Localization And Transport Properties In Quasi 1D Mesoscopic System

The thesis Is. concentrates on the transport properties of electrons in a quasi-one dimensional mesoscopic necklace system. In the frame of single-electron tight-binding approximation, we have carried out the numerical calculations on the relationships between periodic, quasi-periodic, or random distribution of adjustable parameters (such as site energy and flux), and the changes of transmission and energy spectrums. Our aim is to explore the physical mechanisms of new effects in such a mesoscopic system, to develop physical models and supply theoretical basis in designing novel quantum devices with desired properties. The thesis is divided into four chapters, which are described as follows.Chapter 1 is the introduction for the whole thesis, which illustrates the fundamental concepts, the research background and recent development, the models and the methods for numerical calculations relevant to our work.In Chapter 2, a review and expansion on the transmission properties for periodic distribution of system parameters is given. Firstly, we give the energy spectrum for such a periodic system analytically. In the second, by using transfer matrix method, we give a general expression of transmission coefficient t. Furthermore, we calculate the transmission spectrum for the periodic and a reduced Anderson-like random case. In the latter case, there exist transmitted states, which is different from the conclusion that any weak randomness will induce localization in one-dimensional system, drawn by Anderson et. al. Finally, along the way of finding the AB Cages in 2D periodic systems, we show that, this kind of new localization effect induced by competition between lattice geometry and magnetic flux can be found in the necklace mesoscopic system, too.In Chapter 3, we will discuss the effects induced by quasi-periodic distribution of site energy or flux. First, we give the evolution of transmission spectrum by changing the site energy distribution where the homogeneous flux is on or not, and the corresponding energy spectrum are given. Next, we show the effects induced by enclosing a quasi-periodic distribution of flux on the system when the site energy distributed uniform. The transmission spectrum and that of energy are given. In the periodic distribution of site energy or flux, there are low-energy physics involved, i.e., the lower energy region is more sensitive to different distribution of parameters. So, we will discuss those distribution effects on thecentral transmission gap intensively. In the flux case, with all site energy follows Fibonacci (or Thue-Morse) sequence, where is fixed, is changeable, we found that, the width of central forbidden band A changes linear with respect to the variation of An onset point occurs when the effective site energy (defined as a weight average of site energy in given distribution) ff = 0, there exists a Localization-Delocalization (LD) transition. If we turn the flux on, the LD transition disappears, and curve becomes a second order polynomial of As for the case of flux in quasi periodic distribution, where all the site energies are uniform, we found that the curve can be fitted well as a third order polynomial of before it increases abruptly at a special point When, all the states of system are localized. At last, we give an approximate relation to get the position of for a given , and analysis are given.In Chapter 4, we summarize the results of our work briefly, reveal some unsettle-up problems and look ahead for future research.