Superconducting pump manipulated by non-topologically quasi and topological interface states

We propose an adiabatic superconducting charge pump based on massive Dirac electrons. A superconductor is sandwiched in between two pumping sources, which are formed by introducing the time-dependent and out-of-phase staggered potentials in graphene as pumping parameters. The pump is shown to be characterized by not only the topological interface state (TIS) but also the non-topologically quasi interface state (QIS). Hereafter, our attention is focused on the pumping currents ILNR and ILAR from the normal and Andreev reflections, respectively, which predominate by making the electron energy reside in the effective energy gap. It is found that modulating the energy E, superconductor length L 0, and pumping source length LP results in the considerable variation of competitive behaviors between ILNR and ILAR . In particular, the reversal effect of current direction can be realized by tuning LP . More interestingly, the current-phase relationship exhibits the platform behaviors, which can be manipulated by LP and the pumping strength. All the above pumping properties are attributed to the adiabatic evolution of TIS and non-topologically QIS, particularly the conversion between each other is the crucial origin. We also obtain the quantized pumping current by adjusting LP and L 0, and present the corresponding qualitative explanation through the pumping contour circled by the two parameters. In addition, we discuss the features of pumping current based on the armchair graphene as well.