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

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