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系統識別號 U0002-1303200919303000
中文論文名稱 強束縛電子激發態及其傳播行為之研究: Bethe-Salpeter 方法
英文論文名稱 Strongly bound local charge excitations and their propagations: Bethe-Salpeter equation method
校院名稱 淡江大學
系所名稱(中) 物理學系博士班
系所名稱(英) Department of Physics
學年度 97
學期 1
出版年 98
研究生中文姓名 葉承霖
研究生英文姓名 Chen-Lin Yeh
學號 890180010
學位類別 博士
語文別 英文
口試日期 2009-01-16
論文頁數 79頁
口試委員 指導教授-薛宏中
委員-陳正弦
委員-林倫年
委員-曾文哲
委員-杜昭宏
中文關鍵字 線性響應  Wannier 函數  激子  等效雙粒子跳躍核心因子  BSE  鹼金屬鹵化物 
英文關鍵字 linear response  Wannier function  exciton  effective two-particle kinetic kernel  BSE  alkali halides 
學科別分類
中文摘要 藉由運用GW近似與BSE理論並結合不同基底(平面波 或 Wannier函數)展開的方式, 我們已經完成在鹼金屬鹵化物中考慮多體效應影響下的第一原理激發態計算。
新穎的第一原理Wannier 函數很適合用於瞭解強束縛Frenkel激子的傳播行為。 特別是用以解釋長久以來對於Frenkel 激子特性爭辯的問題。 儘管在鹼金屬滷化物中 ( 例如: 鋰化氟 ) 電子電洞對並不是藉由相同原子上的交互作用束縛在一起, 但是我們仍然可以鋰與氟原子Wannier 軌道所組成的”超級原子”的角度來理解這一類非常局域化的激子行為。 我們可以發現在將局域化的電子電洞對Wannier波函數相乘並做傅利葉轉換後很明顯的與角度有關。 而這個結果可以直接用於解釋非彈性x光散射實驗角度相依性的由來. 為了更進一步有效率的求得強交互作用系統中的線性響應函數, 我們將提出一個新的構想那就是”等效的雙粒子跳躍核心因子” . 這個等效的核心因子包含了所有激子如何移動的資訊而且也是造成局域化線性響應方程變寬的主要原因之一. 這個一般性的理論可以直接運用於描述強關聯系統裡局域化的激發態行為中
英文摘要 Using the combination of GW approximation and solving Bathe-Salpeter equation (BSE) in different bases (Plane-wave or Wannier bases), we perform ab inito excitation calculations for alkali halides with taking into account the many-body effects.
A general new first-principles Wannier function method is proposed to explore the propagation of strongly bound Frenkel excitions. Specifically, long-standing debate of the Frenkel nature of the excitons can be explained well under this framework. Even the electron-hole pair in the alkali halides (such as LiF) is not bound through an on-site interaction its strongly localized excitonic character can be studied by the formation of a “super-atom” consisting of Wannier orbitals from both Li and F atoms. We find strongly angular dependence of the excitons by means of a direct product of the Fourier transform of the local particle-hole wave function. This result can straightforward explain the angular resolved inelastic x-ray scattering experiment. Furthermore, in order to solve response function of strongly interacting system within the linear response scheme more effectively, a new approach is proposed by formulating the “effective two-particle kinetic kernel” which contains all the mobility information of excitons. This general theoretical framework can be directly applied to the study of propagation of local excitations of strongly correlated systems.
論文目次 Contents
Chapter 0 Introduction 1
1.1 Non-Relativistic Hamiltonian 2
1.1.1 The Lagrangian for many-body system 2
1.1.2 Non-relativistic Hamiltonian 2
1.1.3 Model Hamiltonian for electrons 4
1.2 Experiment 7
1.2.1 Non-resonance inelastic photon scattering 7
Chapter 2 Linear Density Response and Many-body theorem 10
2.1 Linear density response function 10
2.1.1 Time dependent perturbation theory (TDPT) 10
2.1.2 Density-density response function 11
2.1.3 Excitation energy of N-particle system [Lehmann representation] 13
2.1.4 Electron-hole correlation function( L ) and time-order density-density response function 15
2.2 Bethe-Salpter equation and Electron-hole correlation function ( L ) 22
2.3 Luttinger-Ward “free-energy” 25
Chapter 3 First-principles calculation under plane-wave basis 27
3.1 Introduction 27
3.2 Quasi-particle energy correction 29
3.3 Effective two-particle Hamiltonian for BSE 30
3.4 The GW and BSE calculation for LiF and KBr system 32
3.5 Summary 39
Chapter 4 First-principles Wannier function approach 40
4.1 Introduction 40
4.2.1 Generate Green’s function G0 in Wannier basis 43
4.2.2 Electronic band structure in Wannier basis 44
4.2.3 The super-atom approximation 47
4.3 Matrix element and susceptibility 49
4.3.1 Fourier transform of charge susceptibility χ 49
