Transport properties of superconducting and ferromagnetic hybrid structures

The following thesis is devoted to a theoretical description of superconducting and ferromagnetic hybrid systems, where nanostructures, as quantum dot molecules or metallic island single electron transistors are tunnel coupled to leads with the respective material property. The work is divided into three parts, presenting at first a general transport theory, which is then used to address the superconducting and ferromagnetic case. In the first part of the thesis a formally exact equation of motion for the reduced density matrix of the nanostructure is presented, accounting for the full information about the entanglement of the nanostructure and the leads. A systematic expansion of this equation in terms of the tunnel coupling allows to use it as a basis for the description of various transport regimes. The second part addresses the transport properties of superconducting hybrid systems. Firstly, in the sequential tunneling regime, the peculiarities arising from the superconducting leads and their influence on the transport characteristics are analyzed. Furthermore, we stress the possibility of finding subgap features stemming from thermally activated quasiparticles, which are opening new transport channels for temperatures comparable to the superconducting gap. Specifically, we demonstrate that they allow to observe excited system states even in the subgap transport. The experimental relevance of the predicted effects is demonstrated in the subsequent chapter, where we analyze a transport experiment of a carbon nanotube quantum dot coupled two superconducting niobium leads. We show how subgap spectroscopy of thermally excited quasiparticles can be done, proposing a particular useful method to determine the charge configuration from the transport characteristic. Finally, the intermediate coupling regime is addressed, where charge fluctuation processes significantly influence the transport characteristics. They lead to a self energy contribution in the transition rates, inducing correlation effects between the two leads, and also between many-body states of different particle number subspaces. In the non-interacting case we compare the dressed second order approximation (DSO) to the more advanced resonant tunneling approximation of Koenig et al., which in addition to the charge fluctuation processes accounts also for vertex corrections and is exact in this limit. An analytical comparison of the linear conductance allows to identify an additional spurious term in the DSO conductance formula. The requirement that the additional term is negligible compared to the exact one, generally sets the limits of applicability of the DSO approximation. The third part of the thesis is about the transport properties of ferromagnetic hybrid systems. In particular, we interpret the transport properties of nanoconstrictions in the diluted magnetic semiconductor (Ga,Mn)As. The transport behavior of these systems is governed by the so called Coulomb blockade anisotropic magneto resistance, which is leading to differential conductance stability diagrams reminiscent of the transport through metallic islands. A peculiarity of the investigated devices is a transport gap opening at some charge degeneracy points. To account for these effect, a transport theory is derived treating explicitly an energy dependent density of states in the metallic islands.