Pumping current in interacting helical liquids with two time-dependent magnetic scatterers

We study the pumping current of interacting helical liquids in the presence of two time-dependent magnetic impurities. Breaking time reversal (TR) symmetry is crucial for pumping, since backscattering is prohibited in the presence of TR invariant perturbations. We show that the pumping current has dc contributions due to scattering at a single impurity and an ac contribution which originates from quantum interference between the two impurities. Only if the ac frequencies are equal does the interference contribution affect the charge transport in the system. We also show that the interference term is strongly affected by the presence of electron interactions.