此研究中在探討4乘4的非球形對稱勒廷格哈密頓算符中規範場對電子動力學以及自旋流的影響。非球形對稱的勒廷格哈密頓算符並不像球形對稱的勒廷格哈密頓矩陣有很好的解析解，但大部分的半導體材料較適用於非球形對稱的勒廷格哈密頓算符，例如: GaAs、InAs以及InP等等，因此我們做此研究。在計算上因為非球形對稱的勒廷格哈密頓矩陣的波函數較為複雜，因此研究方法採用海森堡的動態方程來進行數值運算。我們將各個簡倂的自旋流總合，我們發現由規範場所得到的自旋流大小與各個能帶上之貝瑞曲率大小無關，而實際上是由規範場還是貝瑞曲率來決定自旋流的大小要由實驗上來做確認。

The main goal of this research is to realize the spin dynamics and the spin current in the non-spherical Luttinger Hamiltonian, which is a 4 by 4 matrix represented by two heavy hole states and two light hole states. Although spin dynamics in the spherical Luttinger Hamiltonian has been studied comprehensively, it has not been solved in the non-spherical Luttinger Hamiltonian. Most semi-conductor materials satisfy non-spherical Luttinger Hamiltonian. For this reason we start this research. The wave function of non-spherical Luttinger Hamiltonian is extremely complicated, so we use Heisenberg picture with numerical calculation to solve the spin dynamics. Since the system has more than one degenerate state, we calculate spin conductivity by summing all degenerate states. We also calculate the Berry curvature. As a result, the magnitude of spin current which is calculated from gauge field is irrelevant to the Berry curvature. However which mechanisms resulting spin current should be determined by experiment result.

論文審定書 i
摘　要 ii
目錄 iv
圖次 v
表次 ix
第一章、緒論 1
第二章 研究動機 4
第三章、自旋磁矩與軌道角動量的交互作用 5
第四章、理論方法 8
4.1海森堡繪景以及海森堡動態方程 8
4.2使用海森堡動態方程來處理球形對稱勒廷格哈密頓矩陣 9
第五章、非球形對稱的勒廷格哈密頓矩陣中的自旋動力學 13
第六章、計算非球形對稱的勒廷格哈密頓矩陣的自旋流 29
6.1 勒廷格哈密頓矩陣的自旋流 29
6.2 貝瑞曲率 34
第七章、結論與討論 43
附錄A、勒廷格哈密頓矩陣 44
A.1勒廷格哈密頓矩陣之推導 46
A.2球形對稱的勒廷格哈密頓矩陣 50
附錄B、絕熱近似計算勒廷格哈密頓矩陣中電子的動力學 51
參考文獻 54

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