本研究是在探討拓樸極化的計算方法，並加以分析拓樸邊緣態與拓樸角態之 間的相互關聯性，為了詳細研究拓樸極化，本研究選擇了正方晶格，並分別在正 方晶格x方向和y方向的上對波向量分量進行劃分，我們將其切成25等分，每個 分點的波向量值都會計算出其相對應的札克相。 在計算得到相對應的札克相後，我們進一步對其進行平均值的處理，我們通 過求取這些25個分點札克相的平均值，將其代入拓樸極化的公式中，從而計算得 到拓樸極化𝑃 ⃑ =(𝑃𝑥，𝑃𝑦)的具體數值。 透過這些計算結果，我們驗證了不同的拓樸結構下之極化特性，並且進一步 去觀察這些特性是否與拓樸邊緣態與拓樸角態的出現相符。

This study explores the computational methods for topological polarization and analyzes the correlation between topological edge states and topological corner states. To study topological polarization in detail, we chose a square lattice and divided the wavevector components along both the x and y directions of the lattice. The wavevector was divided into 25 segments, and for each point, the corresponding Zak phase was calculated. After calculating the corresponding Zak phases, we further averaged these values. By calculating the average of the Zak phases at these 25 points, we substituted the values into the formula for topological polarization to compute the specific values of topological polarization 𝑃 ⃑ = (𝑃𝑥，𝑃𝑦). Through these calculations, we validated the polarization characteristics under different topological structures and further observed whether these characteristics were consistent with the emergence of topological edge states and topological corner states.

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