We analyse the full counting statistics of charge transfer through a Majorana bound state coupled to an STM tip and show how they can be used for an unambiguous identification of the bound state at the end of the wire. Additionally, we show how to ge
nerate Majorana bound states in a simple setup involving a ferromagnetic wire on a superconducting substrate.
We investigate the effects of Coulomb interaction on charge transfer through a quantum dot attached to a normal and a superconducting lead. While for voltages much larger than the gap we recover the usual result for normal conductors, for voltages mu
ch smaller than the gap superconducting correlations lead to a drastically different behavior. Especially, the usual charge doubling in the normal case is reflected in the occurence of quartets due to the onsite interaction.
We analyze the nonequilibrium dynamics and steady-state behavior of the two-terminal Anderson-Holstein model with a superconducting and a normal conducting lead. In the deep Kondo limit we develop an analytical description if no phonons are included
and a rate equation approach when phonons are present. Both cases are compared with the numerically exact diagrammatic Monte Carlo method obtaining a good agreement. For small voltages we find a pronounced enhancement of phonon sidebands due to the SC DOS.
We analyze the transport properties of a semiconductor based bilayer system under non-equilibrium conditions with special emphasis on the charge transfer statistics in the regime dominated by the exciton transport. We consider two different models. I
n one of them the transport occurs incoherently and is dominated by incoherent tunneling processes of individual excitons, while in the other system no disorder is present and transport processes are fully coherent. We find that the strength of cross correlations of currents in different layers is only insignificantly affected by the disorder and shows up similar behaviour in both systems. We discuss possible experimental realizations and make predictions for measurable quantities.
We study the interplay of superconducting and ferromagnetic correlations on charge transport in different geometries with a focus on both a quantum point contact as well as a quantum dot in the even and the odd state with and without spin-active scat
tering at the interface. In order to obtain a complete picture of the charge transport we calculate the full counting statistics in all cases and compare the results with experimental data. We show that spin-active scattering is an essential ingredient in the description of quantum point contacts. This holds also for quantum dots in an even charge state whereas it is strongly suppressed in a typical Kondo situation. We explain this feature by the strong asymmetry of the hybridisations with the quantum dot and show how Kondo peak splitting in a magnetic field can be used for spin filtering. For the quantum dot in the even state spin-active scattering allows for an explanation of the experimentally observed mini-gap feature.
