Estimating ground-state properties of quantum dot arrays using a local Thomas-Fermi-Dirac approximation

An exactly solvable local Thomas-Fermi-Dirac approximation is applied to the calculation of the ground-state density of three-dimensional quantum dot arrays, where we give estimates to properties like total energy, chemical potential, and differential capacitance. Numeric examples are calculated for pairs of quantum dots using a Gaussian confining potential. The computational complexity of the present method is linear in the number of electrons and centers of the system.     

Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

In this article we study the impact of the spin-orbit interaction on the electron quantum confinement for narrow gap semiconductor quantum dots. The model formulation includes: (1) the effective one-band Hamiltonian approximation; (2) the position- and energy-dependent quasi-particle effective mass approximation; (3) the finite hard wall confinement potential; and (4) the spin-dependent Ben Daniel-Duke boundary conditions. The Hartree-Fock approximation is also utilized for evaluating the characteristics of a two-electron quantum dot system. In our calculation, we describe the spin-orbit interaction which comes from both the spin-dependent boundary conditions and the Rashba term (for two-electron quantum dot system). It can significantly modify the electron energy spectrum for InAs semiconductor quantum dots built in the GaAs matrix. The energy state spin-splitting is strongly dependent on the dot size and reaches an experimentally measurable magnitude for relatively small dots. In addition, we have found the Coulomb interaction and the spin-splitting are suppressed in quantum dots with small height. Received 15 May 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

Low-energy spectrum and finite temperature properties of quantum rings

Recently it was demonstrated that the rotational and vibrational spectra of quantum rings containing few electrons can be described quantitatively by an effective spin-Hamiltonian combined with rigid center-of-mass rotation and internal vibrations of localized electrons. We use this model Hamiltonian to study the quantum rings at finite temperatures and in presence of a nonzero magnetic field. Total spin, angular momentum and pair correlation show similar phase diagram which can be understood with help of the rotational spectrum of the ring. Received 18 January 2002 Published online 13 August 2002     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Electronic structure of three-dimensional quantum dots

We study the electronic structure of three-dimensional quantum dots using the Hartree-Fock approximation. The confining potential of the electrons in the quantum dot is assumed to be spatially isotropic and harmonic. For up to 40 interacting electrons the ground-state energies and ground-state wavefunctions are calculated at various interaction strengths. The quadrupole moments and electron densities in the quantum dot are computed. Hund's rule is confirmed and a shell structure is identified via the addition energies and the quadrupole moments. While most of the shell structure can be understood on the basis of the unperturbed non-interacting problem, the interplay of an avoided crossing and the Coulomb interaction results in an unexpected closed shell for 19 electrons. Received 5 November 2001 / Received in final form 12 November 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: vorrath@physnet.uni-hamburg.de     

Magnetic interaction between coupled quantum dots

We study the magnetic coupling in artificial molecules composed of two and four laterally coupled quantum dots. The electronic ground-state configurations of such systems are determined by applying current spin density functional theory which allows to include effects of magnetic fields. While the ground-state of a two-dot molecule with strong enough inter-dot coupling tends to be antiferromagnetic with respect to the spins of the single dot components, we find that a square lattice of four dots has a ferromagnetic ground state. Received 17 February 1999 and Received in final form 1 June 1999     

Signature of Kondo effect in silicon quantum dots

We report observation of the Kondo effect in the Coulomb blockade oscillations of an impurity quantum dot (IQD). This IQD is formed in the channel of a 100 nm gate length Silicon MOSFET. The quantitative analysis of the anomalous temperature and voltage dependence for the drain-source current over a series of Coulomb blockade oscillations is performed. It strongly supports the Kondo explanation for the conductance behavior at very low temperature in this standard microelectronics device. Received 13 November 2001 and Received in final form 18 February 2002     

Magnetic properties and spin waves of bilayer magnets in a uniform field

The two-layer square lattice quantum antiferromagnet with spins 12 shows a zero-field magnetic order-disorder transition at a critical ratio of the inter-plane to intra-plane couplings. Adding a uniform magnetic field tunes the system to canted antiferromagnetism and eventually to a fully polarized state; similar behavior occurs for ferromagnetic intra-plane coupling. Based on a bond operator spin representation, we propose an approximate ground state wavefunction which consistently covers all phases by means of a unitary transformation. The excitations can be efficiently described as independent bosons; in the antiferromagnetic phase these reduce to the well-known spin waves, whereas they describe gapped spin-1 excitations in the singlet phase. We compute the spectra of these excitations as well as the magnetizations throughout the whole phase diagram. Received 23 April 2001     

