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研究生: 詹敦皓
Chan, Tun-Hao
論文名稱: 格林函數在不同切口奈米碳管的研究
Green’s Function Study for Carbon Nanotube Leads of Various cuts
指導教授: 陳穎叡
Chen, Yiing-Rei
學位類別: 碩士
Master
系所名稱: 物理學系
Department of Physics
論文出版年: 2020
畢業學年度: 108
語文別: 英文
論文頁數: 50
中文關鍵詞: 奈米碳管格林函數態密度緊束縛模型邊界態
英文關鍵詞: carbon nanotubes, Green's funciton, density of states, tight-binding method, edge states
DOI URL: http://doi.org/10.6345/NTNU202001086
論文種類: 學術論文
相關次數: 點閱:98下載:0
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  • 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.

    摘要 i Abstract ii 致謝 iii Contents iv 1 Introduction 1 2 Theory 3 2.1 Density of State 3 2.2 Non-Equilibrium Green’s Functions formalism 4 2.3 Surface Green’s Function 6 2.4 Green’s function and response 8 2.5 Transmission and Current 9 2.5.1 Device’s response when having an incoming wavefunction 9 2.5.2 Current 11 3 Method 13 3.1 System configuration 13 3.2 Tight-Binding Model 15 3.3 Iteration 15 3.4 Integration 16 3.5 Comparing Results 18 4 Result and Discussion 19 4.1 Density of States with Respect to Energy 19 4.2 Bulk Density of States 19 4.2.1 Armchair CNTs 19 4.2.2 Zigzag CNTs 24 4.3 Local Density of State of the outermost layer 29 4.3.1 Cross-cut Armchair CNT 30 4.3.2 Cross-cut Zigzag CNT 32 4.3.3 Angled-Cut Armchair CNT 34 4.4 Local Density of State with Respect to Layers 36 4.4.1 Cross-Cut Armchair CNT 36 4.4.2 Cross-Cut Zigzag CNT 37 4.4.3 Angled-Cut Armchair CNT 40 4.5 Transmission 42 4.5.1 Bulk (8, 8) Armchair CNT Transmission 43 4.5.2 Transmission of Angled-Cut (8,8) Armchair CNT leads Through Polyene Junction 43 4.5.3 Transmission of Cross-Cut (12,0) zigzag CNT leads Through Polyene Junction 46 5 Conclusion 47 Bibliography 49

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