二十世紀量子力學的發展，使我們能夠以量子的角度去探討材料的特性。
在1970 年代，密度泛函數理論有了堅實的理論基礎，被廣泛應用於凝態材料計
算領域，造就不需要實驗提供任何參數的第一原理蓬勃發展。
本文是對真實存在的材料鉍化鎳與鉍化鉑進行拓樸與超導特性的研究。理論
預測鉍化鎳與鉍化鉑金屬為具有 Z2 拓樸的電子聲子超導體。兩材料在塊材電
子能帶上有狄拉克點，並於表面電子能帶上有拓樸的表面態，判別兩材料屬於
拓樸狄拉克半金屬。利用威爾遜迴圈方法，觀察瓦尼爾函數中心演變判別兩材
料屬於強拓樸狄拉克半金屬且Z2拓樸數為1。利用電子聲子耦合的一階近似計
算，由麥克米蘭-艾倫-戴恩斯超導溫度公式判別兩材料屬於弱耦合的電子聲子
超導體。懷疑兼具超導與拓樸的材料比想像更加豐富，展望新穎材料能運用於
未來尖端科技。

The development of quantum mechanics in the twentieth century allowed us to explore the properties of materials from a quantum perspective. In the 1970s, density functional theory (DFT) had a solid theoretical foundation and was widely used in the field of condensed material calculations, making the first principle to flourish. This thesis is mainly to study the topological and superconducting properties of real materials. It is predicted that the NiBi and PtBi metals are electron-phonon superconductors with Z2 topology. Using the Wilson loop method and the electronic band structure to distinguish that both belong to the strong topological Dirac semimetal materials and use the McMillan-Allen-Dynes superconducting temperature formula
to distinguish that both belong weakly coupled electron-phonon superconductors. I suspect that materials with both topology and superconductivity are richer than imagined. Looking forward novel materials can be applied to most advanced science and technology in the future.

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