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 $I_{\text{AB}}$ 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 $P\left(E\right)$ theory describing tunneling of interacting electrons.

Figure 1

The ring-shaped quantum dot structure under consideration.

Figure 2

Diagrammatic representations of different contributions originating from expansion of the effective action in powers of the central barrier transmissions: (a) second-order (AES) terms and [(b) and (c)] different fourth-order terms.

Figure 3

(Color online) The ratio $I_{\text{AB}}/I_{\text{AB}}^{\left(0\right)}$ versus temperature at different values of dimensionless conductance $g$.

Figure 4

(Color online) The ratio $I_{\text{AB}}/I_{\text{AB}}^{\left(0\right)}$ as a function of dimensionless conductance $g$ at $T=0$ and ${\tau }_D/{\tau }_{RC}=10$.

Figure 5

Diagrammatic representation for vertices ${\Gamma }_d\left({\mathbf{x}}_{\mathbf{1}},{\mathbf{x}}_{\mathbf{2}};\omega \right)$ and ${\Gamma }_c\left({\mathbf{x}}_{\mathbf{1}},{\mathbf{x}}_{\mathbf{2}};\omega \right)$ and for averages $X_d\left({\mathbf{x}}_{\mathbf{1}},{\mathbf{x}}_{\mathbf{2}};\epsilon \right)$ and $X_c\left({\mathbf{x}}_{\mathbf{1}},{\mathbf{x}}_{\mathbf{2}};\epsilon \right)$.

Figure 6

Diagrams which define the average $X_k\left({\mathbf{x}}_{\mathbf{1}},{\mathbf{x}}_{\mathbf{2}};\epsilon \right)$.