Dynamic correlations induced by Coulomb interactions in coupled quantum dots

Time-dependent transport through two capacitively coupled quantum dots is studied in the framework of the generalized master equation. The Coulomb interaction is included within the exact diagonalization method. Each dot is connected to two leads at different times, such that a steady state is established in one dot before the coupling of the other dot to its leads. By appropriately tuning the bias windows on each dot we find that in the final steady state the transport may be suppressed or enhanced. These two cases are explained by the redistribution of charge on the many-body states built on both dots. We also predict and analyze the transient mutual charge sensing of the dots.

Figure 1

The system: a double dot and four leads.

Figure 2

(Color online) [(a) and (b)] The total currents in the leads for two bias windows: (a) ${\mu }_{\text{La}}={\mu }_{\text{Lb}}=4.25$, ${\mu }_{\text{Ra}}={\mu }_{\text{Rb}}=3.75$; (b) ${\mu }_{\text{La}}={\mu }_{\text{Lb}}=4.75$, ${\mu }_{\text{Ra}}={\mu }_{\text{Rb}}=4.35$. The insets show the bias windows and the MES chemical potentials. (c) Partial charge for the states involved in (a) (see text). (d) Total charge on each dot for (a) and (b).

Figure 3

(Color online) The partial currents carried by the two- and three-particle states in ${\text{QD}}_{\text{a}}$ and ${\text{QD}}_{\text{b}}$. (a) and (b) corresponding to Fig. 2a; (c) and (d) corresponding to Fig. 2b.

Figure 4

(Color online) [(a) and (b)] The contributions of the ground state (2,1) and of the excited states $\left(2,1_x\right)$ to the currents in the leads. ${\mu }_{\text{La}}={\mu }_{\text{Lb}}=4.75$, ${\mu }_{\text{Ra}}={\mu }_{\text{Rb}}=4.35$. ${\text{QD}}_{\text{b}}$ initially contains one electron. (c) The evolution of total charge in each dot. (d) Populations of the three-particle states.

Figure 5

(Color online) The effect of the bias applied on ${\text{QD}}_{\text{b}}$ on the currents $J_{\text{La},\text{Ra}}$. (a) ${\mu }_{\text{La}}={\mu }_{\text{Lb}}=4.25$, ${\mu }_{\text{Ra}}=3.75$. (b) ${\mu }_{\text{La}}={\mu }_{\text{Lb}}=4.75$, ${\mu }_{\text{Ra}}=4.35$. The same line type is used for the left and right currents.