Diagrammatic Perturbation Technique for a Quantum Dot Connected to Superconducting Leads

We study spectral properties of a quantum dot attached to two superconductors with nonzero phase difference. The system is described as a single-impurity Anderson model coupled to BCS superconducting leads. We utilize diagrammatic perturbation expansion in the Coulomb interaction to capture relevant physical phenomena, particularly the effect of the Coulomb interaction on the Andreev bound states present in the electronic spectrum. Results of the Hartree-Fock and the random phase approximations at zero temperature are presented.