Kondo Effect In A Mesoscopic Ring With An Coupled Double Quantum Dots

The Kondo effect, studied widely in condensed matter physics, is a well-known physics phenomenon. Recent advances in nanofabrication technology have made it possible to investigate various aspects of this effect. One used a Quantum Dot (QD) coupled to electrodes by tunneling barriers under controlled circumstances experimentally, which has aroused new interest in this phenomenon. In contrast to the enhancement of the resistivity due to the Kondo effect in a bulk metal, the Kondo resonance near the Fermi level, localized at the QD, provides a new channel for the mesoscopic current and leads to an increase of the conductance in a QD . More recently, a great effort has also been dedicated to the study of the equilibrium properties of the ground states of a A-Bring with a QD. Main matters of interest are: (i) the effect of the Kondo resonance on the persistent current (PC) induced by a magnetic flux in this dot-ring system; (ii) the possibility of detecting the Kondo correlation length by measuring the Kondo-assisted PC in this system. In spite of many approximate methods available for attacking those problems, few theoretical consensuses have emerged on various aspects of the mesoscopic Kondo effect. By means of a one-impurity Anderson model, my supervisor theoretically study the Kondo effect inan Aharonov-Bohm ring with an in-line quantum dot, and the Hamiltonian is solved by means of employing the slave-boson technique in mean-field theory. The results of the calculations show that a suppressed Kondo effect exists in this system when the mean level spacing of electrons is larger than the bulk Kondo temperature, and the physical quantities of this system depend sensitively on both the parity of this system and the size of rings, as well as the rich physical behavior of this system can be attributed to the coexistence of both the finite-size effect and the Kondo screening effect in this system. On the one hand, when increasing the ring circumference to gK IL < 0.5, the system crosses over from an incompletely screened single ground state to a fully screened one. On the other hand, when S/T^<\, the finite-size effect will disappear. Therefore, the physic properties of the system will undergo a dramatic change, respectively, at ^KIL?t0.5 and S/T^?l, with the change of the ring circumference. The results also show that it is possible to detect the Kondo screening cloud by measuring the persistent current and the zero field impurity susceptibility directly in future experiments. At the same time, my supervisor and his first student study the persistent current in a mesoscopic ring with a side-coupled quantum dot. They have probed the problems by using the one-impurity Anderson Hamiltonian and treating it with the Slave-Boson Mean field theory. It is shown that the persistent current in this system have the spin fluctuations and in the limit of S/Tï¿¡ ?1, the charge transfers between two subsystems is suppressed. The persistent current measurement provides an opportunity to detect the Kondo screening cloud.In this paper, we study the properties of the ground state of a series-coupled double quantum dot embedded in a mesoscopic ring in the Kondo regime by means of a two-impurity Anderson Hamiltonian, and the Hamiltonian is solved by means of the slave-boson mean-field theory. Fromthe results of our calculations, one can see that the disappearance of the parity effects and the single current-phase relation are basic characteristic of the weak dot-dot coupling systems, and this moment, two Kondo states do not combine into two molecule states. On the contrary, the double quantum dot system has richer physics in the strong dot-dot coupled regime, where the strong dot-dot tunneling coupling leads to the splitting molecule orbits formed by the coherent superposition of the Kondo states of each dot, which can be reflected on the appearance of parity effects and the rich current-phase relation in this system. We also study the properties of the ground state of a mesoscopic ring with a paralleled double quantum dots in the Kondo regime. It is shown that in this system the persistent current induced by a magnetic flux depends sensitively on both the parity of this system and the size of the ring; Two dots can be coupled coherently, which is reflected in the giant current peak in the strong coupling regime. Therefore these systems might also be a possible candidate for future device applications.