We have investigated in experiments and theory the effects of quantum coherence and interactions on the electron transport in nanostructures. Major successes include the demonstration of a room-temperature single-atom quantum-conductance switch and a circuit with two independent atomic transistors on one chip. We have studied transport through superconductor-ferromagnet heterostructures and found that the spin polarization decreases systematically with increasing contact diameter in the nm-range, and could attribute this effect to spin-orbit scattering in the contact region. The competition between the two types of order in the superconductor and the ferromagnet induces a superconducting triplet component, which explains the long-range proximity effect observed in recent experiments. For graphene, a material with fascinating properties and numerous prospective applications including carbon-based nano-electronics, we have calculated the conductivity with different types of impurities and explained other remarkable properties such as the absence of localization or the anomalous quantum Hall effect. We have investigated the role of spin-orbit interaction on quantum transport properties, as well as its effect on geometric phases and the resulting loss of electron spin coherence in quantum dots.
With the reduction of the size of electronic devices, interaction effects gain importance, and their study is an important part of the work in B2. Single-electron effects, dominated by the Coulomb interaction, show up in many weakly coupled nanoelectronic devices and molecular structures. Of current interest is the analysis of fluctuations and correlations, as well as of spin-resolved transport properties. Because of many fundamental (sometimes even pardoxi-cal) properties of entangled quantum states, as well as their use in quantum information processing and communication the interest in these states is very high. We suggested ways, exploiting the interaction effects, to entangle electron spins in different quantum dots and also to detect the entanglement. Studying one-dimensional disordered wires, where the single particle states are localized, we have demonstrated that interactions lead to a finite conductivity by destruction of quantum phase coherence. Similarly, we have shown how a finite bias voltage affects the quantum coherence of collective many-body states like the Kondo state, in that case reducing the conductance dramatically. In the still unexplored regime of strong interactions and finite bias voltage we obtained the first reliable results on the conductance using the numerical density-matrix renormalization method.