Effects of interaction on an adiabatic quantum electron pump

TL;DR

This paper investigates how electron-electron interactions influence charge pumping in an adiabatic quantum system, showing that interactions lead to quantized charge transfer at low temperatures and relate to transmission properties.

Contribution

It introduces a renormalisation group approach to analyze interaction effects on quantum charge pumps, demonstrating quantization and scaling behaviors.

Findings

Pumped charge approaches a quantized value at low temperatures or large system sizes.

Maximum pumped charge depends on the number of barriers, given by Q_max = n_b - 1.

Charge quantization relates to transmission maxima enclosed by the pumping contour.

Abstract

We study the effects of inter-electron interactions on the charge pumped through an adiabatic quantum electron pump. The pumping is through a system of barriers, whose heights are deformed adiabatically. (Weak) interaction effects are introduced through a renormalisation group flow of the scattering matrices and the pumped charge is shown to {\it always} approach a quantised value at low temperatures or long length scales. The maximum value of the pumped charge is set by the number of barriers and is given by $Q_{\rm max} = n_b -1$. The correlation between the transmission and the charge pumped is studied by seeing how much of the transmission is enclosed by the pumping contour. The (integer) value of the pumped charge at low temperatures is determined by the number of transmission maxima enclosed by the pumping contour. The dissipation at finite temperatures leading to the non-quantised values of the pumped charge scales as a power law with the temperature ($Q-Q_{\rm int} \propto T^{2\alpha}$), or with the system size ($Q-Q_{\rm int} \propto L_s^{-2\alpha}$), where $\alpha$ is a measure of the interactions and vanishes at $T=0 ~(L_s=\infty)$. For a double barrier system, our result agrees with the quantisation of pumped charge seen in Luttinger liquids.