Nonequilibrium transport properties of a double quantum dot in the Kondo regime

We analyze the nonequilibrium transport properties of a parallel double quantum dot in terms of its full counting statistics (FCS). The parameters of the setup are assumed to be such that both subsystems are driven into the Kondo regime. After a series of transformations, the Hamiltonian is then mapped onto a Majorana resonant level model, which effectively describes the Toulouse point of the respective double-impurity two-terminal Kondo model. Its FCS is then obtained at arbitrary constellation of voltage, temperature, and local magnetic fields. We identify two different transport processes corresponding to single-electron tunneling as well as an electron pair process, and we give the respective effective transport coefficients. In the most universal linear-response regime, the FCS turns out to be of a binomial shape with an effective transmission coefficient. Furthermore, we find a complete transport suppression (antiresonance) at a certain parameter constellation, which is similar to the one found in the noninteracting quantum dots. By an explicit expansion around the Toulouse point, we show that the antiresonance is universal and should be observable in the generic Kondo dot setup. We discuss experimental implications of our predictions as well as possible routes for generalizations of our approach.

Figure 1

Parallel double quantum dot. The two quantum dots are coupled symmetrically (under exchange of the dots) to metallic leads. $H_{1,2}$ (small arrows) are the in-plane magnetic fields. The dot spins are represented by larger arrows. The coupling is represented by the double-headed arrows.

Figure 2

The nonlinear $I\left(V\right)$ for the double QD setup at zero temperature. The plots show the current for ${\Delta }_1=2$ and ${\Delta }_2=5$. The different graphs correspond to $K_{+}=0$ and $K_{-}=1$ (dash-dotted line), $K_{+}=2$ and $K_{-}=2$ (short dashed line), $K_{+}=1$ and $K_{-}=0$ (solid line), and $K_{+}=0$ and $K_{-}=0$ (long dashed line). All energies are measured in units of $K_{\mathrm{LR}}^2$.

Figure 3

Fano factor for fixed magnetic fields ${\Delta }_1=2$ and ${\Delta }_2=5$ as a function of bias voltage. The different graphs correspond to $K_{+}=0=K_{-}$ (dash-dotted line), $K_{+}=0.5=K_{-}$ (short dashed line), $K_{+}=0.5$ and $K_{-}=0$ (solid line), and $K_{+}=0$ and $K_{-}=0.5$ (long dashed line). The solid line $F\left(V\right)=0.5$ is only a guide for the eye.

Figure 4

Fano factor as a function of bias voltage for different temperatures and fixed magnetic fields ${\Delta }_1=2$ and ${\Delta }_2=5$, and $T=0.005$ (dash-dotted line), $T=0.05$ (solid line), and $T=0.1$ (dashed line). The divergence of the Fano factor for $V\to 0$ can be explained by expanding noise and current (see text). Inset: Current as a function of bias voltage at different temperatures: $T=0.005$ (dash-dotted line), $T=0.5$ (solid line), and $T=1.$ (dashed line). The solid line $F\left(V\right)=0.5$ is only a guide for the eye.