Floating Wigner molecules and possible phase transitions in quantum dots

A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or translational symmetry of the underlying jellium background. We study properties of a floating Wigner molecule in few-electron spin-polarized quantum dots, and show that the floating solid has the lower energy than the standard Wigner crystal with fixed lattice points. We also argue that internal rotational symmetry of individual dots can be broken in arrays of quantum dots, due to degenerate ground states and inter-dot Coulomb coupling. Received 12 September 2001 / Received in final form 24 April 2002 Published online 9 July 2002     

Analytic study of electron transmission through serial mesoscopic metallic rings

We investigate the electron transmission through a structure of serial mesoscopic metallic rings coupled to two external leads. A set of analytical expressions based on the quantum waveguide transport and the transfer matrix method are derived and used to discuss the effects of geometric configurations on transmission probabilities. It is found that in the contact ring case the existence of an applied magnetic flux is necessary to create transmission gaps, while in the non-contact ring case transmission gaps always appear irrespective of whether there is an applied magnetic flux or not. The transmissions for periodic rings with a defect ring and periodic rings built by two sorts of rings are also briefly studied. It is also found that the transmission periodicity with wave vector must be ensured by the commensurability of two characteristic lengths, i.e., of the half perimeter of a ring and the connecting wire between two adjacent rings. The special points of wave vector and magnetic flux which give rise to the transmission resonance and antiresonance are analyzed in detail.     

Coupling and dissociation in artificial molecules

We show that the spin-and-space unrestricted Hartree-Fock method, in conjunction with the companion step of the restoration of spin and space symmetries via Projection Techniques (when such symmetries are broken), is able to describe the full range of couplings in two-dimensional double quantum dots, from the strong-coupling regime exhibiting delocalized molecular orbitals to the weak-coupling and dissociation regimes associated with a Generalized Valence Bond combination of atomic-type orbitals localized on the individual dots. The weak-coupling regime is always accompanied by an antiferromagnetic ordering of the spins of the individual dots. The cases of dihydrogen (H₂, 2e) and dilithium (Li₂, 6e) quantum dot molecules are discussed in detail. Received 19 December 2000     

Polaronic effects in one-dimensional quantum antidot arrays

We study the effect of polaronic corrections arising from theelectron-longitudinal optical phonon interaction on the energyspectrum of a two-dimensional electron system with a one-dimensionalperiodic antidot array geometry created by a weak electrostaticmodulation potential, and subjected to a weak magnetic fieldmodulation as well as a uniform strong perpendicular staticmagnetic field. To incorporate the effects of electron-phononinteractions within the framework of Fröhlich polaron theory, wefirst apply a displaced-oscillator type unitary transformation todiagonalise the relevant Fröhlich Hamiltonian, and we thendetermine the parameters of this transformation together with theparameter included in the electronic trial wave function . On thebasis of this technique, it has been shown that the polaroniccorrections have non-negligible effects on the electronic spectrumof a two-dimensional electron system with a quantum antidot array,since switching such an interaction results in shifting thedegeneracy restoring points of Landau levels wherein the flatbandcondition is fulfilled, thus suppressing the Weiss oscillations.     

Investigation of excitation energies and Hund's rule in open shell quantum dots by diffusion Monte Carlo

We use diffusion Monte Carlo to study the ground state, the low-lying excitation spectrum and the spin densities of circular quantum dots with parabolic radial potentials containing N = 16 and N = 24 electrons, each having four open-shell electrons and compare the results to those obtained from Hartree-Fock (HF) and density functional local spin density approximation (LSDA) calculations. We find that Hund's first rule is obeyed in both cases and that neither HF nor LSDA correctly predict the ordering of the energy levels. Received 20 November 2001 and Received in final form 20 February 2002 Published online 6 June 2002     

Polarization dependence of emission spectra of multiexcitons in self-assembled quantum dots

We have investigated the polarization dependence of the emission spectra of p-shell multiexcitons of a quantum dot when the single particle level spacing is larger than the characteristic energy of the Coulomb interactions. We find that there are many degenerate multiexciton states. The emission intensities depend on the number of degenerate initial and final states of the optical transitions. However, unlike the transition energies, they are essentially independent of the strength of the Coulomb interactions. In the presence of electron-hole symmetry the independence is exact.     

