Single-electron tunneling and Coulomb blockade in carbon-based quantum dots

Single-electron tunneling (SET) and Coulomb blockade (CB) phenomena have been widely observed in nanoscaled electronics and have received intense attention around the world. In the past few years, we have studied SET in carbon nanotube fragments and fullerenes by applying the so-called “Orthodox” theory [28]. As outlined in this review article, we investigated the single-electron charging and discharging process via current-voltage characteristics, gate effect, and electronic structure-related factors. Because the investigated geometric structures are three-dimensionally confined, resulting in a discrete spectrum of energy levels resembling the property of quantum dots, we evidenced the CB and Coulomb staircases in these structures. These nanostructures are sufficiently small that introducing even a single electron is sufficient to dramatically change the transport properties as a result of the charging energy associated with this extra electron. We found that the Coulomb staircases occur in the I–V characteristics only when the width of the left barrier junction is smaller than that of the right barrier junction. In this case, the transmission coefficient of the emitter junction is larger than that of the collector junction; also, occupied levels enter the bias window, thereby enhancing the tunneling extensively.      

Carrier tunneling in asymmetric coupled quantum dots

Exciton spin relaxation at low temperatures in InAlAs–InGaAs asymmetric double quantum dots embedded in AlGaAs layers has been investigated as a function of the barrier thickness by the time-resolved photoluminescence measurements. With decreasing the thickness of the AlGaAs layer between the dots, the spin relaxation time change from 3 ns to less than 500 ps. The reduction in the spin relaxation time was considered to originate from the spin-flip tunneling between the ground state in InAlAs dot and the excited states in InGaAs dot, and the resultant tunneling leads to the spin depolarization of the ground state in InGaAs dot.     

Charge and spin configurations in the coupled quantum dots with Coulomb correlations induced by tunneling current

We investigated the peculiarities of non-equilibrium charge states and spin configurations in the system of two strongly coupled quantum dots (QDs) weakly connected to the electrodes in the presence of Coulomb correlations. We analyzed the modification of non-equilibrium charge states and different spin configurations of the system in a wide range of applied bias voltage and revealed well pronounced ranges of system parameters where negative tunneling conductivity appears due to the Coulomb correlations.     

Electronic states and tunneling times in coupled self-assembled quantum dots

Electron energy levels in single dots, and energy splitting and tunneling times in stacked quantum dots are calculated as functions of structure parameters. An effective mass approach is used to solve the Schrödinger equation for cylindrical dots with finite confinement potentials. Strong confinement due to small sizes produces quantized energy levels in single dots and strong interactions of the wavefunctions with adjacent dots. This electronic coupling induces significant energy splittings and short tunneling times for characteristic structures used in experiments. This coupling may even yield coherent artificial molecular states with different optical properties.     

Superluminal optical soliton via resonant tunneling in coupled quantum dots

We demonstrate the formation of superluminal optical soliton in an symmetry semiconductor double quantum dot (QD) driven coherently by a weak pulsed laser using the tunnel coupling. It is shown that the group velocity of the soliton can be larger than the vacuum light speed c, i.e., superluminal soliton can be produced. The results obtained can be used for the development of new types of nanoelectronic devices for realizing high-speed optical modulation and rapidly responding quantum switching.     

Effects of Coulomb interactions on spin states in vertical semiconductor quantum dots

The effects of direct Coulomb and exchange interactions on spin states are studied for quantum dots contained in circular and rectangular mesas. For a circular mesa a spin-triplet favored by these interactions is observed at zero and nonzero magnetic fields. We tune and measure the relative strengths of these interactions as a function of the number of confined electrons. We find that electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle state degeneracy, and find that the spin-configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states. For a rectangular mesa we observe no signatures of the spin-triplet at zero magnetic field. Due to the anisotropy in the lateral confinement single-particle state degeneracy present in the circular mesa is lifted, and Coulomb interactions become weak. We evaluate the degree of the anisotropy by measuring the magnetic field dependence of the energy spectrum for the ground and excited states, and find that at zero magnetic field the spin-singlet is more significantly favored by the lifting of level degeneracy than by the reduction in the Coulomb interaction. We also find that the spin-triplet is recovered by adjusting the level degeneracy with magnetic field. Received: 14 April 2000 / Accepted: 17 April 2000 / Published online: 6 September 2000     

Coulomb effects in semiconductor quantum dots

This paper presents a new model for the Internet graph (AS graph) based on the concept of heuristic trade-off optimization, introduced by Fabrikant, Koutsoupias and Papadimitriou in [5] to grow a random tree with a heavily tailed degree distribution. We propose here a generalization of this approach to generate a general graph, as a candidate for modeling the Internet. We present the results of our simulations and an analysis of the standard parameters measured in our model, compared with measurements from the physical Internet graph.Received: 9 February 2004, Published online: 14 May 2004PACS: 89.75.-k Complex systems - 89.75.Hc Networks and genealogical trees - 89.75.Da Systems obeying scaling laws - 89.75.Fb Structures and organization in complex systems - 89.65.Gh Economics; econophysics, financial markets, business and managementLRI: http: //www.lri.fr/~ihameli; CNRS, LIP, ENS Lyon : http: //www.ens-lyon.fr/~nschaban     

