Andreev interference in adiabatic pumping

Within the scattering approach, we develop a model for adiabatic quantum pumping in hybrid normal-superconductor systems where several superconducting leads are present. This is exploited to study Andreev-interference effects on adiabatically pumped charge in a three-arm beam splitter attached to one normal and two superconducting leads with different phases of the order parameters. We derive expressions for the pumped charge through the normal lead for different parameters for the scattering region, and elucidate the effects due to Andreev interference. In contrast to what happens for voltage-driven transport, Andreev interference does not yield, in general, a pumped current which is a symmetric function of the superconducting-phase difference.