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

We consider the adiabatic pumping of charge through a mesoscopic one-dimensional wire in the presence of electron-electron interactions. A model of static potential in-between two-delta potentials is used to obtain exactly the scattering matrix elements, 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 us 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(e - Q) behavior, reminiscent of the reduction in noise in quantum wires by T(1 - 7), where T is the electron transmission coefficient. For large pumping amplitudes, this charge vanishes, and noise also decreases but slower than the charge.