二維材料的電子結構理論研究：第一原理及緊密束縛法計算

Abstract

2004年，單層石墨烯被成功單獨分離出來，開啟了二維材料研究領域的熱潮。若要更深入的認識二維材料的物理特性，電子結構的研究是不可或缺的。我的研究以此為目標，並希望能建立簡單的能帶理論模型。 我的工作主要分為兩個部分： 第一部分，我應用密度泛函理論(Density Functional Theory)，使用VASP軟體，以石墨烯為例，建立單層、雙層，乃至於奈米緞帶結構的電子結構計算方法流程，進而應用於單層及雙層二硫化鉬的能帶計算。 第二部分，我應用第一部分的密度泛函理論計算結果，以石墨烯為例，利用wannier90程序，建構Wannier函數，並以此為基礎，嘗試建立簡單的緊密束縛法模型。 隨著這些基礎的研究方法的建立，期許未來能應用在其他不同的二維材料上。

Until 2004, graphene, an allotrope of carbon in the form of a two-dimensional, was successfully produced by mechanical exfoliation. For "groundbreaking experiments regarding the two-dimensional material graphene," Andre Geim and Konstantin Novoselov, who for the first time produce monolayer graphene, awarded the Nobel Prize in Physics 2010. After the pioneering work, till now, there have been research about different kinds of 2D material, like: Boron nitride, transition-metal dichalcogenide (TMD), etc. The electronic structure studies are important for the understanding of the properties of 2D material. In my work, I use density functional theory(DFT) to calculate the band structure of different type graphene crystal structures, including monolayer, bilayer, and nanoribbon. Also, I calculate the band structure of monolayer MoS2, which is a kind of TMD, in the same way. Based on the DFT calculated results, I employ the package “wannier90”, and construct Wannier functions (WF) by maximally localized Wannier functions method. Using those WFs as basis, I could have a simple Hamiltonian. Even more, fitting parameter in tight-binding model is possible from this Hamiltonian. As an example, monolayer graphene tight-binding band structure with fitting parameter is presented in my work.