Charge pumping and noise in a one-dimensional wire with weak electron-electron interactions

TL;DR

This paper studies adiabatic charge pumping in a one-dimensional wire with electron-electron interactions, deriving exact formulas for charge, noise, and Fano factor, and showing how interactions can enhance charge quantization and reduce noise.

Contribution

It provides analytical expressions for charge pumping, noise, and Fano factor in an interacting 1D wire, highlighting the role of interactions in optimizing charge quantization.

Findings

Near resonance, charge quantization approaches one electron per cycle.

Interactions improve charge quantization and reduce noise.

Large pumping amplitudes lead to vanishing charge and slower noise decrease.

Abstract

We consider the adiabatic pumping of charge through a mesoscopic one dimensional wire in the presence of electron-electron interactions. A two-delta potential model is used to describe the wire, which allows to obtain exactly the scattering matrix coefficients, which are renormalized by the interactions. Two periodic drives, shifted one from another, are applied at two locations of the wire in order to drive a current through it in the absence of bias. Analytical expressions are obtained for the pumped charge, current noise, and Fano factor in different regimes. This allows to explore pumping for the whole parameter range of pumping strengths. We show that, working close to a resonance is necessary to have a comfortable window of pumping amplitudes where charge quantization is close to the optimum value: a single electron charge is transferred in one cycle. Interactions can improve the situation, the charge $Q$ is closer to one electron charge and noise is reduced, following a $Q (1-Q)$ behavior, reminiscent of the reduction of noise in quantum wires by $T (1-T)$, where $T$ is the energy transmission coefficient. For large pumping amplitudes, this charge vanishes, noise also decreases but slower than the charge.