Pseudospin Kondo correlations versus hybridized molecular states in double quantum dots

A double quantum dot is coupled in parallel for studying the competition between the pseudospin Kondo correlations and strongly hybridized molecular states. Cryogenic measurements are performed in the regime of weak coupling of the two dots to leads under linear transport conditions. A detailed theoretical model is presented which verifies the finding of the transition between the two different regimes.

Figure 1

(a) Parallel double quantum dot with each dot connected to source and drain with the chemical potentials ${\mu }_S$, ${\mu }_D$. The interdot tunnel coupling is denoted by $t$. (b) Resonant first-order level scheme in relative energy $\epsilon$: the chemical potentials ${\mu }_n$ and ${\mu }_m$ [for $n\left(m\right)$ electrons being on ${\text{dot}}_1\left({\text{dot}}_2\right)$] are aligned to the chemical potentials of the leads. The open box depicts the interdot tunneling barrier. (c) For levels being off resonant the resonant state generated by correlated tunneling processes (dashed line) at the Fermi level can be detected. In this configuration the phase transition between first- and second-order tunneling is traced. (d) Schematic phase diagram of a double quantum dot in response to two gate voltages $V1$ and $V2$: black lines illustrate phase boundaries $\alpha$, $\beta$, and $\gamma$ between two ground-state configurations.

Figure 2

(a) Pseudospin Kondo regime: logarithmic gray scale plot of a measured phase diagram (white $⩽0$, $0.1e^2∕h⩽$ black). Only second-order tunneling processes occur along the degenerate phase boundary between dot configurations $\left(n,m-1\right)$ and $\left(n-1,m\right)$. The inset depicts the comparison of the model (solid line) to experimental data (open circles) along line $\gamma$. (b) Equivalent phase diagram at a perpendicular magnetic field of $1.5\mathrm{T}$.

Figure 3

(a) Phase transition: in addition to second-order processes, first-order processes (e.g. black arrow) are detectable (white $⩽0$, $0.1e^2∕h⩽$ black). (b) State with frozen pseudospin: along all phase boundaries only first-order processes can be traced. The white circles denote triple points where three charge configurations are degenerate.

Figure 4

(a) Single conductance traces along line $\gamma$ for different interdot couplings, showing the transition from the molecular ordered state to the pseudo-Kondo regime (data open boxes; theory, solid lines). The topmost trace corresponds to Fig. 3b, the trace labeled 6 refers to Fig. 3a and the lowest trace to Fig. 2a. The line plots are displayed with an offset of $0.09e^2∕h$ for clarity. (b) Fitted sequential tunneling rates ${\Gamma }_S$, showing a decrease for curves from 6 (black triangle) to 11 with a straight line as a guide to the eyes. (c) Fitted cotunneling rates ${\Gamma }_{\cot }$ show a rapid increase at lowest tunnel couplings.