Kondo effects and shot noise enhancement in a laterally coupled double quantum dot

Spin and orbital Kondo effects and the related shot noise for a laterally coupled double quantum dot are studied taking account of coherent indirect coupling via a reservoir. We calculate the linear conductance and shot noise for various charge states to distinguish between the spin and the orbital Kondo effects. We find that a novel antiferromagnetic exchange coupling can be generated by the coherent indirect coupling, and it works to suppress the spin Kondo effect when each quantum dot holds just one electron. We also show that we can capture the feature of the pseudospin Kondo effect from the shot noise measurement.

Figure 1

Schematics of laterally coupled DQDs with a separated drain reservoir. $s_{12}$ is the minimum distance that electrons propagate in the source reservoir. (a) The source and drain reservoirs are both completely separated, namely, there is no coupling between two QDs via the reservoirs. This situation corresponds to $s_{12}\to \infty$. (b) The source reservoir is common and the drain reservoir is separated. (c) There is maximal coherence between two QDs via the reservoirs. This condition corresponds to $s_{12}=0$.

Figure 2

Total linear conductance $G$ for $\alpha =0$ and $U_1/\hslash \Gamma =U_2/\hslash \Gamma =2V_{\mathrm{inter}}/\hslash \Gamma =6$. (a) The charge configuration is shown as $(N_1,N_2)$. The dotted white line indicates the charge degeneracy line schematically. (b) $\Delta \epsilon$ dependence of the linear conductance along the solid white line in (a). Dashed, dotted, and solid lines indicate the conductance $G_1$, the conductance $G_2$, and the total conductance $G$, respectively.

Figure 3

Reduction of the linear conductance caused by coherent indirect coupling and the spin-spin correlation function. (a) $\Delta G_{\alpha }$ for $\alpha =0.5$. (b) $G$ for ${\epsilon }_1={\epsilon }_2$. Solid, dashed, dotted, and dash-dotted line lines indicate $\alpha =0$, $\left|\alpha \right|=0.5$, $\left|\alpha \right|=0.8$, and $\left|\alpha \right|=1$, respectively. Inset: $\left|\alpha \right|$ dependence of the linear conductance at ${\epsilon }_1/\hslash \Gamma ={\epsilon }_2/\hslash \Gamma =-6$ indicated by the filled (green) circle in (a). (c) $\left|\alpha \right|$ dependence of the spin-spin correlation function at ${\epsilon }_1/\hslash \Gamma ={\epsilon }_2/\hslash \Gamma =-6$ indicated by the filled (green) circle in (a).

Figure 4

Shot noise $S(0)$ and shot noise difference $\Delta S_{\alpha }$ for $U_1/\hslash \Gamma =U_2/\hslash \Gamma =6$, $V_{\mathrm{inter}}/\hslash \Gamma =3$, and ${\mathit{eV}}_{\mathit{SD}}/\hslash \Gamma =0.1$. The charge configuration is shown as $(N_1,N_2)$. (a) $S(0)$ for $\alpha =0$. (b) $\Delta S_{\alpha }$ for $\left|\alpha \right|=0.5$. (c) $S(0)$ for ${\epsilon }_1={\epsilon }_2$. Solid, dashed, dotted, and dash-dotted line lines indicate $\alpha =0$, $\left|\alpha \right|=0.5$, $\left|\alpha \right|=0.8$, and $\left|\alpha \right|=1$, respectively. (d) $\left|\alpha \right|$ dependence of the zero-frequency shot noise at ${\epsilon }_1/\hslash \Gamma ={\epsilon }_2/\hslash \Gamma =-6$ indicated by the filled (green) circle in (b).

Figure 5

For various quotients between ${\alpha }_S$ and ${\alpha }_D$, $\left|{\alpha }_S\right|$ dependence of the spin-spin correlation function at ${\epsilon }_1/\hslash \Gamma ={\epsilon }_2/\hslash \Gamma =-6$, indicated by the filled (green) circle in Fig. 3a.