Ruderman-Kittel-Kasuya-Yosida and Magnetic-Field Interactions in Coupled Kondo Quantum Dots

We investigate theoretically the transport properties of two independent artificial Kondo impurities. They are coupled together via a tunable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For strong enough antiferromagnetic RKKY interaction, the impurity density of states increases with the applied in-plane magnetic-field. This effect can be used to distinguish between antiferromagnetic and ferromagnetic RKKY interactions. These results may be relevant to explain some features of recent experiments by Craig et al. [Science 304, 565 (2004)].

Figure 1

Schematic picture of the setup containing two quantum dots. Each dot $1(2)$ is strongly connected to an open central conducting region (C) through the tunneling couplings ${\gamma }_{1(2)}$ and very weakly connected to its respective lead $L(R)$ by ${\Gamma }_{L(R)}$. Thus, the differential conductance ($dI/d{V}_{\mathrm{S}\mathrm{L}(\mathrm{R})}$) between the $S$ and $L(R)$ through dot 1(2) will reflect the DOS in dot 1(2).

Figure 2

(a) DOS for dot 1 in the symmetric case (${\gamma }_1={\gamma }_2$) for $I/T_K^1=1$ (solid line), $I/T_K^1=2$ (dotted line), and $I/T_K^1=3$ (dashed line) [the cases for $I/T_K^1=1,2,[<(I/T_K^1{)}_c]$ are indistinguishable since the peak width is governed by the same energy scale $T_K^1$ before the splitting occurs]. The critical value at which the splitting occurs is $(I/T_K^1{)}_c\approx 2.54$. (b) DOS for dot 1 in the asymmetric case (${\gamma }_2={\gamma }_1/2$) for $I/T_K^1=1$ (solid line), $I/T_K^1=2$ (dotted line), and $I/T_K^1=3$ (dashed line). Here the critical value at which the splitting occurs is $(I/T_K^1{)}_c\approx 1.27$. Inset: Critical value $(I/T_K^1{)}_c$ vs ${\gamma }_2/{\gamma }_1$ at which the transition from the Kondo state to a singlet state occurs. The boundary (denoted by the solid line) separates both phases.

Figure 3

(a) DOS for dot 1 for $I=1.5T_K^1$ at different values $H$. (b) DOS for dot 1 for $H=1.5T_K^1$ at different values of $I/T_K^1$. Upper inset: DOS for dot 1 for $H=I=4T_K^1$. Lower inset: DOS at $E_F$ for dot 1 as a function of $I/T_K^1$ for $H=1.5T_K^1$. We set ${\gamma }_1={\gamma }_2$ and $T_K^1=T_K^2$.