Transport through side-coupled double quantum dots: From weak to strong interdot coupling

We report low-temperature transport measurements through a double-quantum-dot device in a configuration where one of the quantum dots is coupled directly to the source and drain electrodes, and a second (side-coupled) quantum dot interacts electrostatically and via tunneling to the first one. As the interdot tunneling coupling increases, a crossover from weak to strong interdot tunneling is observed in the charge stability diagrams that present a complex pattern with mergings and apparent crossings of Coulomb blockade peaks. While the weak-coupling regime can be understood by considering a single level on each dot, in the intermediate- and strong-coupling regimes, the multilevel nature of the quantum dots needs to be taken into account. Surprisingly, both in the strong- and weak-coupling regimes, the double-quantum-dot states are mainly localized on each dot for most values of the parameters. Only in an intermediate-coupling regime does the device present a single dotlike molecular behavior as the molecular wave functions weight is evenly distributed between the quantum dots. At temperatures larger than the interdot coupling energy scale, a loss of coherence of the molecular states is observed.

Figure 1

(a) SEM image of the device. The red gates are pushed far in the pinch-off regime. The interdot tunnel coupling is controlled via the yellow gates. All Ohmic contacts are set to the same potential ($V_0$) except the top small-dot lead where the bias voltage $V_{\mathrm{bias}}$ is applied. The energies and occupancies of each dot are changed with the use of the green plunger gates. (b) Weak-coupling stability diagram (30 mK). The differential conductance (color scale) is plotted versus the small-dot and large-dot plunger gate voltages $V_{gd}$ and $V_{gD}$, respectively.

Figure 2

(a), (b) Low-temperature (30 mK) stability diagrams (2D and 3D) with a coupling between the dots stronger than in Fig. 1b. At such low temperatures, a complex conductance modulation pattern is found.

Figure 3

(a) Low-temperature stability diagram (30 mK) corresponding to a larger scan than previously shown. The white dashed rectangle corresponds to the gate scan seen in Figs. 1b and 2. Due to crosstalk between the plunger gates and the middle gates defining the interdot tunneling, two different regimes can be identified in the diagram. As tunneling increases, we go from a two-level system behavior to a multilevel system behavior. (b) Color plot of the high-temperature stability diagram monitored at 500 mK in the same plunger gate voltages range made initially [Fig. 1b]. (c) Three-dimensional representation of the above diagram. At high temperature, the conductance follows a periodic pattern. One can clearly identify the addition of electrons in one quantum dot or the other.

Figure 4

Three-dimensional representation of the calculated conductance for a double quantum dot with $3\times 3$ levels, including a gate voltage dependence of $t_{dD}=0.015$ meV $+0.01$ meV$({\mathcal{N}}_D+{\mathcal{N}}_d/3)$ and $k_{\mathrm{B}}T=0.0075$ meV.

Figure 5

Calculated conductance maps for a double quantum dot with $3\times 3$ levels, including a gate voltage dependence of $t_{dD}=0.015\mathrm{meV}+0.01\mathrm{meV}({\mathcal{N}}_D+{\mathcal{N}}_d/3)$ and different values of the temperature: (a) $k_{\mathrm{B}}T=0.0075\mathrm{meV}$, (b) $k_{\mathrm{B}}T=0.02\mathrm{meV}$, (c) $k_{\mathrm{B}}T=0.04\mathrm{meV}$, and (d) $k_{B}T=0.05\mathrm{meV}$. Other parameters are $U_d=0.7\mathrm{meV}$, $U_D=0.25\mathrm{meV}$, $U_{dD}=0.1\mathrm{meV}$, ${\Delta }_d=0.15\mathrm{meV}$, and ${\Delta }_D=0.02\mathrm{meV}$.

Figure 6

Calculated conductance maps for a double quantum dot with $3\times 3$ levels, for different values of the interdot hopping $t_{dD}$ (a) $0\mathrm{meV}$, (b) $0.02\mathrm{meV}$, (c) $0.04\mathrm{meV}$, (d) $0.05\mathrm{meV}$, and (e) $0.08\mathrm{meV}$. Other parameters are $U_d=0.7\mathrm{meV}$, $U_D=0.25\mathrm{meV}$, $U_{dD}=0.1\mathrm{meV}$, ${\Delta }_d=0.15\mathrm{meV}$, and ${\Delta }_D=0.02\mathrm{meV}$. The high $t_{dD}$ and low $t_{dD}$ with segments of high conductance are clearly observed.