance induced by spin-charge separation.

Spin-charge states of correlated electrons in a one-dimensional quantum dot attached to interacting leads are studied in the nonlinear transport regime. With nonsymmetric tunnel barriers, regions of negative differential conductance induced by spin-charge separation are found. They are due to a correlation-induced trapping of higher-spin states without magnetic field and are associated with a strong increase in the fluctuations of the electron spin.

Antiresonance of electron tunneling through a quantum dot array

Electronic transport through a one-dimensional quantum dot array is theoretically studied. In such a system both electron reservoirs of continuum states couple with the individual component quantum dots of the array arbitrarily. When there are some dangling quantum dots in the array outside the dot(s) contacting the leads, the electron tunneling through the quantum dot array is wholly forbidden if the electron energy is just equal to the molecular energy levels of the dangling quantum dots, which is called as antiresonance of electron tunneling. Accordingly, when the chemical potential of the reservoir electrons is aligned with the electron levels of all quantum dots, the linear conductance at zero temperature vanishes if there are odd number dangling quantum dots; Otherwise, it is equal to 2e2/h due to resonant tunneling if the total number of quantum dots in the array is odd. This odd–even parity is independent of the interdot and the lead–dot coupling strength.

Transport properties of quantum wires

Electron transport in Luttinger liquids connected by tunnel barriers is reviewed. The non-analytic temperature behavior of the conductance of a single tunnel barrier is derived. An overview of charge and spin transport properties through a one-dimensional quantum dot formed by two impurities is given. The temperature and voltage dependences of conductance peaks reveal the non-Fermi liquid correlations. Several spin effects in the linear as well as non-linear transport are predicted. These include a parity effect in linear transport which is due to the Pauli exclusion principle, and negative differential conductances in non-linear transport. The latter are due to charge and spin selection rules and non-Fermi liquid correlations which lead to correlation-induced trapping of higher-spin states. The possibility for experimental verification of this novel effect is discussed.

Role of In desorption for formation of self-organized (In,Ga)As quantum wires on GaAs(1 0 0) during superlattice formation

We investigate the role of In desorption for (In,Ga)As self-organized quantum wire (QWR) formation on GaAs (1 0 0) based on elongated island formation, annealing, and stacking in (In,Ga)As/GaAs superlattice growth. We observe well-defined QWR formation only in the presence of thin GaAs capping of the elongated islands before annealing. Without thin GaAs capping, the In composition becomes too low for controlling the nucleation of (In,Ga)As islands in subsequent layers, necessary for QWR formation. Hence, thin GaAs capping is crucial to reproducibly balance In desorption for formation and vertical correlation of well-defined QWRs, serving as unique template for one-dimensional quantum dot ordering.

Theory of measuring the Luttingergof a one-dimensional quantum dot

We study electron transport through a quantum dot in a Tomonaga-Luttinger liquid with an inhomogeneity induced either by a non-uniform electron interaction or by the presence of tunnel resistances of contacts. The non-analytic temperature behavior of the conductance peaks show crossovers determined by the different energy scales associated with the dot and the inhomogeneity despite the Coulomb blockade remains intact. This suggests an explanation of recent findings in semiconductor quantum wires and carbon nanotubes.

Shell filling in closed single-wall carbon nanotube quantum dots.

We observe twofold shell filling in the spectra of closed one-dimensional quantum dots formed in single-wall carbon nanotubes. Its signatures include a bimodal distribution of addition energies, correlations in the excitation spectra for different electron number, and alternation of the spins of the added electrons. This provides a contrast with quantum dots in higher dimensions, where such spin pairing is absent. We also see indications of an additional fourfold periodicity indicative of K-K' subband shells. Our results suggest that the absence of shell filling in most isolated nanotube dots results from disorder or nonuniformity.

Dynamic Localization of a One-Dimensional Quantum DotArray in an ac Electric Field

We investigate the dynamics of two interaction electronsconfined to one-dimensional quantum dot array in an ac electric field.We find that initially localized electrons will remain localizedin the absence of Coulomb interaction if the ratio of the ac fieldmagnitude to the frequency is a root of theordinary zero-order Bessel function. In contrast to the case withoutCoulomb interaction, no matter what the value is,the electrons are delocalized and the delocalization effectdepends on the ratio U/ω and eaE/ω, where U isthe strength of Coulomb interaction, a is the lattice constant, and Eand ω are the ac field amplitude and frequency, respectively.

Alternating-current response of one-dimensional quantum dotarrays

A general approach is presented for calculating the dynamicconductance of coupled quantum dot systems. To consider thelong-range Coulomb interaction, we introduce the capacitancesbetween the leads and dots, gate electrodes and dots, and dots anddots. The displacement currents are also taken into account. Ourresults fulfil charge and current conservation requirements, as wellas current and charge response invariance under an overall potentialshift. We apply our approach to a one-dimensional quantum dot arrayby use of the non-equilibrium Green function techniques. Thenumerical results are presented for a three-quantum-dot system.Three-peak resonant structure of the alternating-current conductanceis observed at low temperature. The effect of the capacitance onthe frequency-dependent conductance is obvious, but less so at lowfrequency. The low-frequency conductance shows either capacitive orinductive behaviour depending on the chemical potential of theelectron reservoirs, but sufficiently large capacitances may changethis situation.

Photoconductance of a one-dimensional quantum dot

The ac-transport properties of a one-dimensional quantum dot with non-Fermi liquid correlations are investigated. It is found that the linear photoconductance is drastically influenced by the interaction. Temperature and voltage dependences of the sideband peaks are treated in detail. Characteristic Luttinger liquid power laws are founded.

