本研究藉由計算過渡金屬二硫族化物(TMDs)的超導溫度，了解其性質，與現有實驗文獻做比較後，得知TMDs材料結構對超導溫度的影響，由此為基礎尋找具發展性的超導材料，計算在2001年所發現擁有超導溫度39K的理論計算MgB2 (空間群P6/mmm)，也從中了解本研究方法與結果如何分析，進而發現NbB2、TcB2和LaB2也同樣具有超導現象，NbB2 (塊材/單層)的超導轉變溫度分別為8.2K /9.8K，TcB2 (塊材/單層)的超導轉變溫度分別為22K /3.8K，LaB2 (塊材)的超導轉變溫度為17K，另外TcB2和LaB2在有自旋軌道耦合的模擬計算下，費米能階附近會出現連續間隙，經過計算Z_2拓撲不變量，判定為弱拓撲材料，往後可以繼續研究這些材料是否有多超導間隙或是拓撲表面態。

In this study, we calculated the superconducting temperature of transition metal dichalcogenides (TMDs) and understood their properties. After comparing with the existing experimental literature, we learned the influence on the superconducting temperature by the TMDs. MgB2 found in 2001 with transition temperature of 39K (Space group is P6/mmm). We use the calculation of MgB2 to understand how the research methods and results are analyzed and then found that NbB2, TcB2 and LaB2 also have superconductivity Phenomenon. The superconducting transition temperature of NbB2 (bulk/1 unit layer) is 8.2K and 9.8K. The superconducting transition temperature of TcB2 (bulk/1 unit layer) is 22K and 3.8K. The superconducting transition temperature of LaB2 bulk is 17K. In addition, under the simulation calculation of TcB2 and LaB2 with spin-orbit coupling, there will be continuous gaps near the Fermi level. After calculating Z2 topological invariant, they are determined as the weak topological material. In the future, we can continue to study whether these materials have multiple superconducting gaps or topological surface state.

摘要------------------------------------------------------------i
Abstract--------------------------------------------------------ii
誌謝------------------------------------------------------------iii
第一章-緒論-----------------------------------------------------1
1-1 多體物理理論Many-body Hamiltonian---------------------------1
1-2 近似法Born-Oppenheimer approximation------------------------1
1-3 密度泛函理論Density function theory(DFT)--------------------1
1-4 密度泛函微擾理論Density function Perturbation theory(DFPT)--5
1-5 電子-聲子交互作用與超導溫度---------------------------------7
1-6 Z2拓撲不變量------------------------------------------------8
第二章-理論計算過渡金屬二硫族化物-------------------------------13
2-1 晶體結構----------------------------------------------------13
2-2 能量狀態密度與電子能帶結構----------------------------------13
2-3 聲子能譜與超導溫度------------------------------------------14
2-4 本章節插圖--------------------------------------------------17
第三章-理論計算XB2----------------------------------------------24
3-1 晶體結構----------------------------------------------------24
3-2 能量狀態密度與電子能帶結構----------------------------------24
3-3 聲子能譜與超導溫度------------------------------------------25
3-4 LaB2和TcB2威爾遜迴圈----------------------------------------27
3-5 本章節插圖--------------------------------------------------29
參考文獻--------------------------------------------------------48
附錄------------------------------------------------------------51

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