The Metal-Insulator Transition in Correlated Systems and Quasicrystals
Date Issued
2009
Date
2009
Author(s)
Lai, Jian-An
Abstract
The main purpose of this thesis is to analyze the electronic properties of quasicrystals and correlated disordered systems using the concept of Anderson localization, and understand the metal-insulator transition. We will start from introducing periodic ordered systems, and discuss the correlated disordered systems, especially the random-dimer model. Then we will investigate the new structure that had been discovered lately, namely the quasicrystals, and discuss the trace maps of one-dimensional Fibonacci models. We will give the concepts of extended and localized states intuitively. Our fundamental models for numerical analysis are random-dimer model and one-dimensional Fibonacci model. We will use these models to analyze the transmission coefficient, band structures, and wave functions. In correlated disordered systems, the merging of transmission peaks has been verified. In one-dimensional Fibonacci models, we observe the spectral-splitting, self-similarities of wave functions, and three kinds of localization, including extended, critical and localized states.
Subjects
Anderson localization
quasicrystals
metal-insulator transition
trace map
Type
thesis
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