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研究生: 王奕鈞
Wang, Yi-Chun
論文名稱: 電子對和聲子的交互作用研究
A Study of Electron Pair and Phonon Interaction
指導教授: 許正餘
Hsu, Jang-Yu
學位類別: 碩士
Master
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2014
畢業學年度: 102
語文別: 英文
論文頁數: 51
中文關鍵詞: 超導現象庫柏對擴散蒙地卡羅法
外文關鍵詞: Superconductivity, Cooper Pair, Diffusion Monte Carlo
相關次數: 點閱:105下載:6
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  • 二硼化鎂的超導臨界溫度相對高於其他常規超導,再加上分子結構相對於其他高溫超導體簡單許多,這有助於我們重新檢查常規超導的BCS理論與高溫超導之間的關聯。我們重新假定BCS理論的庫柏對是由單位晶胞裡的一對電子和裸聲子零點能交互作用形成,但這樣的模型並不如預期的形成庫柏對。接下來採用更接近庫珀的模型,改為討論一對電子和穿衣粒子的交互作用,其中穿衣粒子為包含離子聲波的準粒子。這個模型中,晶格震盪的零點能和離子電漿頻率之間的比例,會影響是否形成超導態。

    The relatively high critical temperature and simple structure of MgB2 superconductor motivated the current study to revisit the BCS theory. The Cooper pair effect is reexamined by studying the interaction of an electron pair and a bare phonon of zero point energy (ZPE) in a unit cell. It is found that there is no Cooper pair effect in this theoretical model. The interaction of electron pair of dressed particle model that includes the ion sound wave and the electron screening is proposed that reveals similar effect as Cooper originally suggested. The effect of ZPE is to be included in this latter model and it suggests the importance of the ratio of ion plasma frequency and the lattice oscillation frequency of ZPE.

    Ch1. Introduction 1 1.1. Superconductivity 1 1.2. The Room Temperature Superconductor 2 1.3. The Diboride Superconductor 3 1.4. Purpose of this Study 4 1.5. Cooper pair 5 Ch2. Theoretical Approach 9 2.1. variational principle 9 2.2. Monte Carlo method 10 Ch3. Diffusion Quantum Monte Carlo 12 3.1. Theory 12 3.2. Algorithm 15 3.3. Examples 16 3.3.1. 1-D harmonic oscillator 16 3.3.2. Hydrogen Atom 17 3.3.3. 3-D harmonic oscillator 18 CH4. Electron Pair 20 4.1. The variational method 20 4.2. Diffusion quantum Monte Carlo method 21 Ch5. Interaction of Electron Pair and Bare Phonon 25 5.1. The variational method analysis 26 5.2. Quantum diffusion Monte Carlo method analysis 29 5.2.1 The preliminary analysis of interaction 29 5.2.2. The improvement of DQMC 31 5.2.3. The algorithm result 32 Ch6. Interaction of dressed particles 36 6.1. Electron Pair and Phonon Sea 36 6.2. Electron-Electron Interaction under Phonon Sea 38 Ch7. Conclusion 41 Appendix 42 Appendix A (London equation) 42 Appendix B (Ginzburg-Landau Equation) 43 Appendix C (Phonon) 46

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