Pumping through a quantum dot in the proximity of a superconductor

We study adiabatic pumping through a quantum dot tunnel-coupled to one normal and one superconducting lead. We generalize a formula which relates the pumped charge through a quantum dot with Coulomb interaction to the instantaneous local Green's function of the dot, to systems containing a superconducting lead. First, we apply this formula to the case of a non-interacting, single-level quantum dot in different temperature regimes and for different parameter choices, and we compare the results with the case of a system comprising only normal leads. Then we study the infinite-U Anderson model with a superconducting lead at zero temperature, and we discuss the effect of the proximity of the superconductor on the pumped charge.