Aharonov-Bohm oscillations in coupled quantum dots: Effect of electron-electron interactions

We theoretically analyze the effect of electron-electron interactions on Aharonov-Bohm (AB) current oscillations in ring-shaped systems with metallic quantum dots pierced by external magnetic field. We demonstrate that electron-electron interactions suppress the amplitude of AB oscillations I(AB) at all temperatures down to T=0, and we formulate quantitative predictions which can be verified in future experiments. We argue that the main physical reason for such interaction-induced suppression of I(AB) is electron dephasing, while Coulomb blockade effects remain insignificant in the case of metallic quantum dots considered here. We also emphasize a direct relation between our results and the so-called P(E) theory describing tunneling of interacting electrons.