本論文探討 Su-Schrieffer-Heeger (SSH) 模型以及其相關的推廣模型的邊緣態。當引入實數布洛赫波向量時，根據週期性邊界條件所導出的哈密頓算符僅能得到系統之拓樸與體態能譜，得不到邊緣態能譜與邊緣態解。一般而言，後者必須藉由開放性邊界條件在開鍊情況下才能解出。引入了複數布洛赫波向量後，就可以藉由解析週期性哈密頓算符而解出對應於開放性邊界條件中的邊緣態。本篇探討的系統，除了原始的 SSH 模型外，還有具有 PT 對稱之 SSH 模型以及利用左右躍遷不對稱之非厄米特 SSH 模型。引入複數布洛赫波向量能使週期性邊界條件與開放性邊界條件的物理有對應關係。

This thesis investigates the edge states of the Su-Schrieffer-Heeger (SSH) model and its related extended models. When real Bloch wave vectors are introduced, the
Hamiltonian derived from periodic boundary conditions can only obtain the system's topology and bulk energy spectrum, but not the edge state energy spectrum and edge state solutions. Generally, the latter must be solved using open boundary conditions in an open chain scenario. However, by introducing complex Bloch wave vectors, the edge states corresponding to those in open boundary conditions can be obtained through analytic continuation of the periodic Hamiltonian. This study examines not only the original SSH model but also the PT-symmetric SSH model and the non-Hermitian SSH model with nonreciprocal left and right hopping coefficients. The introduction of complex Bloch wave vectors enables a correspondence between the physics of periodic boundary conditions and open boundary conditions.

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