Daniela Pfannkuche

Theory of quantum dot helium

Abstract The competition between the Coulomb interaction and the binding forces due to the confinement and the magnetic field induces transitions of the ground state of quantum dots with few electrons. We demonstrate that for quantum dot helium these transitions occur between states with differently strong correlations between the electrons. By the response of quantum dot helium to far infrared radiation we exemplify that a proper treatment of the correlation effects may be essential for a correct interpretation of experimental data on quantum dots with few electrons.

Selection rules for transport excitation spectroscopy of few-electron quantum dots

Tunneling of electrons traversing a few-electron quantum dot is strongly influenced by the Coulomb interaction leading to Coulomb blockade effects and single-electron tunneling. We present calculations which demonstrate that correlations between the electrons cause a strong suppression of most of the energetically allowed tunneling processes involving excited dot states. The excitation of center-of-mass modes, in contrast, is unaffected by the Coulomb interaction. Therefore, channels connected to these modes dominate the excitation spectra in transport measurements.

Hofstadter-type energy spectra in lateral superlattices defined by periodic magnetic and electrostatic fields.

We calculate the energy spectrum of an electron moving in a two-dimensional lattice which is defined by an electric potential and an applied perpendicular magnetic field modulated by a periodic surface magnetization. The spatial direction of this magnetization introduces complex phases into the Fourier coefficients of the magnetic field. We investigate the effect of the relative phases between electric and magnetic modulation on band width and internal structure of the Landau levels.

Far-infrared response of quantum dots: From few electron excitations to magnetoplasmons

Abstract We study the far-infrared (FIR) response of quantum dots with a variable number Ns of electrons and a non-parabolic confinement in a magnetic field B. For few electrons we compare the results of a Hartree (H) and a Hartree-Fock (HF) approach with those obtained by an exact diagonalization of the few-particle Hamiltonian. A good qualitative agreement is found between the HF approximation and the exact calculation. The resonance spectra are fingerprints of the ground state of the electron system and depend therefore strongly on Ns and B. With an increasing number of electrons, the H- and the HF-calculations show new features evolving in the FIR spectra. These features resemble the non-local mode coupling effects observed in the magnetoplasmon dispersion of two- and one-dimensional systems marking the transition to a quasi-classical hydrodynamic behaviour.

Electron interactions, classical integrability, and level statistics in quantum dots

Abstract The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple system is made strongly non-integrable in the classical regime by the introduction of particle interactions. In particular, we present a two-particle classical system contained in a d -dimensional billiard with hard walls. Similarly, a corresponding two-dimensional quantum dot problem with three particles is shown to have interesting spectral properties as function of the interaction strength and applied magnetic fields.

Magnetoresistance oscillations of a 2DEG in a weak lateral superlattice: manifestation of “Hofstacker's butterfly”

Abstract The resistance oscillations of a two-dimensional electron gas subject to a weak periodic modulation in both lateral directions are calculated as a function of the applied perpendicular magnetic field B . The calculation is based on a quantum-mechanical picture taking consistently into account the effect of the lateral superlattice on the energy spectrum and the effect of randomly distributed impurities on collision broadening and transport scattering rate. The superlattice potential splits each Landau level into a complicated energy spectrum, visualized by the famous self-similar “Hofstadter butterfly”. The effect of this peculiar energy spectrum on the magnetoresistance is investigated and provides the key for the understanding of recent experiments by D. Weiss. A. Menschig, K. von Klitzing and G. Weimann.

Few Electron Quantum Dots: Correlations and Collective Response

Spectroscopy is a widely used method to investigate the properties of atoms and molecules. Similarly, spectroscopy of quantum dots is supposed to reveal basic properties of these artificial atoms. We review results from calculations on few-electron quantum dots which relate the features of both, far-infrared and transport spectroscopy, to the basic properties of the few-particle wave functions. It turns out that both spectroscopical methods are dominated by the collective response of the electron system. While in the far-infrared spectroscopy this originates from the excitation mechanism, correlations in the electronic wave functions hinder the excitation of single particles in transport measurements, and thus favor collective modes.