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 = 4I N p , which should be compared with the result of conductance GNS = 2GN . Numerical results are also provided for the strong pumping regime showing interesting Andreev assisted pumping behaviour. 73.23.Ad,73.40.Gk,72.10.Bg,74.50.+r Typeset using REVTEX 1 Current can flow under zero bias when two system parameters of a nanostructure are varied in a cyclic fashion. The physics of this parametric electron pump has been analyzed by several authors [1,2]. Recently, it has been realized experimentally by switkes et. al. [3] confirming many of the theoretical predictions. So far, investigations on parametric pumping are focused on normal nanostructures. It will be interesting to study a hybrid structure where a superconducting lead is present. In the presence of normal conductor-superconductor (NS) interface, an incoming electron-like excitation can be Andreev reflected as a hole-like excitation. This current doubling effect gives rise to the relation for conductance GNS = 2GN for hybrid quantum point contacts and quantum dots at resonance [4]. For dirty NS contacts, de Jong and Beenakker [5] found that the shot noise at subgap voltages is also doubled with respect to its value in normal state which has been confirmed experimentally [6]. To further explore how does Andreev reflection modify quantum interference in the normal state, we have investigated the parametric pumping phenomenon in the presence of a superconducting lead. We find that due to quantum interference of the direct reflection and the multiple Andreev reflection, the pumped current is greatly enhanced. For quantum point contact and quantum dot at resonance, we obtained a relation for the pumped current, I p = 4I N p in the weak pumping regime. Numerical results are presented in the strong pumping regime showing interesting Andreev assisted pumping behaviour which can be verified experimentally. We consider a parametric pump which consists of a double barrier tunneling structure attached to a normal left lead and a superconducting right lead. The double barrier structure is modeled by potential V (x) = V1δ(x + a) + V2δ(x − a) where V1 = V0 + Vp sin(ωt) and V2 = V0+Vp sin(ωt+φ) and Vp is the pumping amplitude. We further apply a gate voltage vg to control the energy level of the structure. The units are fixed by setting h̄ = 2m = q = 1 in the following analysis [7]. At low frequencies, the adiabatic pumped current in the presence of superconducting leads is [1,8]