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

TL;DR

This paper investigates nonadiabatic charge pumping in a one-dimensional non-interacting electron system using Floquet theory and numerical methods, revealing the significant influence of bound states on pumped charge.

Contribution

It introduces a comprehensive analysis of nonadiabatic charge pumping with oscillating potentials, highlighting the role of bound states and providing exact and numerical results.

Findings

Charge pumped per cycle is proportional to frequency at low frequencies.

Bound states significantly affect the pumped charge when excited by oscillating potentials.

Numerical simulations confirm the impact of bound states on charge pumping.

Abstract

Using a tight-binding model, we study one-parameter charge pumping in a one-dimensional system of non-interacting 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.