Hybrid superconductor - quantum dot systems like carbon nanotubes
coupled to superconducting electrodes have attracted much attention in
recent years. They provide an almost ideal system where the interplay
between superconducting order and electronic correlations can be
studied in a controlled way. Such systems can be modeled by a
single-impurity Anderson model coupled to BCS superconducting leads.
We use diagrammatic perturbation techniques in the Coulomb interaction
to capture the relevant physical phenomena, particularly the effect of
the Coulomb interaction on the Andreev bound states present within the
superconducting gap. Results of the Hartree-Fock approximation,
second-order perturbation theory and the random phase approximation are
presented.