在這個論文中我們透過格林函數研究了三種不同切口的奈米碳管的態密度及局部態 密度。這三種切口分別為：(1) 正切 (n, n) 扶倚奈米碳管、(2) 正切 (n, n) 鋸齒奈米碳 管以及 (3) 斜切 (n, n) 扶倚奈米碳管。我們透過兩種方法計算格林函數：(1) 迭代法以 及 (2) 積分法，其中迭代法利用到半無限系統的幾何自相似的特質，而積分法則是把石 墨烯上的 k 態來線性組合成符合邊界條件的態並對所有允許的態除以 (E − E λ k + i η ) 求 和。透過比較態密度與局部態密度我們發現在正切扶倚奈米碳管有週期性震盪、正切 鋸齒奈米碳管有邊界態，而這兩個現象在斜切扶椅奈米碳管都有發現。我們並利用拿 表面格林函數來研究斜切 (8, 8) 扶倚奈米碳管的透射率。

In this thesis, we study the density of states (DOS) and the local density of states (LDOS) of three different types of carbon nanotube (CNT electrodes): (1) cross-cut (n, n) armchair CNTs, (2) cross-cut (n, 0) zigzag CNTs, (3) angle-cut (n, n) armchair CNTs, by exploiting the relation between the Green’s function and the DOS. We employ two ways to calculate the Green’s function : (1) The iterative method which makes use of the recursive structure of a semi-infinte system, and (2) the integration method, through which we construct linear combined wavefunctions out of bulk CNT states, so as to meet the boundary conditions of the cut. By comparing the DOS and the LDOS we find oscillations of a 3-layer cycle in cross-cut armchair CNTs and localized edge states in both cross-cut zigzag CNTs and in angle-cut armchair CNTs. The surface Green’s functions calculated in this work are used in the study of transmission, also performed in our group.

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