8 -10 -8 -6 -4 -2 0 2 4 E= $_{a}$/ a 0 0.2 0.4 0.6 0.8 1 G(E,T) t/D=0.003 a) -10 -8 -6 -4 -2 0 2 4 E= $_{a}$/ a 0 0.2 0.4 0.6 0.8 1 G(E,T) t/D=0.006 b) -10 -8 -6 -4 -2 0 2 4 E= $_{a}$/ a 0 0.2 0.4 0.6 0.8 1 G(E,T) 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 T/D t/D=0.01 c) -10 -8 -6 -4 -2 0 2 4 E= $_{a}$/ a 0 0.2 0.4 0.6 0.8 1 G(E,T) 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 T/D 0 0.2 0.4 0.6 0.8 1 G(E,T) -0.5 -1 -2 -4 -8 T/D E t/D=0.001 U$_{d}$=U$_{a}$=D $_{d}$=0 T$_{K}$ 0 a a b b c c d e d e 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 a) b) Figure 11: (Color online) Conductance curves for the fully interact- ing case with U d /D = U a /D = 1 , δ d = 0 , for increasing inter-dot tunneling t . The arrow indicates the direction of the increasing tem- perature T . Figure 10: (Color online) a) Conductance curves for the fully inter- acting case with U d /D = U a /D = 1 , δ d = 0 , for a range of differ- ent temperatures. b) Temperature dependence of the conductance for a range of energies of the side-coupled dot. temperature; for chosen t/D = 0 . 001 , we indeed find that for T/D = 10 − 5 ≈ 0 . 1 T 0 $_{K}$, the conductance form takes the form of a nearly symmetric anti-resonance, in agreement with the experiment. The minimum of the anti-resonance is located at lower value of E = ϵ a / Γ a as compared to the non-interacting case (where it is found exactly at E = 0 ), since the physi- cal mechanism for its occurrence is completely different: in the non-interacting case we observe a complete suppression of the conductance due to quantum interference between dif- ferent conductance pathways, while in the interacting case the incomplete suppression results from the separation of the en- ergy scales T 0 K and T 2 K with the experimental temperature set on an intermediate scale so that T 2 K < T < T 0 $_{K}$. The shift from E = 0 is not observable experimentally, since the exact value of the parameter ϵ a is not known: it has to be inferred indirectly from known gate voltages on the electrodes and the capacitances. mally suppressed second-stage Kondo screening is supported by the experimental results for the temperature-dependence of the resonant conductance (Fig. 2c in Ref. 34) which indicate a logarithmic behavior. This temperature variation corresponds to the high-temperature range in Fig. 10b). The experimen- tal results do not indicate any saturation of G for the lowest experimentally accessible temperatures, however this might simply indicate that the temperature is not sufficiently bel ow T K , or that t is indeed very small and thus T 2 K is exponentially low. Further confirmation for the interpretation in terms of the two-stage Kondo effect could be obtained by also consid- If the inter-dot tunneling t is increased so that the exchange coupling becomes comparable or exceeds the Kondo temper- ature, the conductance curves no longer exhibit a Fano-like antiresonance, not even at elevated temperatures, see Fig. 11. Instead, as E is reduced so that the side-coupled dot becomes occupied by one electron, the two electrons (one from each quantum dot) bind to a local singlet on the temperature scale of J ∼ 4 t $^{2}$/U and there are no other lower temperature scales. The interpretation of the anti-resonance in terms of a ther-