Transconductance of a Double Quantum Dot System in the Kondo Regime

We consider a lateral double-dot system in the Coulomb blockade regime with a single spin-$1/2$ on each dot, mutually coupled by an antiferromagnetic exchange interaction. Each of the two dots is contacted by two leads. We demonstrate that the voltage across one of the dots will have a profound influence on the current passing through the other dot. Using poor man’s scaling, we find that the Kondo effect can lead to a strong enhancement of this transconductance.

Figure 1

Double quantum dot system: Two Kondo impurities denoted $L$, $R$ each connected to two leads 1, 2 and 3, 4, respectively, and coupled to each other by a spin exchange interaction $K$.

Figure 2

Polarization $p=n_s-n_t$ versus voltage $e{V}_R/K$ for different values of $K/T_K$ at $T/T_K=0.1$ and voltage $V_L=0$. Inset shows the derivative of the curves in the main panel.

Figure 3

Differential conductance $d{I}_L/d{V}_L$ in units of $e^2/h$ for fixed $T/T_K=0.1$ and $1/\ln (K/T_K)=0.2$ versus $e{V}_L/K$ at different values of $e{V}_R/K$. Inset: $d{I}_L/d{V}_L$ at $V_L\to 0$ versus $e{V}_R/K$. Solid circles: perturbative RG; open circles: second order PT.

Figure 4

Transconductance $d{I}_L/d{V}_R$ in units of $e^2/h$ multiplied by ($K/e{V}_L$) versus $e{V}_R/K$ for fixed $T/T_K=0.1$, probing voltage $e{V}_L/K=0.05$, and different values of $K/T_K$. Inset: Transconductance for $1/\ln (K/T_K)=0.2$ and different $e{V}_L/K$.