Quantum transport in a one-dimensional quantum dot array

In this paper we study electronic transport through a quantum dot array containing an arbitrary number of quantum dots connected in a series by tunnel coupling under dc bias. The on-site Coulomb interaction is ignored. The retarded self-energy of any dot in the array is made up of left and right components and is of staircase type, terminating at corresponding electron reservoirs. We calculate the dc current based on the nonequilibrium Green's function formalism developed by Jauho et al. [A.-P. Jauho, Ned S. Wingreen, and Y. Meir, Phys. Rev. B 50, 5528 (1994)]. The dc current in both finite and infinite number dots in the array is calculated. The electronic spectrum of the system is found to fall within an interval centered at ${\ensuremath{\epsilon}}_{0}$ (the dot energy level) with a width of two times the tunnel coupling amplitude between two neighboring dots. The electronic charge in each dot is plotted for the finite number dot array.

Kondo physics in carbon nanotubes.

The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically contacted single-walled carbon nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far greater tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron numbers (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.

Charge and spin addition energies of a one-dimensional quantum dot

We derive the effective action for a one-dimensional electron island formed between a double barrier in a single-channel quantum wire including the electron spin. Current and energy addition terms corresponding to charge and spin are identified. The influence of the range and the strength of the electron interaction and other system parameters on the charge and spin addition energies and on the excitation spectra of the modes confined within the island is studied. We find by comparison with experiment that spin excitations in addition to nonzero range of the interaction and inhomogeneity effects are important for understanding the electron transport through one-dimensional quantum islands in cleaved-edge-overgrowth systems.

Optical and transport properties of low-dimensional structures fabricated by cleaved edge overgrowth

Recent progress in the fabrication of GaAs/AlGaAs low-dimensional structures by cleaved edge overgrowth (CEO) — a molecular beam growth technique that involves one or two regrowth steps on the sidewalls of an in situ cleaved layer structure — is reviewed. Ballistic electron transport in modulation-doped quantum wires prepared in this way is characterized by pronounced quantization of the conductance in integer multiples < 2e 2 h . A magnetic field oriented perpendicular to the quantum wires is found to increase the quantized conductance values. While for a 400 Å wide channel the canonical values of n × 2e 2 h are almost reached at a magnetic field strength of 4 T the corresponding conductance rise in a 250 Å wide channel is much slower. In addition, the magnetic field dependence of the positions of the conductance steps as a function of an applied gate voltage which controls the electron density is distinctly different for wires of 400 and 250 Å width. The optical properties of atomically precise quantum dots which originate at the right angle intersection of three quantum wells are characterized by narrow “atom-like” emission lines. Two different types of quantum dot structures have been investigated using microscopic photoluminescence spectroscopy: linear arrays of weakly coupled dots, i.e. an one-dimensional quantum dot superlattice and single as well as paired quantum dots. The latter allow the assembly of “artificial molecules” out of almost identical quantum dots which can be considered as “artificial atoms” as the dot-to-dot distance is varied.

Addition spectrum, persistent current, and spin polarization in coupled quantum dot arrays: Coherence, correlation, and disorder

The ground state persistent current and electron addition spectrum in two-dimensional quantum dot arrays and one-dimensional quantum dot rings, pierced by an external magnetic flux, are investigated using the extended Hubbard model. The collective multidot problem is shown to map exactly into the strong field noninteracting finite-size Hofstadter butterfly problem at the spin polarization transition. The finite size Hofstadter problem is discussed, and an analytical solution for limiting values of flux is obtained. In weak fields we predict novel flux periodic oscillations in the spin component along the quantization axis with a periodicity given by $\nu h/e$ ($\nu \le 1$). The sensitivity of the calculated persistent current to interaction and disorder is shown to reflect the intricacies of various Mott-Hubbard quantum phase transitions in two- dimensional systems: the persistent current is suppressed in the antiferromagnetic Mott-insulating phase governed by intradot Coulomb interactions; the persistent current is maximized at the spin density wave - charge density wave transition driven by the nearest neighbor interdot interaction; the Mott-insulating phase persistent current is enhanced by the long-range interdot interactions to its noninteracting value; the strong suppression of the noninteracting current in the presence of random disorder is seen only at large disorder strengths; at half filling even a relatively weak intradot Coulomb interaction enhances the disordered noninteracting system persistent current; in general, the suppression of the persistent current by disorder is less significant in the presence of the long-range interdot Coulomb interaction.

Energy-Dependent Effective Mass Approximation in One-Dimensional Quantum Dots

We extend the effective mass approximation by taking into account the energy dependence of the effective mass. The effective Hamiltonian with an energy-dependent effective mass is applied to one-dimensional quantum dots. The eigenvalues of the effective Hamiltonian agree well with the energy levels of confined states in the dots, even in the energy region where the usual effective mass approximation is not useful. The energy dependence of the effective mass, which is common to any size of quantum dot, is derived from the nonparabolic conduction band of bulk materials.

Interacting electrons in a one-dimensional quantum dot

The spectral properties of up to four interacting electrons confined within a quasi-one-dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground-state energy is investigated as a function of the electron number and of the system length. The limitations of a description in terms of a capacitance are demonstrated. The energetically lowest-lying excitations are physically explained as vibrational and tunneling modes. The limits of a dilute, Wigner-type arrangement of the electrons, and a dense, more homogeneous charge distribution are discussed.

Co-tunneling via the one-dimensional Wigner lattice

We have calculated the rates of the two-electron co-tunneling via Wigner lattice confined to a one-dimensional quantum dot. The co-tunneling rate is shown to be suppressed by the formation of the Wigner lattice more strongly that the rate of the single-electron tunneling.