臺灣博碩士論文加值系統

二維電子系統的物理是如此的豐富與多樣，其中又以量子霍爾效應的理論與實驗最引人注意。
自 1980 年發現量子霍爾效應後，已使得二維電子系統的研究進入了一個新的階段。
因此量子霍爾效應的發現，是近年來凝聚態物理領域最重要的發現之一。
本篇論文先討論整數量子霍爾效應的發現，基礎理論的架構與模型後，
再針對「局域─非局域相變」以及「量子霍爾態─絕緣態相變」兩大主題，進行分析。
最後再以最近兩年之實驗結果做一比較與討論。

In the past two decades, remarkable progress has been made in the study of two-dimensional (2-D)
electron systems. During this period, clear recognition of the 2-D character of interface electron,
development of different types of 2-D electron systems, and disclosure of very important and
unusual properties have taken place. The recent discovery of the quantum Hall effect has brought
the study of these electrons to a new stage in which solid state physics is linked with quantum
electrodynamics.
In this paper, only some classical theory and models of integer quantum Hall effect will be
discussed. Efforts will be made to avoid encyclopedic presentation and to achieve coherence
and uniformity. Emphasis will be placed on the phase transition of ''localized state-
delocalized state'' and ''quantum Hall state-insulating state''. Some latest discovery of the
quantum Hall effect in experiments will be discussed at the end of this paper.

1 導論
1.1 Hall 效應之發現
1.2 從 Drude model 分析 Hall 效應
1.3 單電子模型 ─ Landau 能階
2 無序位能中的電子
2.1 半古典近似
2.2 馬鞍點近似法
2.3 網絡模型
3 量子相變 I：局域─非局域相變
3.1 單參數標度理論 ─ Anderson 局域化
3.2 雙參數標度理論 ─ 整數量子 Hall 效應
3.3 量子展透與臨界指數
4 量子相變 II：量子 Hall 態─絕緣態相變
4.1 量子 Hall 態之弱磁場極限
4.2 延展態之漂浮 ─ 以網路模型為例
4.3 量子 Hall 效應之全域相圖

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