We analyze the transport properties of a double quantum dot device with bothdots coupled to perfect conducting leads and to a finite chain of Nnon-interacting sites connecting both of them. The inter-dot chain stronglyinfluences the transport across the system and the Local Density of States ofthe dots. We study the case of small number of sites, so that Kondo box effectsare present, varying the coupling between the dots and the chain. For odd N andsmall coupling between the inter-dot chain and the dots, a state with twocoexisting Kondo regimes develops: the bulk Kondo due to the quantum dotsconnected to leads and the one produced by the screening of the quantum dotsspins by the spin in the finite chain at the Fermi level. As the coupling tothe inter-dot chain increases, there is a crossover to a molecular Kondoeffect, due to the screening of the molecule (formed by the finite chain andthe quantum dots) spin by the leads. For even N the two-Kondo temperaturesregime does not develop and the physics is dominated by the usual competitionbetween Kondo and antiferromagnetism between the quantum dots. We finally studyhow the transport properties are affected as N is increased. For the study weused exact multi-configurational Lanczos calculations and finite U slave-bosonmean-field theory at T = 0. The results obtained with both methods describequalitatively and also quantitatively the same physics.
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