本論文以拓樸能帶理論為基礎，探討在蜂窩晶格系統中引入第三種原子所形成之正三角晶格的能帶結構與拓樸邊緣態性質。首先回顧SSH、Haldane與Kane-Mele模型在一維與二維系統中的拓樸行為，並介紹卷繞數與陳數等拓樸不變量。接著推導正三角晶格的緊束縛哈密頓量，分析不同躍遷強度與原子位能對能帶結構及邊緣態分佈的影響。最後進一步將Floquet週期性驅動引入正三角晶格系統作分析，結果顯示即使在靜態情況下為拓樸平凡系統，仍可透過週期性驅動誘發具有手徵性的Floquet拓樸邊緣態。;This paper is based on topological band theory to explore the band structure and topological edge states of a honeycomb lattice system when a third type of atom is introduced to form a regular triangular lattice. First, the topological behaviors of the Su-Schrieffer-Heeger, Haldane, and Kane-Mele models in one-dimensional and two-dimensional systems are reviewed, along with an introduction to topological invariants such as winding numbers and Chern numbers. Next, the tight-binding Hamiltonian for the regular triangular lattice is derived, and the effects of different hopping strengths and atomic potentials on the band structure and edge state distribution are analyzed. Finally, the Floquet periodic driving is further introduced into the regular triangular lattice system for analysis. The results show that even when the system is topologically trivial in a static state, Floquet topological edge states with chiral characteristics can still be induced through periodic driving.
