一維non-Hermitian 拓樸模型

Abstract

本文首先介紹在一維拓樸絕緣體常討論的Su-Schrieffer-Heeger (SSH) model以及其推廣的模型，我們可以用bulk-edge correspondence去預測拓樸系統中邊界態數目。接下來將上述的模型推廣到non-Hermitian (NH)的形式，我們發現在NH系統中存在skin effect以及exceptional point，這些是當系統為Hermitian時不具有的性質。我們利用解析解計算研究exceptional points (EPs)在不同的模型下出現的條件，並了解其性質。

In this thesis we will introduce the Su-Schrieffer-Heeger (SSH) model, which is a prototype of one dimension topological insulator and its extended versions. It is known that bulk-edge correspondence may be used to predict the number of edge state on the boundary of a topological system. Next we extended these models to non-Hermitian (NH) Form, we found that in a NH system there exists skin effect and exceptional points which cannot be found in a Hermitian system. We use analytical calculation to find the condition of exceptional points (EPs) in different models, and study their property.