Quantum pumping of electrons by a moving modulated potential

Quantum pumping holds great potential for future applications in microtechnology and nanotechnology. Its main feature, which is the dissipationless charge transport, is theoretically possible via several different mechanisms. However, since no unambiguous verification has been experimentally demonstrated, the question of finding a viable mechanism for pumping remains open. Here, we study quantum pumping in an one dimensional electron waveguide with a single time-dependent barrier. The quantum pumping of electrons by using a potential barrier whose height and position are harmonically varied is analytically analyzed and by numerically solving the time-dependent Schrödinger equation. The pumped charge is analytically modeled by including two contributions in linear response theory. First, the scattering of electrons off a potential moving slowly through matter waves gives a contribution independent of the translational velocity of the potential. Second, Doppler-shifted scattering events give rise to a velocity dependent contribution, which is found in general to be small in comparison with the first one. The relative phase between the oscillations of the height and position is found to be the factor that determines to what extent either contribution is present.