Transport and topological states in strongly correlated nanostructures

One of the most important technological inventions during the last century was the transistor, which has enabled the subsequent computational revolution. For future progress in this field two main aspects are of relevance. First, further shrinkage of transistor sizes will soon make quantum effects inevitably relevant. Related to this, the heat transport will also be of great interest as already today the cooling of the transistors is one of the main bottlenecks for further increase of computational speed. The second main aspect is to pave the way for computer architectures that no longer rely on the discrete charge degree of freedom as information carrier, but utilize the spin degree of freedom. This is closely connected with the goal of building a quantum computer, which utilizes quantum properties like entanglement to speed up certain applications beyond what would be possible with classical computer architectures. Throughout this thesis we will discuss how these aspects can be understood by studying transport through a quantum dot. A quantum dot is a strongly confined region, where only a few energy levels are effectively accessible with respect to transport through this region. We study how the heat flow through the quantum dot deviates from classical Joule heating and how the strong confinement effects are imprinted onto the heat flow through the system. Afterwards, we make a connection between the two main themes discussed prior by studying how such a quantum dot can be utilized to manipulate the spin flow through it. We especially focus here on the manipulation and readout of attached nano magnets. These nano magnets may serve as a building element for quantum computation. We also study the purely quantum computational aspects of strongly correlated systems by investigating how disorder and interactions interplay regarding the stability of the topological Majorana edge modes of the Kitaev chain