Parametric pumping at finite frequency

Abstract

We report on a first principles theory for analyzing the parametric electron pump at a finite frequency. The pump is controlled by two pumping parameters with phase difference φ. In the zero frequency limit, our theory predicts the well known result that the pumped current is proportional to sin φ. For the more general situation of a finite frequency, our theory predicts a non-vanishing pumped current even when the two driving forces are in phase, in agreement with the recent experimental results. We present the physical mechanism behind the nonzero pumped current at φ = 0, which we found to be due to photon-assisted processes.73.23. Ad,73.40.Gk,72.10.Bg Parametric electron pump 1-7 is an interesting device which delivers a finite DC current to the outside world at zero bias potential, by cyclic variations of two device control parameters. Recently, an adiabatic quantum electron pump was reported in an open quantum dot where the pumping signal was produced in response to the cyclic deformation of the confining potential 2 . It was found that the pumping signal, V dot (φ), is sinusoidal in the phase difference φ between the two deforming potentials in the weak pumping regime, and it becomes non-sinusoidal in the strong pumping regime. The amplitude of the pumping signal increases linearly with the frequency of the deformation. Most notable, however, was the data 2 showing V dot (0) = 0 significantly at strong pumping, whereas V dot (π) ≈ 0 for all pumping strength. Even in the weaker pumping regime, small deviations from V dot (0) = 0 could already be seen 2 . The traditional and successful parametric pumping theory 3,4 , valid in the adiabatic regime and up to first order in frequency, requires two pumping parameters which traverse in a closed path in parameter space in each cyclic period and the pumping signal is proportional to the enclosed area by the path. Accordingly, if the two pumping parameters are in phase so that the enclosed area is zero, the pumping signal V dot (0) should vanish. It is extremely puzzling that the experimental data 2 consistently showed V dot (0) = 0, a fact which has not been understood so far, and, clearly, it calls for the development of a first principle theory going beyond the adiabatic regime and low frequencies.It is the purpose of this letter to present a theory for parametric pumping which is valid at finite frequency. Using this theory we investigate the frequency dependence of the pumping current I p (φ) = G dot V dot (φ) with G dot a constant, and it allows us to understand why it is possible to have a pumping signal even when the pumping forces are exactly in-phase. When frequency is low, our theory recovers the traditional results 3,4 . As the frequency increases, we predict a nonzero I p (0) which is a consequence of photon assisted processes, and our theory also predicts I p (π) ≈ 0. These results allows us to reach the conclusion that the experimental data 2 showing V dot (0) = 0 and V dot (π) ≈ 0, are generic nonlinear transport features of parametric pumps at fi...

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