Adiabatic quantum pumping in normal-metal–insulator–superconductor junctions in a monolayer of graphene

We investigate adiabatic quantum pumping through a normal-metal–“insulator”–superconductor (NIS) junction in a monolayer of graphene. The pumped current is generated by periodic modulation of two gate voltages, applied to the insulating and superconducting regions, respectively. In the bilinear response regime and in the limit of a thin high insulating barrier, we find that the presence of the superconductor enhances the pumped current per mode by a factor of 4 at resonance. Compared to the pumped current in an analogous semiconductor NIS junction, the resonances have a $\pi /2$ phase difference. We also predict experimentally distinguishable differences between the pumped current and the tunneling conductance in graphene NIS junctions.

Figure 1

(a) Sketch of the graphene NIS junction. The variable gate voltage $V_0$ creates the insulating barrier (I) of length $d$ and the gate voltage $U_0$ is applied to the superconducting electrode (S). (b) Schematic of the energy levels in the three regions. (c) The area enclosed in the $(U_0,V_0)$ parameter space during one pumping cycle.

Figure 2

(a) The pumped current $I_g^{\mathit{\text{NIS}}}$ [Eq. (7)] as a function of the potential barrier strength $\chi$ in a graphene (g) NIS junction. (b) The analogous pumped current $I_{sc}^{\mathit{\text{NIS}}}$ [Eq. (10)] in a semiconductor (sc) NIS junction, where $\sqrt{2m{E}_F}d/\hslash =10$.

Figure 3

Ratio of the pumped current (left) and the conductance (right) of the NIS junction and the NIN junction in graphene versus $\chi$ for $\epsilon =0$ and $U_0=0$.