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The unique electronic band structure of graphene gives rise to remarkable properties when in contact with a superconducting electrode. In this thesis two main aspects of these junctions are analyzed: the induced superconducting proximity effect and the non-local transport properties in multi-terminal devices. For this purpose specific models are developed and studied using Green function techniques, which allow us to take into account the detailed microscopic structure of the graphene-superconductor interface. It is shown that these junctions are characterized by the appearance of bound states at subgap energies which are localized at the interface region. Furthermore it is shown that graphene-supercondutor-graphene junctions can be used to favor the splitting of Cooper pairs for the generation of non-locally entangled electron pairs. Finally, using similar techniques the thesis analyzes the transport properties of carbon nanotube devices coupled with superconducting electrodes and in graphene superlattices.

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Preface and outline.- Background and theoretical framework.- Green functions techniques for graphene layers with edges.- The graphene-superconductor interface. - Nonlocal transport in graphene.- Cooper pair beam splitters in double quantum dots.- Summary and conclusions.- Methodology: Green functions techniques.- Transport in superlattices on single layer graphene.- Scattering amplitudes at the graphene-superconductor interface.- Green functions techniques applied to carbon nanotubes.- Equation of motion approach to include interactions.

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Pablo Burset is a postdoctoral researcher at Wuerzburg University (Germany). He received his bachelor´s degree from Universidad Complutense Madrid and his Ph.D. from Universidad Autonoma Madrid, both in Physics. His theoretical research focuses on the quantum transport properties of graphene, carbon nanotubes and topological insulators when in electrical contact with superconducting electrodes.

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