Resonance approximation and charge loading/unloading in adiabatic quantum pumping

TL;DR

This paper analyzes how resonant transmission influences charge transfer in adiabatic quantum pumping, providing a quantitative model for electron exchange during resonance crossings using Green functions and the Breit-Wigner approximation.

Contribution

It introduces a detailed quantitative framework for understanding charge loading/unloading in quantum dots during adiabatic pumping, emphasizing resonance effects and approximate Green function expressions.

Findings

Charge exchange per resonance is related to lead coupling strengths.

Quantized charge transfer occurs when a resonance is dominated by a single lead.

Fractional charges can be derived from transmission peaks.

Abstract

Quantum pumping through mesoscopic quantum dots is known to be enhanced by resonant transmission. The pumped charge is close to an integer number of electrons when the pumping contour surrounds a resonance, but the transmission remains small on the contour. For non-interacting electrons, we give a quantitative account of the detailed exchange of electrons between the dot and the leads (to the electron reservoirs) during a pumping cycle. Near isolated distinct resonances, we use approximate Breit-Wigner expressions for the dot's Green function to discuss the loading/unloading picture of the pumping: the fractional charge exchanged between the dot and each lead through a single resonance point is related to the relative couplings of the dot and the leads at this resonance. If each resonance point along the pumping contour is dominated by the coupling to a single lead (which also implies a very small transmission), then the crossing of each such resonance results in a single electron exchange between the dot and that lead, ending up with a net quantized charge. When the resonance approximation is valid, the fractional charges can also be extracted from the peaks of the transmissions between the various leads.