Coherent transport through interacting quantum dots

The present thesis is composed of four different works. All deal with coherent transport through interacting quantum dots, which are tunnel-coupled to external leads. There a two main motivations for the use of quantum dots. First, they are an ideal device to study the influence of strong Coulomb repulsion, and second, their discrete energy levels can easily be tuned by external gate electrodes to create different transport regimes. The expression of coherence includes a very wide range of physical correlations and, therefore, the four works are basically independent of each other. Before motivating and introducing the different works in more detail, we remark that in all works a diagrammatic real-time perturbation theory is used. The fermionic degrees of freedom of the leads are traced out and the elements of the resulting reduced density matrix can be treated explicitly by means of a generalized master equation. How this equation is solved, depends on the details of the problem under consideration. In the first of the four works adiabatic pumping through an Aharonov-Bohm interferometer with a quantum dot embedded in each of the two arms is studied. In adiabatic pumping transport is generated by varying two system parameters periodically in time. We consider the two dot levels to be these two pumping parameters. Since they are located in different arms of the interferometer, pumping is a quantum mechanical effect purely relying on coherent superpositions of the dot states. It is very challenging to identify a quantum pumping mechanism in experiments, because a capacitive coupling of the gate electrodes to the leads may yield an undesired AC bias voltage, which is rectified by a time dependent conductance. Therefore, distinguishing features of these two transport mechanisms are required. We find that the dependence on the magnetic field is the key feature. While the pumped charge is an odd function of the magnetic flux, the rectified current is even, at least in the linear-conductance regime. The second work deals with the ratio of coherent processes in transport through quantum dots. To this end, a quantum dot is embedded in one of the arms of an Aharonov-Bohm interferometer. In former theoretical as well as experimental works it has been observed that an important source of decoherence are cotunneling processes that flip the dot's spin. In order to elucidate the role of spin in more detail, we assume one of the leads to be ferromagnetic and the other one to be normal. The main motivations of our work are the two questions: (1) What fraction of the total current through a single-level quantum dot weakly coupled to the electrodes is coherent? (2) How and under which circumstances can this fraction be extracted from a current measurement in an Aharonov-Bohm setup? The measurable quantity in such an experiment is the magnetic-flux dependent ratio of the total current. It turns out that the answers of the two questions strongly depend on the dot level position, the polarization of the ferromagnet, and the transport direction. Especially the flux-dependent and the coherent ratios are not necessarily the same. The main motivation of the third work is to identify crossed Andreev reflection in quantum dots, that is, a Cooper pair splits into two single electrons, which are transferred into different quantum dots in one coherent process. We consider a setup, where two quantum dots are tunnel coupled to the same superconductor and each dot is additionally coupled to a normal conductor. In previous works a bias voltage has been applied between the superconductor and the normal conductors. Then, three processes sustain transport. Beside crossed Andreev reflection also local Andreev reflection, where both electrons of the Cooper pair tunnel into the same dot, and single-particle tunneling occur. This complicates the identification of crossed Andreev reflection. Therefore, we propose the transport mechanism of adiabatic pumping in the absence of any bias voltage. The two pumping parameters are the energy levels of the two dots. Since they are spatially separated and a finite pumping signal requires two pumping parameters, a net transport relies on nonlocality. As a consequence local Andreev reflection does not contribute to the pumping current. In order to clearly identify crossed Andreev reflection it has to be distinguished from single-particle tunneling arising due to superpositions of the states of the two dots. We find that the dependence of the current on the average dot level position as well as the symmetry of the coupling strengths between dots and normal conductors clearly distinguishes the two processes from each other. This is an important advantage of the pumping current, for example, in comparison to the linear conductance. Finally, we focus on the AC Josephson transport through a strongly interacting quantum dot. To this end, we extent a diagrammatic theory on the DC Josephson transport to the time dependent case taking into account the Coulomb repulsion nonperturbatively. This general formalism is applied to a three-terminal device, where a quantum dot is tunnel coupled to a normal conductor and two superconductors with an infinite superconducting gap. Since the AC Josephson effect requires the presence of two superconductors, in lowest order of the perturbation expansion a finite AC signal between dot and superconductor S1 relies on the induction of superconducting correlations on the dot exclusively by superconductor S2. The main advantage of employing a normal conductor is that the average dot occupation can easily be tuned by the chemical potential of the normal conductor. Therefore, in the considered three-terminal device, in contrast to conventional Josephson junctions, not only the frequency but also the amplitude of the AC signal can be controlled by a DC bias voltage applied between the normal conductor and the two superconductors.