固態之聲子與電聲子計算:密度泛函微擾理論之研究

Phonon and electron-phonon coupling calculations in solids : Density-Functional Perturbation Theory study

李世綸(Shih-Lun Lee)

指導教授 ： 薛宏中

淡江大學/理學院/物理學系碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00831

摘要

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。

關鍵字

聲子 ； 超導相變溫度 ； 密度泛函微擾論

並列摘要

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.

並列關鍵字

phonon ； electron-phonon coupling ； linear response

參考文獻

[1] Richard M. Martin, “Electronic structure”, Chapter 6, 2004

[2] W. Kohn and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects”, Phys. Rev. 140:1133, 1965

[3] Richard M. Martin, “Electronic structure”, Chapter 8, 2004

[4] M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopouios,“Iterative minimization techniques for ab initio total energy calculations molecular dynamics and conjugate gradients” Phys. Rev. Mod. 64:1045, 1992

[5] A. K. Ghatak and L. S. Kothari, “An introduction to lattice dynamics”, Chapter 5, 1971