Probing the Shape of Quantum Dots with Magnetic Fields

A tool for the identification of the shape of quantum dots is developed. By preparing a two-electron quantum dot, the response of the low-lying excited states to a homogeneous magnetic field, i.e. their spin and parity oscillations, is studied for a large variety of dot shapes. For any geometric configuration of the confinement we encounter characteristic spin singlet - triplet crossovers. The magnetization is shown to be a complementary tool for probing the shape of the dot.Comment: 11 pages, 4 figure

Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition

We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions when the normal derivative of {\psi} vanishes on an irregular closed curve. Unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as opposed to earlier schemes where the perturbation parameter is an artificial one. The efficacy of the proposed scheme is gauged by calculating the eigenvalues for elliptical and supercircular boundaries and comparing with the results obtained numerically. We also present a simple and interesting semi-empirical formula, determining the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the Neumann condition for a supercircular boundary. A comparison of the eigenspectrum for several low-lying modes obtained by employing the formula with the corresponding numerical estimates shows good agreement for a wide range of the supercircular exponent.Comment: 26 pages, 12 figure

Two-electron anisotropic quantum dots

A detailed investigation of the effects of interaction and anisotropy in the electronic structure and dynamical properties of two-electron quantum dots is performed. It is shown that a small anisotropy eliminates the shell structure and represents a rapid path to chaos. The level clustering, energy gaps and the accompanying classical dynamics are investigated among others for the frequency ratios ωy : ωx = n : 1. For n = 2 the system is integrable and the corresponding constant of motion is constructed. The eigenstates pair in singlet-triplet degenerate subspaces. In between these ratios avoided crossings dominate the spectra. For very strong anisotropies, the classical dot comprises the complete regime from softly interacting to kicked oscillators. Its quantum counterpart shows remarkable spectral patterns

Probing the shape of quantum dots with magnetic fields

A tool for the identification of the shape of quantum dots is developed. By preparing a two-electron quantum dot, the response of the low-lying excited states to a homogeneous magnetic field, i.e., their spin and parity oscillations, is studied for a large variety of dot shapes. For any geometric configuration of the confinement we encounter characteristic spin singlet-triplet crossovers. The magnetization is shown to be a complementary tool for probing the shape of the dot

Effects of anisotropy and magnetic fields on two-electron parabolic quantum dots

An investigation of the combined effects due to the electronic interaction, anisotropy and the magnetic field interaction for two-electron quantum dots with harmonic confinement is performed. The electronic level structure and the dynamics of the dot are studied with varying field strength and anisotropy. The magnetization is derived for the complete deformation regime covering the regime of weak to strong fields. The cases without and with inclusion of the spin Zeeman interaction for a GaAs semiconductor are considered. The classical dynamics of the interacting electrons is studied and exhibits near integrability for field strengths leading to ratios ω1:ω2 = 1:n