- 學位論文
二維材料緊密束縛法能帶參數化之研究
Theoretical studies of the parameterized tight-binding model for the band structures of 2D materials
摘要
在電子能帶理論中，緊密束縛模型(Tight-binding model) 是一個較為廣為人知的參數化模型。該模型是以原子軌域相關函數為波函數基底，並在此基底下建構漢米爾頓矩陣(Hamiltonian matrix)，從而求解其特徵值獲得相應之能帶圖形。 本論文利用Wannie90 軟體， 將第一原理(First Principles)的計算結果轉換成緊密束縛模型，再藉由 Least squares method的擬合方法，尋找與第一原理(First Principles)的能帶相擬合的模型參數。 本論文將探討擬合參數的唯一性及如何最小化擬合參數的數目。
並列摘要
The tight-binding model is an empirical band theory that is formulated on the basis of the linear combination of atomic orbitals and in terms of the limited number of fitting parameters. The parametrized model is advantageous because of its simplicity and its ability to interpret transparent physical pictures in real spaces; the model is also widely used for the calculation of band structures of solids. However, the usefulness of the tight-binding model is limited by the nonuniqueness and nontransferability of the empirical parameters that are typically determined by the first principles (FP) or experimental results. Herein, I used the open package “Wannier90” to transform the FP VASP-calculated band structure of hexagonal BN monolayer into a tight-binding model. Then, I employed the least-squares method to determine the fitting parameters of the FP-based energy bands and the tight-binding Hamiltonian matrix of the two-dimensional material. Moreover, I discuss the uniqueness of the fitting parameters encountered in the approach and the validity of the minimal model with a reduced number of fitting parameters.