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

Pierre Devillard (1, 2) , Vladimir Gasparian (1, 3, 2) , Thierry Martin (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 CSUB - Department of Physics, Cal State Bakersfield

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.

Mots clés: mesoscopic physics; adiabatic; charge pumping; noise; electron interactions

Domaines: Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

Pierre Devillard, Vladimir Gasparian, Thierry Martin. Charge pumping and noise in a one-dimensional wire with weak electron-electron interactions. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2008, 78 (8), pp.085130. ⟨hal-00198739v2⟩