第一原理計算在研究固態系統有著不可或缺的貢獻，隨著科技進步，計算的速度也有顯著的提升，使得我們能使用更精確的計算方式，又或是能計算更複雜的系統，本文將以此方法計算二維異質結構的能帶變化，結構的組成為兩片磁性或過渡金屬二硫化物中夾了雙層的石墨烯或類石墨烯材料，研究主要著重在費米能量附近的狄拉克椎能帶結構，此能帶來自於中間的雙層石墨烯或類石墨烯材料，而上下兩層材料則可視為是影響能帶分裂的工具。
影響的方式分為電子的交換耦合和自旋軌道耦合，自旋軌道耦合的影響可分為Rashba和Ising兩種，而自旋軌道耦合和交換耦合會產生不同的能量分裂現象，在過去大都認為Rashba和Ising的能量分裂來自於自旋軌道耦合，然而近幾年的研究顯示，以磁性材料(交換耦合)也能形成類似的能帶分裂現象。
此研究將由石墨烯與類石墨烯材料的電子能帶結構出發，一步步嘗試由不同的材料組成異質結構，來對比石墨烯與某些類石墨烯材料的能帶表現，然後以此做為基礎，在排除電子自旋軌道耦合影響的情況下，調整磁性材料中，各原子的磁矩結構，使得二維材料的能帶呈現出類似Rashba或Ising自旋軌道耦合的特徵。

Ab initio calculations have made indispensable contributions to the study of solid-state systems. With advancements in technology, computational speed has significantly improved, allowing us to employ more accurate calculation methods and tackle more complex systems. In this study, we utilize this approach to calculate the band structure variations of two-dimensional heterostructures. The structures consist of bilayer graphene or graphene-like materials sandwiched between two magnetic or transition metal dichalcogenide layers. Our focus is primarily on the Dirac cone band structure near the Fermi energy, which arises from the intermediate bilayer graphene or graphene-like material, while the upper and lower layers act as tools affecting the band splitting.
The influences can be categorized into electronic exchange coupling and spin-orbit coupling. The effects of spin-orbit coupling can be further classified into Rashba and Ising types. It has been commonly believed that the energy splitting associated with Rashba and Ising arises from spin-orbit coupling. However, recent research has shown that similar band splitting phenomena can also be induced by magnetic materials (exchange coupling).
This study starts from the electronic band structures of graphene and graphene-like materials, systematically explores heterostructures composed of different materials, and compares the band behaviors with those of graphene and certain graphene-like materials. Based on these findings, we adjust the magnetic moment structures of the magnetic materials, excluding the influence of electron spin-orbit coupling, in order to achieve Rashba or Ising-like spin-orbit coupling characteristics in the two-dimensional materials.

摘要 i
Abstract ii
第一章 簡介 1
第二章 計算方法與理論 7
2.1 第一原理計算方法 7
2.2 密度泛函理論的細節 9
2.2 密度泛函理論的一些修正方法 10
2.4 反轉對稱破壞 12
第三章 雙層石墨烯與類雙層石墨烯結構材料 14
3.1 雙層石墨烯能帶 14
3.2 類雙層石墨烯結構之材料 15
第四章 四層異質結構計算 20
4.1 結構說明 20
4.2 磁性材料 21
4.2.1 BLG+VI2 21
4.2.2 雙層矽烯+VI2 25
4.2.3 雙層鍺烯+VI2 30
4.3 過渡金屬二硫化合物 32
4.3.1 BLG+MoTe2 32
4.3.2 雙層矽烯+MoSe2 34
4.3.3 雙層鍺烯+MoTe2 49
4.4 總結 54
第五章 反鐵磁計算 56
5.1 石墨烯 56
第六章 結論 60
參考資料 62

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