固態物理中的非阿貝爾貝利相位

Abstract

自從Michael Berry 在1983年發表了他對Geometric phase(也稱為Berry phase)的研究後，一些在實驗上無法解釋的現象，都因此得到了解答。而且我們會發現在物理研究中，很多領域都會使用到相關概念。我們在此探討主要分為兩大部份，阿貝爾(Abelian)和非阿貝爾(Non-Abelian)的結構，非阿貝爾(Non-Abelian)的結構涉及到簡併態的問題，所以在計算上並沒有像阿貝爾情形(非簡併)單純。因此，本論文主要是利用理論的推導並搭配數值計算探討非阿貝爾(Non-Abelian) Berry phase的結構及其特性。我們將計算方法應用於半導體的Luttinger model，搭配量子化條件後，可算出Berry phase效應對Landau level的修正。

In 1983 Michael Berry propose the his study about Berry phase, some phenomena that can't be explained on the experiment, have been all answered. And we will find in physical research, many field will use relevant concepts. Here we will discuss two major parts, abelian and non-abelian structure, non-abelian structure involved the problem of degeneracy, so the calculation of non-abelian case is not simple as abelian case. In this paper, we use the theoretical derivation and match number value to discuss the sturctue and characteristic of the non-abelian Berry phase. We apply the computing technology to Luttinger model of the semiconductor, after matching the quantization condition, we can calculate the revision of Landau level of Berry phase effect.