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is not achieved at intermediate temperatures even in the case of well separated energy scales (three orders of magnitude for t/D = 0 . 0001 ). For larger t , the conductance peaks near T ∼ Γ a , where both competing effects are equally suppressed by t hermal fluctuations. 

<img src='content_image/404226.jpg'>

It is also worthwhile to compare the temperature- dependence of the conductance G ( T ) with the energy- dependence of the zero-temperature spectral function A d ( ω, T = 0) , see Fig. 7. A common approximation in discussing the transport properties of quantum dot systems is to assume that the temperature variation of the conductance simply follows the energy variation of the zero-temperature spectral function, i.e., G ( T ) ≈ π Γ d A d ( T, 0) . While this is true on the qualitative level, the numerical results shown significant qualitative differences: the conductance curv es are generally significantly broader and, accordingly, thei r maxima are lower. In particular, while the spectral function often attains values very close to 1 /π Γ d in some frequency range, the conductance is not unitary in the corresponding temperature range. 

The parameter regime studied in this section corresponds to the model used in Ref. 34 to obtain the conductance plots featuring an anti-resonance, which were proposed to explain the experimentally observed Fano-resonance-like line shapes with small q . It can be noticed, however, that this parameter regime is not appropriate, since it corresponds to a change of occupancy of the side dot by 2, while from the experimentally observed honeycomb stability diagram one can deduce that the electron number changes only by one. We return to this issue in Sec. VI. 

We first study the effect of finite electron-electron repul- sion on the side-coupled dot in the case where the embed- ded dot itself is non-interacting, U d = 0 . In this way we exclude all processes related to the inter-dot exchange inter- action and we may focus on the path-interference physics. 

## V. FULLY INTERACTING CASE 

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To simplify the discussion, we focus solely on the symmet- ric case with ϵ d = 0 . As previously discussed, as long as U a ≪ Γ a , the side-coupled dot is essentially non-interacting and the results are equivalent to those shown in Sec. III A. For larger U a > π Γ a , however, the side-coupled dot will undergo the Kondo effect and its occupancy will be pinned to 1 for ϵ a below several times Γ a . Consequently, the “resonance” line- shape in this regime will take the form of an inverted “Kondo plateau onset”. The evolution from the Fano resonance to the Kondo plateau onset is shown in the upper left panel in Fig. 8, while the associated level occupancy curves are shown in the bottom left panel. (See also Fig. 3 in Ref. 53 where a similar setup is considered.) 

We now finally discuss the fully interacting case, which is the situation which is relevant for the actual experimental con- figuration. The results are shown in the right panels in Fig. 8 . We find a very similar evolution in the conductance and occu- pancy curves with increasing U a as in the U d = 0 case. The transition from the Fano line shape to the Kondo plateau-edge shape occurs in this case for lower values U a , however, and al- ready by U a /D = 0 . 01 we obtain conductance curves which do not change much as U a is further increased. This is very important since it implies that the regime of significantly l arge 

