元素Te，Se，Zr隨著壓力的變化具有豐富的結構相變及超導性質，利用密度泛函理論與密度泛函擾理論，研究其電子結構與晶格振動質，由於超導相變溫度和電子與聲子交互作用有關，所以利用Migdal-Eliashberg理論探討元素Te，Se，Zr在立方晶體(bcc)結構相之超導性質，發現隨著壓力的減少，超導相變溫度上升，與實驗結果一致，其超導相變溫度上變的原因，來自於聲子軟化(Phonon softening)。本論文除了電聲子耦合計算外，亦對微波材料BaMg1/3(Ta/Nb2/3O3，利用密度泛函微擾理論，計算其計算其Gamma點的聲子與振動模式，分析Raman實驗與FTIR實驗。

The elements Te, Se, Zr have rich structural phase transitions and superconductive properties under pressure. With density functional theory and linear response scheme, we study electronic structures and vibrational properties, respectively. Since superconducting critical temperature Tc relates to electron-phonon coupling, so we study the 
superconductivity of Bcc Te, Se, Zr within Migdal-Eliashberg theory. The calculated superconducting critical temperatures under compression are in good agreement with experiment results, and Tc increases with decreasing pressure, which mainly attributed to the phonon softening. In this thesis, we also study the phonon and vibrational normal modes at Gamma point on microwave material BaMg1/3(Ta/Nb)2/3O3, and assign the corresponding normal modes in Raman and FTIR experiments.

第一章　導論	1
1-1研究動機	1
1-2論文架構	4
第二章　基本理論與模擬方法	5
2-0材料模擬方法導論	5
2-1　Density Functional Theory（密度泛函理論）	6
2-1-1　Hohenberg-Kohn 定理	6
2-1-2　Kohn Sham equation	7
2-1-3　交換相干能	8
2-1-4　週期性邊界條件	9
2-1-5　虛位勢 (Pseudopotential)	11
2-2密度泛函微擾理論與聲子計算	13
2-2-1　線性響應方法(linear response)	14
2-3　電子與聲子交互作用(electron-phonon interaction)	22
2-4　Raman光譜與紅外線吸收光譜學	28
第三章 Bcc結構Te Se及Zr 之電聲子計算	32
3-0　 Te,Se及Zr之材料結構介紹	32
3-1　Bcc結構Te之電聲子計算	33
3-1-1　電子結構計算	33
3-1-2　聲子計算	35
3-1-3　電聲子計算	37
3-2　Bcc結構Se之電聲子計算	42
3-2-1　電子結構計算	42
3-2-2　聲子計算	43
3-2-3　電聲子計算	46
3-3　Bcc結構Zr之電聲子計算	51
3-3-1　電子結構計算	51
3-3-2　聲子計算	53
3-3-3電聲子計算	55
第四章 BaMg1/3(Ta/Nb)2/3O3 之聲子計算..........59
4-0 晶格結構介紹...............................................................................................59
4-1 電子結構計算...............................................................................................60

4-2 點聲子計算..............................................................................................63
第五章 結論......................................................70
Reference ..............................................................71
圖表目錄
圖2-1 虛位能示意圖.................................................................................12
圖3-1-1 不同壓力下bcc Te 的電子能態密度.........................................34
圖3-1-2 不同壓力下bcc Te 的電子能帶結構.......................................34
圖3-1-3 於不同壓力下之Bcc Te 之聲子頻譜.......................................36
圖3-1-4 N 點到Γ 點和Γ 到H 點間之bcc Te 聲子頻譜.....................36
圖3-1-5 於不同壓力下，bcc Te 之聲子態密度....................................37
圖3-1-6 不同壓力下，隨波向量變化的Phonon linewidth...................39
圖3-1-7 不同壓力下，隨波向量變化的qj λ
與聲子頻譜之比較.........40
圖3-1-8 不同壓力下，超導相變溫度理論計算，其他理論計算[18]與實
驗[19]之比較.........................................................................................41
圖3-2-1 不同壓力下bcc Se 的電子能態密度.......................................42
圖3-2-2 不同壓力下bcc Se 的電子能帶結構.......................................43
圖3-2-3 於不同壓力下之Bcc Se 之聲子頻譜.......................................44
圖3-2-4 N 點到Γ 點間之bcc Se 聲子頻譜.........................................45
圖3-2-5 於不同壓力下，bcc Se 之聲子態密度....................................45
圖3-2-6 不同壓力下，隨波向量變化的Phonon linewidth...................48
圖3-2-7 不同壓力下，隨波向量變化的qj λ
與聲子頻譜之比較.........49
圖3-2-8 不同壓力下，bcc Se 超導相變溫度理論計算與其他計算[20]之
比較......................................................................................................50
圖3-3-2 不同壓力下bcc Zr 的電子能態密度........................................52
圖3-3-3 不同壓力下bcc Zr 的電子能帶結構........................................52
圖3-3-4 不同壓力下之bcc Zr 之聲子頻譜............................................54
圖3-3-5 不同壓力下之bcc Zr 之聲子態密度........................................54
圖3-3-6 bcc Zr 在不同壓力下隨波向量變化的Phonon linewidth .......57
圖3-3-7 不同壓力下，隨波向量變化的 qj λ 與聲子頻譜之比較.......57
圖3-3-8 理論計算與實驗[17]之bcc Zr 壓力與超導相變溫度Tc 關係..58
圖4-0 BaMg1/3(Ta/Nb)2/3O3 晶格結構圖.................................................59
圖4-1-1 BMT 與BMN 中，Ta-O 與Nb-O 八面體之鍵長。...............61
圖4-1-2 BaMg1/3(Ta/Nb)2/3O3 的電子態密度(DOS) .............................61
表格3-1-1 不同壓力下之bcc Te 電聲子計算.......................................40
表格3-1-2 文獻[18]中不同壓力下之bcc Te 電聲子計算.......................41
表格3-2-1 不同壓力下之bcc Se 電聲子計算.......................................48
表格3-2-2 其他文獻中[20]，不同壓力下之bcc Se 電聲子計算...........49
表格3-3-1 不同壓力下，bcc 結構之Zr 電聲子計算...........................58
表格4-1-1 BaMg1/3Ta2/3O3 之晶格結構.................................................62
表格4-1-2 BaMg1/3Nb2/3O3 之晶格結構................................................62
表4-2-1 BMT 與BMN 之點聲子計算的g mode 與Raman 實驗.......66
表4-2-2 BMT 與BMN 中Ta 與Nb 原子的Born effective charge.......66
表4-2-3 BMT 與BMN 中O 原子的Born effective charge...................67
表4-2-4 BMT 之點聲子計算的u mode 與FTIR 實驗......................68
表4-2-5 BMN 之點聲子計算的u mode 與FTIR 實驗.....................69

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