Electronic structure and transport properties of quantum dots

Abstract

The subject of this paper are electronic properties of isolated quantum dots as well as transport properties of quantum dots coupled to two electronic reservoirs. Thereby special focus is put on the effects of Coulomb interaction and possible correlations in the quantum dot states. First, the regime of sequential tunneling to the reservoirs is investigated. It is shown that in case degenerate states participate in transport, the resonance positions in the differential conductance generally depend on temperature and the degree of degeneracy. This effect can be used to directly probe degeneracies in a quantum dot spectrum. A further effect, characteristic for sequential tunneling events, is the complete blocking of individual channels for transport. A generalisation of the well known spin blockade is found for correlated dot states transitions through which are not directly spin-forbidden. In the second part, the electronic structure of spherical quantum dots is calculated. In order to account for correlation effects, the few-particle Schrödinger equation is solved by an exact diagonalization procedure. The calculated electronic structure compares to experimental findings obtained on colloidal semiconductor nanocrystals by Scanning Tunneling Spectroscopy. It is found that the electric field induced by the tunneling tip is gives rise to a Stark effect which can break the spherical symmetry of the electronic ground state density which is in agreement with wave-function mapping experiments. The symmetry breaking depends on the competition between exchange energy and the Stark energy. Moreover, a systematic dependence on particle number is found for the excitation energies of optical transitions which explains recent experimental findings on self-organized quantum dots. In the last part, co-tunneling in the Coulomb blockade regime is studied. For this end the tunneling current is calculated up to the forth order perturbation theory in the tunnel coupling by a real-time Green's function approach for the non-equilibrium case. The differential conductance calculated for a quantum dot containing up to two interacting electrons shows complex signatures of the excitation spectrum which are explained by a combination of co-tunneling and sequential tunneling processes. Thereby the calculations show a peak structure within the Coulomb blockade regime which has also been observed in experiment.