Effects of interaction on an adiabatic quantum electron pump

Abstract

We study the effects of interelectron 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 always approach a quantized 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 ${Q}_{\mathrm{max}}={n}_{b}\ensuremath{-}1$. 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 extra dissipation at finite temperatures leading to the nonquantized values of the pumped charge scales as a power law with the temperature $(Q\ensuremath{-}{Q}_{\mathrm{int}}\ensuremath{\propto}{T}^{2\ensuremath{\alpha}})$, or with the system size $(Q\ensuremath{-}{Q}_{\mathrm{int}}\ensuremath{\propto}{L}_{W}^{\ensuremath{-}2\ensuremath{\alpha}})$, where $\ensuremath{\alpha}$ is a measure of the interactions, and vanishes at $T=0({L}_{W}=\ensuremath{\infty})$. For a double barrier system, our result agrees with the quantisation of pumped charge seen in Luttinger liquids.