Enhanced shot noise in tunneling through a stack of coupled quantum dots

We have investigated the noise properties of the tunneling current through vertically coupled self-assembled InAs quantum dots. We observe super-Poissonian shot noise at low temperatures. For increased temperature this effect is suppressed. The super-Poissonian noise is explained by capacitive coupling between different stacks of quantum dots.     

External field induced switching of a tunneling current in coupled quantum dots

We investigated the tunneling current peculiarities in the system of two quantum dots that are coupled by means of the external field and are weakly connected to the electrodes in the presence of Coulomb correlations. It was found that tuning of the Rabi frequency induces fast multiple tunneling current switching and leads to the negative tunneling conductivity. Special role of multielectron states was demonstrated. Moreover we revealed conditions for bistable behavior of the tunneling current in the coupled quantum dots with Coulomb correlations.     

Coulomb blockade in molecular quantum dots

The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic electrodes via potential barriers. Based on this model, we calculate nonlinear transport characteristics (conductance-voltage and current-voltage dependences) and compare them with the results obtained within a self-consistent field approach. It is shown that the shape of transport characteristics is determined by the combined effect of the electronic structure of molecular quantum dots and by the Coulomb blockade. In particular, the following phenomena are discussed in detail: the suppression of the current at higher voltages, the charging-induced rectification effect, the charging-generated changes of conductance gap and the temperature-induced as well as broadening-generated smoothing of current steps.     

Nonstationary effects in the system of coupled quantum dots influenced by Coulomb correlations

We investigate the time evolution of filling numbers of localized electrons in the system of two coupled single-level quantum dots (QDs) connected with the continuous-spectrum states in the presence of Coulomb interaction. We consider correlation functions of all orders for electrons in the QDs by decoupling higher-order correlations between localized and band electrons in the reservoir. We analyze different initial charge configurations and consider Coulomb correlations between localized electrons both within the dots and between the different dots. We reveal the presence of a dynamical charge trapping effect in the first QD in the situation where both dots are occupied at the initial instant. We also find an analytic solution for the time-dependent filling numbers of the localized electrons for a particular configuration of the dots.     

Coulomb oscillations in partially open quantum dots

We report tunneling measurements of the Coulomb blockade in a single quantum dot at zero magnetic field and dilution refrigerator temperatures with weak tunneling from the dot to one lead (the ‘closed’ lead, conductanceG_closed) and strong tunneling to the other lead (the ‘open’ lead, conductanceG_open). We observe suppression of the Coulomb oscillations withG_open≈2e²/h, and then see the oscillations return forG_open>2e²/h. The oscillations show a strikingly lower threshold temperature atG_open≈2e²/hthan for greater or lesserG_open.     

Weak Coulomb blockade effect in quantum dots

We develop the general nonequilibrium theory of transport through a quantum dot, including Coulomb blockade effects via a 1/N expansion, where N is the number of scattering channels. At lowest order we recover the Landauer formula for the current plus a self-consistent equation for the dot potential. We obtain the leading corrections and compare with earlier approaches. Finally, we show that to leading and to next leading order in 1/N there is no interaction correction to the weak localization, in contrast to previous theories, but consistent with experiments by Huibers et al. [Phys. Rev. Lett. 81, 1917 (1998)], where N=4.     

Excitons in coupled quantum dots

Properties of excitons in vertically coupled GaAs/AlGaAs quantum dots were investigated using the variational method within the envelope function and effective mass approximations. It was found that when the thickness of the spacer layer becomes less than about one exciton Bohr radius, both the exciton binding energy and the fundamental optical transition energy are reduced compared to those in isolated quantum dots. This is a result of increased space extension of exciton due to the penetration of carrier wave functions into the spacer layer and corresponding reduction in confinement energy which dominates over the Coulomb interaction between the electron and the hole.     

Single-dot spectroscopy via elastic single-electron tunneling through a pair of coupled quantum dots

We study the electronic structure of a single self-assembled InAs quantum dot by probing elastic single-electron tunneling through a single pair of weakly coupled dots. In the region below pinch-off voltage, the nonlinear threshold voltage behavior provides electronic addition energies exactly as the linear, Coulomb blockade oscillation does. By analyzing it, we identify the s and the p shell addition spectrum for up to six electrons in the single InAs dot, i.e., one of the coupled dots. The evolution of the shell addition spectrum with magnetic field provides Fock-Darwin spectra of the s and p shells.