Quantum charge pumping through a superconducting double barrier structure in graphene

We consider the phenomenon of quantum charge pumping of electrons across a superconducting double barrier structure in graphene in the adiabatic limit. In this geometry, quantum charge pumping can be achieved by modulating the amplitudes (Δ1 and Δ2) of the gaps associated with the two superconducting strips. We show that the superconducting gaps give rise to a transmission resonance in the Δ1-Δ2 plane, resulting in a large value of pumped charge, when the pumping contour encloses the resonance. This is in sharp contrast to the case of charge pumping in a normal double barrier structure in graphene, where the pumped charge is very small, due to the phenomenon of Klein tunneling. We analyze the behavior of the pumped charge through the superconducting double barrier geometry as a function of the pumping strength and the phase difference between the two pumping parameters, for various angles of the incident electron