Enhancement of parametric pumping due to Andreev reflection

We report properties of parametric electron pumping in the presence of a superconducting lead. Due to a constructive interference between the direct reflection and the multiple Andreev reflection, the pumped current is greatly enhanced. For both quantum point contacts and double barrier structures at resonance, we obtain exact solutions in the weak pumping regime showing that $I_p^{NS} = 4 I_p^N$, which should be compared with the result of conductance $G_{NS} = 2G_N$. Numerical results are also provided for the strong pumping regime showing interesting Andreev assisted pumping behaviour.