Classical and quantum mechanical behaviour in the low-field magneto-resistance in open quantum dots

Electronic transport through open dots has received much attention in recent years. An interesting aspect of this research focuses on the use of such low-dimensional systems to probe the connection between semi-classical physics and quantum mechanics. The purpose of this thesis is to understand the transport properties in a ballistic open quantum dot and dot arrays and to find clear evidence that, although the system is open, still discrete energy states are present. This is achieved by using a classical model calculation and performing DC and microwave experiments in the single open quantum dot and 3-dot array. By comparing the magneto-resistance obtained from the experiment with the calculated magneto-resistance the confining potential of the open quantum dot is found to be a soft parabolic potential. Peaks in the low-field magneto-resistance are attributed to backscattering events in the open dot. At certain magnetic fields classically calculated trajectories are obtained which are backscattered. As a consequence the magneto-resistance is raised. As a consequence of a stability analysis by calculating the Poincare section and estimating the Lyapunov exponent, the single open quantum dot is identified as an integrable system. In the case of an open quantum dot array the symmetry of the single dot is broken. Depending on the magnetic field, the open quantum dot array is characterized as an integrable system or a nonintegrable system with mixed phase space. The mixed phase space exists of chaotic and quasi-periodic trajectories. The quasi-periodic trajectories are attributed to Kolmogorov-Arnol'd-Moser (KAM) islands. These islands are completely decoupled from the surrounding and therefore classically inaccessible. We argue that the closed orbits which generate a series of delta functions in the density of states might be associated with discrete energy states in the open quantum dot. To search for discrete energy states in the open quantum dot microwave irradiation is used. In particular, the peak in the magneto-resistance at B∼0.2 T, which is attributed to a backscattering event, is investigated. The observed frequency dependence of the peak is attributed to a transition from an allowed energy state to another allowed energy state. Therefore, the backscattering peak is reduced and the transmission through the dot is enhanced due to the microwave irradiation. This quantum-mechanical consideration is analogue to the classical description with backscattered and transmitted trajectories. The backscattered trajectories correspond to a gap in the energy spectrum, i.e. the density of state is zero. The obtained results from the classical model calculation and the experiment show that, although the system is open, still discrete energy states are present. (author)