高賢忠Kao, Hsien-Chung張家勳Chang, Chia-Hsun2020-10-192022-08-312020-10-192020http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22G060641041S%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/111380當塊材具有拓樸性質時，其對應的邊界上會存在邊界態，這就是所謂的「塊材與邊 界對應性」。此對應可由簡單的一維模型 − SSH 模型或 extended SSH 模型來做驗證。 我們嘗試將一維 SSH 長鏈交錯編織以推廣成二維系統，並稱之為二維 SSH 模型。 我們發現透過調整二維 SSH 模型的參數，系統有可能為半金屬，弱拓樸絕緣體或 是一般的絕緣體。由於二維 SSH 模型具有時間反演對稱性，我們利用這個特性定義出 一個強拓樸量與兩個弱拓樸量，並用它們來為系統做分類。此外，我們也發現這個分 類方法等價於一個圖像化的分類方式。利用數值方法，我們驗證了二維 SSH 模型的塊 材與邊界對應性。最後，當選取特定的參數與邊界條件時，可以得出不同邊界型態的 奈米碳管的結果。When a system carries non-vanishing topological numbers in the bulk, there will be edge states on the boundary. This is the so-called bulk-edge correspondence. It can be verified explicitly by using the 1D SSH or extended SSH models. In this thesis, we consider the 2D-SSH model which may be constructed by interweaving the 1D SSH chains into a two dimensional system. For the 2D-SSH model, we find that it can be a semimetal, weak topological insulator or trivial insulator depending on the values of the parameters. Because the 2D-SSH model has time reversal symmetry, we may use this to define a strong topological number and two weak topological numbers. We can classify the system by using these topological numbers. Furthermore, we also show that this is equivalent to a graphical way to classify the system. We use numerical calculation to verify the bulk-edge correspondence for the 2D-SSH model. Finally, we can reproduce the results of various carbon nanotubes by choosing specific parameters and boundary conditions.SSH 模型Extended SSH 模型塊材與邊界對應性半金屬弱拓樸絕緣體時間反演對稱性奈米碳管SSH modelExtended SSH modelBulk-edge correspondenceSemimetalWeak topological insulatorTime reversal symmetryGraphene nanotube