Quantum coherent transport through a quadruple quantum-dot structure with one continuous channel and two concrete channels

We investigate the coherent transport through a mesoscopic ring composed of four circularly coupled quantum dots (QDs) by means of nonequilibrium Green's functions. Two QDs of the mesoscopic ring with infinite intradot Coulomb interaction serve as two Kondo impurities, which are coupled together by three channels: the direct interdot coupling channel and the other two QD channels. This quadruple QD (QQD) system, including two subrings, is versatile and intriguing due to its advantages in simultaneous studying of the Kondo, Fano, and Aharonov-Bohm effects. We analytically and numerically studied the quantum transport properties of the symmetrical and asymmetrical QQD in both the absence and presence of a magnetic field. First we focus on the linear transport properties without the magnetic field. In the symmetrical QQD, the linear conductance shows a simple pattern with a single peak or double peak when the interdot coupling between two Kondo impurities is weak. However, by increasing this interdot coupling, the conductance evolves into a pattern characteristic of one deep trough. Sharply different from the symmetrical QQD, the conductance in an asymmetrical QQD shows a double peak or triple peak pattern in the case of the weak coupling between two Kondo impurities, and it shows a double trough pattern for the strong coupling. Moreover, we consider the influences on the transport induced by the magnetic field. It is demonstrated that the conductance shows complex oscillations associated with the Kondo, Fano, and Aharonov-Bohm effects, clearly depicting the competitions among them. The oscillation period as a function of magnetic flux is determined by the magnetic-flux ratio threaded into two subrings. The phase rigidity is clearly observed when one intermediate QD energy level passes through the lead Fermi level. Lastly we extend our results into the system with many QD channels used to connect the two Kondo impurities, which gives a complete picture about the transport properties in such a kind of double impurity QD devices.