Kondo Effect In Mesoscopic Quantum Systems

Mesoscopic physics is one of the most active research areas in con-densed matter physics which treat the systems with the scale from nanome-tre to micrometre. A mesoscopic device is governed by quantum mechan-ics. There are three kind of interesting phenomena in mesoscopic sys-tems, namely quantum interference effect, quantum confinement effect, and charging effect. Recently, mesoscopic physics are extensively investi-gated both in experimental and theoretical aspects due to the potential applications in information technology and building nano-devices.In the first part, we introduce some quantum interference effects and electron correlation effects in mesoscapic physics, such as Aharonov-Bohm effect. Fano resonance. Andreev reflection,Kondo effect, and so on.In chapter two, we introduce the nonequilibrium Green function the-ory, which is a powerful tool to treat the electron transport through meso-scopic devices. Electron transport in several interacting quantum systems is investigated by taking advantage of the Green's function theory. Some of them will be introduced in the following.In chapter three, we study theoretically the Kondo effect in carbon nanotube quantum dot attached to polarized electrodes. Since both spin and orbit degrees of freedom are involved in such a system, the electrode po-larization contains the spin-and orbit-polarizations as well as the Kramers polarization in the presence of the spin-orbit coupling. We focus on the compensation effect of the effective fields induced by different polariza-tions by applying magnetic fields. We find the effective fields induced by the spin-and orbit-polarizations remove the degeneracy in the Kondo ef-fect, while the effective field induced by the Kramers polarization enhances the degeneracy. The effective field induced by the orbit-polarization can be compensated, but the effective field induced by the spin-polarization can not be compensated by applying magnetic field. The presence of the spin-orbit coupling does not change the compensation behavior observed in the case without the spin-orbit coupling.In chapter four, the Kondo effect of a single magnetic ad atom on the surface of graphene is investigated systematically by the nonequilibrium Green's function theory. It was shown that the unique linear dispersion relation near the Dirac points in graphene makes it more easy to form the local magnetic moment, which simply means that the Kondo resonance can be observed in a more wider parameter region than in the metallic host. Our result indicates that the Kondo resonance indeed can form ranged from the Kondo regime, to the mixed valence, even to the empty orbital regime. While the Kondo resonance displays as a sharp peak in the first regime, it has a peak-dip structure and/or an anti-resonance in the re-maining two regimes, which result from the Fano resonance due to the significant background resulted from dramatically broadening of the impu-rity level in graphene. We also study the scanning tunneling microscopy (STM) spectra of the adatom and they show obvious particle-hole asym-metry when the chemical potential is tuned by the gate voltages applied to the graphene. Finally, we explore; the influence of the direct tunneling channel between the STM tip and the graphene on the Kondo resonance and find that the line-shape of the Kondo resonance is unaffected, which can be attributed to unusual large asymmetry factor in graphene.In chapter five, we study the realization of the interplay between su-perconductivity and Kondo effect in quantum dot systems. The Andreev reflection in quantum dots strongly coupled to a ferromagnetic and a su- perconducting lead in Kondo regime is discussed through the local density of states. The result shows that the ferromagnetic lead induces an effective exchange field that splits the Kondo resonance and subgap bound states. On one hand, these splitting can be compensated for by applied magnetic fields. On the other hand, the spin-dependent splitting of subgap bound states leads to the suppression of Andreev current in the energy gap. The ferromagnetic electrode induced suppression of the Andreev transport can be partially restored by the external magnetic fields. The coupling between the quantum dot and the ferromagnetic lead do depends on the spin, and the Andreev reflection refers to two electrons with opposite spin orienta-tion. Therefore, the external magnetic fields could not completely recover the Andreev transport.We hope that these results would be realized and observed in future experiments.