本論文研究利用拓樸學的物理特性，探討二維三階非厄米特拓樸絕緣體 （third-order Non-Hermitian topological insulator）。 首先說明厄米特與非厄米特拓 樸矩陣的差異，進一步比較一維與二維系統的特性，並從開邊界條件觀察邊界 態，藉由週期邊界條件找出對應的晶格結構。接著，我們在方形結構中加入電路 元件以實現拓樸絕緣體，將原本每兩個節點間的電容與電阻並聯改為串聯。利用 克希荷夫電路定律（Kirchhoff′s circuit laws）推導出哈密頓矩陣（Hamiltonian matrix）， 得到三階非厄米特矩陣，進而解出其本徵值（eigenvalue）與本徵向量 （eigenvector）。 最後觀察此電路系統模態（modes）的變化，並分析其邊緣態與 角態是否存在。;This thesis explores the use of topological physics to study a two-dimensional third order non-Hermitian topological insulator. We begin by explaining the differences between Hermitian and non-Hermitian topological matrices, then compare the characteristics of one-dimensional and two-dimensional systems. Boundary states are examined under open boundary conditions, while the corresponding lattice structure is identified using periodic boundary conditions. Next, a square structure is constructed with circuit elements to realize the topological insulator, where the originally parallel connection of capacitors and resistors between each pair of nodes is changed to a series connection. Kirchhoff′s circuit laws are applied to derive the Hamiltonian matrix, resulting in a third-order non-Hermitian matrix. The eigenvalues and eigenvectors are then obtained. Finally, we observe changes in the system’s modes and analyze the existence of edge and corner states.
