Green's Function Approach To Physical Properties Of Low Dimensional Mesoscopic System

With the development of material technology and ultra-micro fabrication technique, the semiconductor microstructures with mesoscopic dimension have come within reach. In these low dimensional mesoscopic systems that allow the energy band to be tailored, quantum size effect and quantum interference properties of electron liquids give rise to many novel and marvelous phenomena and thus received much current attention. As the typical representative exhibiting quantum effects, quantum dot (QD) plus Aharoronv-Bohm (AB) ring structures have become one of the most active areas in mesoscopic physics in very recent years. In this thesis, we present in some detail theoretical investigations, using Green's function approach, on the spectral and quantum-transport properties of several geometries of a quantum dot plus an AB ring.The thesis consists of six chapters. Chapter one is an introduction, which reviews some important experimental and theoretical developments of mesoscopic physics, and gives a detailed description of Green's function theory used in the following chapters.In chapter two, we study the spectral properties of a QD embedded in one arm of an AB ring using causal Green's function approach. The system is modeled by an Anderson-type Harmiltonian in which the Coulomb interaction within the dot is taken into account. The Green's functions are derived by an equation-of-motion technique. The numerical results show that the average occupation number of electrons in the QD exhibits staircase features and oscillates with the magnetic flux through the AB ring on the upward stairs; the local density of states depends appreciably on the electron occupation of the dot.Chapter three concerns the quantum transport through a QD embedded in one arm of a double-slit-like AB ring. The magnitude and phase of the transmission amplitude through the QD are calculated by Green's function approach. The numerical results are in good agreement with the experimental observations. Also, the differential conductance of the whole device is also derived using the nonequilibrium Keldysh formalism. It is shown that the oscillating conductance has a continuous bias voltage dependent phase shift in both linear and nonelinear response regime.In chapter four, we propose three kinds of interference geometries of an AB ring plus a QD. Different from previous devices, the QD is at the center of the AB ring and connected to it in different way. The phase behavior of the AB oscillations is investigated using nonequilibrium Keldysh formulism. It is found that the phase behavior of the AB oscillations in these geometries is quite different from each other, which suggests that the phase behavior of the AB oscillations in a system of a mesoscopic ring plus a QD cannot be viewed as the reflection of either the properties of a QD or the special interference effect in the AB ring.Chapter five involves the Kondo problem in QDs. Electron transport through a QD with Kondo correlations is studied using Green's function approach. The QD is embedded in a double-slit-like AB ring. The Green's functions are derived by equation-of-motion technique under the Lacroix's approximation. On this basis, the magnitude and phase of the transmission amplitude through the QD can be numerically calculated.The last chapter presents a conclusion of this thesis and some prospects for this investigation.