非厄米特三階方形拓樸電路系統之研究;The Research of Non-Hermitian Third-Order Topological Square-Lattice Electric Circuit Systems

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题名:	非厄米特三階方形拓樸電路系統之研究;The Research of Non-Hermitian Third-Order Topological Square-Lattice Electric Circuit Systems
作者:	吳崇瑋;Wu, Chung-Wei
贡献者:	光電科學與工程學系
关键词:	拓樸;非厄米特;三階方形;電路;Topological;Non-Hermitian;Third-Order;Circuit Systems
日期:	2025-07-07
上传时间:	2025-10-17 11:43:09 (UTC+8)
出版者:	國立中央大學
摘要:	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.
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