Two-dimensional Thomas-Fermi parabolic quantum dot in a weak magnetic field

The Thomas-Fermi equation, in conjunction with the Poisson equation is solved exactly for the problem of the two-dimensional circular parabolic quantum dot in the presence of a weak magnetic field, in the framework of the local spin-density approximation. The total energy, chemical potential, differential capacitance, degree of polarization, and diamagnetic susceptibility were calculated. Asymptotic solutions were obtained for the limits of strong and weak confinement. Received 19 February 1999 and Received in final form 26 July 1999     

Characteristics of transmission of electrons in a quantum wire tangentially attached to a superconductor ring threaded by magnetic flux

We present numerical investigations of the transmission properties of electrons in a normal quantum wire tangentially attached to a superconductor ring threaded by magnetic flux. A point scatterer with a δ -function potential is placed at node to model scattering effect. We find that the transmission characteristics of electrons in this structure strongly depend on the normal or superconducting state of the ring. The transmission probability as a function of the energy of incident electrons, in the case of a superconductor ring threaded by one quantum magnetic flux, emerges one deep dip, imposed upon the first broad bump in spectrum. This intrinsic conductance dip originates from the superconductor state of the ring. When increasing the magnetic flux from one quantum magnetic flux to two, the spectrum shifts toward higher energy region in the whole. This conductance dip accordingly shifts and appears in the second bump. In the presence of a point-scatterer at the node, the spectrum is substantially modified. Based on the condition of the formation of the standing wave functions in the ring and the broken of the time-reserve symmetry of Schr?dinger equation after switching magnetic flux, the characteristics of transmission of electrons in this structure can be well understood. Received 6 November 2001     

Competition in the carrier capture between InGaAs/AlGaAs quantum dots and deep point defects

The presence of an extrinsic photoluminescence (PL) band peaked at 1.356 eV at low temperature is observed, on a large number of self-assembled InAs and In_0.5Ga_0.5As quantum dot (QD) structures, when exciting just below the GaAs absorption edge. A detailed optical characterization allows us to attribute the 1.356 eV PL band to the radiative transition between the conduction band and the doubly ionized Cu _Ga acceptor in GaAs. A striking common feature is observed in all investigated samples, namely a resonant quenching of the QD-PL when exciting on the excited level of this deep defect. Moreover, the photoluminescence excitation (PLE) spectrum of the 1.356 eV emission turns out to be almost specular to the QD PLE. This correlation between the PL efficiency of the QDs and the Cu centers evidences a competition in the carrier capture arising from a resonant coupling between the excited level of the defect and the electronic states of the wetting layer on which the QDs nucleate. The estimated Cu concentration is compatible with a contamination during the epitaxial growth. Received 13 November 2001 / Received in final form 28 May 2002 Published online 19 July 2002     

Shape dependent electronic structure and exciton dynamics in small In(Ga)As quantum dots

We present a study of the primary optical transitions and recombination dynamics in InGaAs self-assembled quantum nanostructures with different shape. Starting from the same quantum dot seeding layer, and depending on the overgrowth conditions, these new nanostructures can be tailored in shape and are characterized by heights lower than 2 nm and base lengths around 100 nm. The geometrical shape strongly influences the electronic and optical properties of these nanostructuctures. We measure for them ground state optical transitions in the range 1.25–1.35 eV and varying energy splitting between their excited states. The temperature dependence of the exciton recombination dynamics is reported focusing on the intermediate temperature regime (before thermal escape begins to be important). In this range, an important increase of the effective photoluminescence decay time is observed and attributed to the state filling and exciton thermalization between excited and ground states. A rate equation model is also developed reproducing quite well the observed exciton dynamics.     

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. While for weak interaction it shows peak-like resonances, in the strong interaction regime it assumes a step-like behavior. In both cases the photo-transport provides precise informations about the quantized plasmon modes in the dot. Temperature and voltage dependences of the sideband peaks are treated in detail. Characteristic Luttinger liquid power laws are found. Received 23 October 2001