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

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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 ${I}_{\text{AB}}$ 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 ${I}_{\text{AB}}$ 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.