4.3.2 Matrix element in real space and momentum space 51
4.4 Exciton mobility 53
4.4.1 Kernel separating in BSE 53
4.4.2 Two-particle kinetic kernel T 54
4.4.6 F-T from frequency domain to time domain of retarded density response function 67
4.4.7 The propagations of the excion along different directions 69
4.5 Summary 73
Chapter5 Conclusion 75
Bibliography 77


List of Figures
FIG. 2. 1 FEYNMAN DIAGRAM OF TWO PARTICLE GREEN’S FUNCTION G(1,2;1+,2+) 21
FIG. 2. 2 BSE FEYNMAN DIAGRAM 25
FIG. 2. 3 LUTTINGER-WARD FREE-ENERGY FUNCTION WITHIN HATREE-FOCK AND SHIELDED INTERACTION APPROXIMATION 26
FIG. 2. 4 SELF-ENERGY WITHIN HATREE-FOCK AND SHIELDED INTERACTION APPROXIMATION. 26
FIG. 2. 5 BSE-KERNEL WITHIN HATREE-FOCK AND SHIELDED INTERACTION APPROXIMATION. 26
FIG. 3. 1 THE BAND STRUCTURE CALCULATION AND GW CORRECTION FOR LIF 35
FIG. 3. 2 GW CORRECTION ON DIFFERENT ENERGY FOR LIF 35
FIG. 3. 3 THE REAL PART OF LIF DIELECTRIC FUNCTION WITH AND WITHOUT ELECTRON-HOLE INTERACTIOIN 36
FIG. 3. 4 CALCULATED OPTICAL ABSORPTION SPECTRUM OF LIF WITH AND WITHOUT ELECTRON-HOLE INTERACTION. 36
FIG. 3. 5 THE BAND STRUCTURE CALCULATION AND GW CORRECTION FOR KBR 37
FIG. 3. 6 GW CORRECTION ON DIFFERENT ENERGY FOR KBR 37
FIG. 3. 7 THE REAL PART OF KBR DIELECTRIC FUNCTION WITH AND WITHOUT ELECTRON-HOLE INTERACTION 38
FIG. 3. 8 CALCULATED OPTICAL ABSORPTION SPECTRUM OF KBR WITH AND WITHOUGHT ELECTRON-HOLE INTERACTION. 38
FIG. 4. 1 NRIXS DATA FOR LIF WITH DIFFERENT MOMENTUM TRANSFER ALONG DIRECTION. 41
FIG. 4. 2 NRIXS 2D DATA FOR LIF WITH DIFFERENT MOMENTUM TRANSFER ALONG DIRECTION. 41
FIG. 4. 3 FULL POTENTIAL LDA CALCULATION FROM WIEN2K CODE. THE BLUE CIRCLES THAT HIGHER AND LOWER THAN FERMI LEVEL REPRESENTS THE LI 2S-ORBITAL CONTRIBUTION AND F 2P-ORBITAL CONTRIBUTION RESPECTIVELY. OTHER CONTRIBUTION BESIDE BLUE CIRCLES, WHICH BETWEEN ENERGY WINDOW FROM 5~20 EV IS COMES FROM PART OF LI 2P-ORBITAL. 42
FIG. 4. 4 LIF BAND STRUCTURE 46
FIG. 4. 5 FCC PRIMITIVE UNIT CELL AND PRIMITIVE 1ST –BRILLOUIN-ZONE K-POINT PATH. 46
FIG. 4. 6 SUPER-ATOM WANNIER FUNCTION FOR CONDUCTION BAND 48
FIG. 4. 7 SUPER-ATOM WANIIER FUNCTION FOR VALANCE BAND 48
FIG. 4. 8 VISUALIZE EXCITON WAVE-FUNCTION IN REAL SPACE. THE LATTICE CONSTANT A=3.99 Å. 51
FIG. 4. 9 VISUALIZATION OF EXCITON WAVE-FUNCTION IN MOMENTUM SPACE. NOTE THAT THE UNIT LENGTH IS 2Π/A. 52
FIG. 4. 10 EFFECTIVE TWO PARTICLE KINETIC KERNEL T 55
FIG. 4. 11 PROPAGATION OF AN EXCITON 55
FIG. 4. 12 THEORETICAL CALCULATION FOR AND STRUCTURE FACTOR ON KX-KZ PLANE. NOTE THE UNIT OF KZ-AXIS IS BOTH FOR UPPER AND LOWER DIAGRAM, AND THE UNIT OF Y-AXIS IS EV FOR LOWER DIAGRAM. 57
FIG. 4. 13 INFORMATION OF T00 REAL PART 59
FIG. 4. 14 INFORMATION OF REAL PART T AT DIFFERENT N.N. 60
FIG. 4. 15 INFORMATION OF IM PART T AT DIFFERENT N.N. 61
FIG. 4.16 THE BLACK CURVE IS THE REAL PART OF . THE BLACK CIRCLE IS THE ORIGINAL POLE WITH ENERGY OF EXCITON. THE RED CIRCLE IS THE NEW POLE WITH ENERGY OF EXCITON AFTER CONSIDER THE LOCAL INTERACTION OF , THAT IS UDIG.. 63
FIG. 4. 17 THE BLACK CURVE IS THE REAL PART OF TDIAG . THE RED CIRCLE IS THE POLE WITH ENERGY OF EXCITON AND THE BLUE CIRCLE IS THE NEWER POLE WITH ENERGY OF EXCITON AFTER CONSIDERS TLOCAL EFFECT. THE EQUATION OF GREEN LINE IS . 64
FIG. 4. 18 POLARIZATION PROPAGATION ALONG QZ DIRECTION IN LIF SYSTEM. 66
FIG. 4. 19 THE BEHAVIOR OF IMAGERY PART 67
FIG. 4. 20 THE IMAGERY AND REAL PART OF WITH REAL-PART CURVE COLORED RED AND THE IMAGINARY-PART COLORED GREEN. 68
FIG. 4. 21 THE BEHAVIOR OF IMAGERY PART 68
FIG. 4. 22 THE IMAGERY(RED LINE) AND REAL PART(GREEN LINE) OF 69
FIG. 4. 23 ON SITE PROPAGATION OF 71
FIG. 4. 24 PROPAGATION ALONG [011] DIRECTION. 72
FIG. 4. 25 PROPAGATION ALONG [001] DIRECTION. 72
FIG. 4. 26 L0;(0,0.5,0.5) , THE HOPPING PATHS OF EXCITON FROM ORIGIN TO R=(0,0.5,0.5)A 73



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