Two-impurity Anderson model revisited: Competition between Kondo effect and reservoir-mediated superexchange in double quantum dots

We study a series-coupled double quantum dot in the Kondo regime modeled by the two-impurity Anderson model and find a conduction-band-mediated superexchange interaction that competes with Kondo physics in the strong Coulomb interaction limit. Our numerical renormalization-group results complemented with the higher-order Rayleigh-Schrödinger perturbation theory show that the exchange mechanism leads to clear experimental consequences that can be checked in transport measurements through double quantum dots.

Figure 1

(Color online) The sequence of virtual processes of the most significant contribution to the conduction-band-mediated exchange $J_I$ in the large-$U$ limit. Here the circles (rectangles) denote dots (leads).

Figure 2

(Color online) (a) Zero-temperature linear conductance and phase shift difference $\delta ={\delta }_e-{\delta }_o$ in the symmetric case (inset) as functions of $t/\Gamma$, $U=2\left|ϵ\right|$. Lines are guidance for eyes. (b) Linear conductance $G$ (filled symbols) and phase shift as functions of the scaled exchange coupling, $\left(J_{12}-J_c\right)\Gamma /T_{K}t$. Results for the phase shift differences and for conductance collapse well onto universal curves, the scaling functions fitted to the data.

Figure 3

(Color online) Zero-temperature properties of the p-h symmetric model (left panels) and the p-h asymmetric $U=\infty$ model (right panels) for $\Gamma =0.01D$. (a,d) Linear conductance and spin-spin correlation $⟨{\mathbf{S}}_1\cdot {\mathbf{S}}_2⟩$. (b,e) Renormalized parameters, $t^{\ast }$, ${\Gamma }_e^{\ast }$, ${\Gamma }_o^{\ast }$, and $\left|{ϵ}^{\ast }\right|$. In the symmetric model, ${\Gamma }_e^{\ast }={\Gamma }_o^{\ast }$ and ${ϵ}^{\ast }=0$. [(c) and (f)] Renormalized superexchange coupling in the local basis (c) and in the parity basis (f).

Figure 4

(Color online) Zero-temperature linear conductance and phase-shift difference $\delta ={\delta }_e-{\delta }_o$ (inset) in the large-$U$ case $\left(U=\infty \right)$. Lines are guidance for eyes. The dashed line is obtained from the SBMFT calculation (Ref. 4).

Figure 5

(Color online) The conductance-peak position $t_c/\Gamma$ as a function of the Coulomb energy $U$ for different values of $\Gamma$: $\Gamma /D=0.012$ (red, lower) and 0.02 (black, upper). The dotted and solid lines are the peak positions estimated from the condition $J_U=2.2T_K$ and $J_U+J_I=2.2T_K$, respectively. Inset: the relative strength of $J_I$ with respect to the total superexchange coupling.