Phase effects on the conductance of a double-dot system in a ring structure threaded by a magnetic flux are studied. The Aharonov-Bohm effect combined with the dot many-body charging effects determine the phases of the currents going through each arm of the ring. The cases for zero magnetic flux or half a quantum of flux are discussed in detail. It is shown that, depending upon the magnetic flux and the state of charge of the dots, controlled by gate potentials, the dephasing of the upper and lower arm current gives rise to a S = 1/2 or S = 1 Kondo regime.We also show that even in the absence of a magnetic flux there can be a circulating current in the ring, depending on the system parameters. 73.63.Kv In the last years attention has been focused on the properties of double-quantum-dot systems 1 since they are expected to be basic building blocks for quantum computing 2 . In this context mesoscopic coherent transport is a key phenomenon that can probe entanglement 3 and phases accumulated by electrons traversing the system. The phase-coherent transport effects can be analyzed by embedding the dots into an Aharonov-Bohm ring threaded by a magnetic flux and connected to leads. Theoretical 4 and experimental 5 works have discussed the transmission phase shifts of single and double quantum dot systems in the Coulomb blockade regime. More recently the effect of Kondo correlation on the transmission phase of a quantum dot has been measured 6 and theoretically discussed 7,8,9,10,11,12 .The two-quantum-dot system is particularly interesting since, when each dot is inserted into one arm of a ring connected to leads, as represented in Fig. 1, it presents two paths for the electrons to go through, producing interferences that depend upon the phase in each arm.The effect of the interferences on the spectral densities of such a system has been studied 14 , taking the intra and inter-dot Coulomb repulsion to be infinite. This limit restricts the study

Confinement and surface roughness (SR) effects on the magnitude of the persistent current are analyzed for ballistic bidimensional metallic samples. Depending on the particular geometry, localized border states can show up at half-filling. These border states contribute coherently to the persistent current and its magnitude is enhanced with respect to their value in the absence of confinement. A linear scaling of the typical current I(typ) with the number of conduction channels M is obtained. This result is robust with respect to changes in the relevant lengths of the samples and to the SR. Possible links of our results to experiments are also discussed.

The transport properties of a system of two interacting dots, one of them directly connected to the leads constituting a side-coupled configuration (SCD), are studied in the weak and strong tunnel-coupling limits. The conductance behavior of the SCD structure has new and richer physics than the better studied system of two dots aligned with the leads (ACD). In the weak coupling regime and in the case of one electron per dot, the ACD configuration gives rise to two mostly independent Kondo states. In the SCD topology, the inserted dot is in a Kondo state while the side-connected one presents Coulomb blockade properties. Moreover, the dot spins change their behavior, from an antiferromagnetic coupling to a ferromagnetic correlation, as a consequence of the interaction with the conduction electrons. The system is governed by the Kondo effect related to the dot that is embedded into the leads. The role of the side-connected dot is to introduce, when at resonance, a new path for the electrons to go through giving rise to the interferences responsible for the suppression of the conductance. These results depend on the values of the intradot Coulomb interactions. In the case where the many-body interaction is restricted to the side-connected dot, its Kondo correlation is responsible for the scattering of the conduction electrons giving rise to the conductance suppression.

In the present work, we investigate the electronic transport through a T-shape double quantum dot system coupled to two normal leads and to one superconducting lead. We explore the interplay between Kondo and Andreev states due to proximity effects. We find that Kondo resonance is modified by the Andreev bound states, which manifest through Fano antiresonances in the local density of states of the embedded quantum dot and normal transmission. This means that there is a correlation between Andreev bound states and Fano resonances that is robust under the influence of high electronic correlation. We have also found that the dominant couplings at the quantum dots are characterized by a crossover region that defines the range where the Fano-Kondo and the Andreev-Kondo effect prevail in each quantum dot. Likewise, we find that the interaction between Kondo and Andreev bound states has a notable influence on the Andreev transport.