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Using a tight-binding model, we study one-parameter charge pumping in aone-dimensional system of non-interacting electrons. An oscillating potentialis applied at one site while a static potential is applied in a differentregion. Using Floquet scattering theory, we calculate the current up to secondorder in the oscillation amplitude and exactly in the oscillation frequency.For low frequency, the charge pumped per cycle is proportional to the frequencyand therefore vanishes in the adiabatic limit. If the static potential has abound state, we find that such a state has a significant effect on the pumpedcharge if the oscillating potential can excite the bound state into thecontinuum states or vice versa. Finally, we use the equation of motion for thedensity matrix to numerically compute the pumped current for any value of theamplitude and frequency. The numerical results confirm the unusual effect of abound state.

Nonadiabatic charge pumping in a one-dimensional system of noninteracting electrons by an oscillating potential