Adiabatic Quantum Pumping of Coherent Electrons

TL;DR

This paper reviews theoretical models of adiabatic quantum pumping in mesoscopic devices, highlighting how quantum interference and resonant transmission lead to quantized charge transfer per cycle.

Contribution

It derives a systematic expression for the pumped charge considering time-dependent scattering states, connecting quantum interference effects with quantized charge transfer.

Findings

Resonant transmission correlates with almost integer charge transfer.

The derived formulas extend the Landauer approach to adiabatic pumping.

Surface acoustic waves can effectively pump charge through quantum channels.

Abstract

We review recent theoretical calculations of charge transfer through mesoscopic devices in response to slowly-oscillating, spatially-confined, potentials. The discussion is restricted to non-interacting electrons, and emphasizes the role of quantum interference and resonant transmission in producing almost integer values (in units of the electronic charge $e$) of the charge transmitted per cycle, $Q$. The expression for the pumped charge is derived from a systematic expansion of the system scattering states in terms of the temporal derivatives of the instantaneous solutions. This yields the effect of the modulating potential on the Landauer formula for the conductance in response to a constant bias on one hand, and the corrections to the widely-used adiabatic-limit formula (in which the modulation frequency is smaller than any electronic relaxation rate) on the other hand. The expression for $Q$ is used in connection with simple models to exemplify the intimate relationship between resonant transmission through the mesoscopic device and almost integral values of $Q$, and to analyze the charge pumped by a surface acoustic wave coupled to a quantum channel by the piezoelectric effect. \keywords{interference in nanostructures, quantum pumping, surface acoustic waves, resonant transmission.