石墨烯電子具有被稱為能谷類自旋的新自由度，可用於實現能谷電子學—一種利用能谷作為信息載子的電子學。吳教授的團隊提出了一種全電性控制的能谷閘，而其操作原理源自於所謂的“能谷-軌道交互作用（VOI）”電流過濾現象。其將能谷類自旋與平行平面之外加橫向電場耦合，形式恰類似自旋軌道交互作用（SOI）。在本研究中，我們使用最鄰近緊束縛模型模擬單層/雙層扶手椅石墨烯奈米帶（ML/BL AGNR）能谷閘中電子的彈道運輸。能谷閘的基本單元由一對能谷濾波器組成。二濾波器之平面橫向電場方向呈平行或反平行排列。一濾波器“極化”（入射）電子到特定一個能谷，然後根據平行或反平行排列，而讓第二個濾波器放行或阻擋來自第一個濾波器的電子。雜質和缺陷散射是介觀運輸研究中的重要課題。由於大的動量改變才足以“翻轉”能谷類自旋，我們的構架於VOI原理上的能谷閘自然是穩定邏輯閘的最佳之選。此篇論文另探索了各種有關子課題，如界面散射，長距和短距雜質以及粗糙邊緣散射，濾波間間距，雙能谷閘以及單軸應變等方面的影響。

Graphene electrons carry the novel degree of freedom known as valley pseudospin that can be used to implement valleytronics ― electronics with valley pseudospin being the information carrier. Wu’s group has proposed an all electrically driven valley valve that filters current based on the so-called “valley-orbit interaction (VOI)”, which couples valley pseudospin to in-plane, transverse electric field and is an analogue of spin-orbit interaction (SOI). In this study we simulate the ballistic transport of electrons in valves of monolayer/bilayer armchair graphene nanoribbon (ML/BL AGNR), using nearest-neighbor tight-binding model calculation. The basic unit of a valve consists of a pair of valley filters with in-plane, transverse DC electric fields aligned in parallel or anti-parallel. A filter specializes in “polarizing” (the incident) electrons to one of the valleys; a second filter then allows passage of or blocks electrons from the first depending on the parallelism or anti-parallelism, respectively. Impurity and defect scatterings are important issues in mesoscopic transport studies. Owing to the great momentum change it requires to “flip” the valley pseudospin, our VOI-based valley valve is a natural candidate for robust logic gate. Various effects, such as those of interface scattering, long- and short-range impurity and edge roughness scatterings, inter-filter spacing, increasing number of valley filters, and uniaxial strain were explored to verify such point.

ABSTRACT (Chinese) i
ABSTRACT ii
PREFACE & ACKNOWLEDGMENTS iii
CONTENTS iv
I. INTRODUCTION
A. Valley as a Unique Degree of Freedom in Graphitic Systems 1
B. Effective Schrödinger Theory and Valley-Orbit Interaction 1
C. Valley Filter and Valley Valve 1
II. STUDY CATEGORIES AND CONSIDERATIONS
A-C. General Considerations 4
D. Impurity Scattering 7
E. Edge Roughness 8
F. Two valley valves in series (Three-filter layout) 9
G. Inter-filter spacer effect 10
H. Uniform Strain 12
III. THEORETICAL METHOD
A. Formulation of the Electron Transmission Problem 12
B. Probability Current Operator 14
C. Tight-binding Model 16
D. Numerical Test of the Formulation 18
VI. RESULTS
A. VOI in MLG and BLG Valves 20
B. Correspondence between filtering efficiency
and switching capability 26
C. Transverse Fields 29
D. Impurity Scattering
1. Long-range impurity 30
2. Short-range impurity 32
E. Edge Roughness 33
F. Two valley valves in series (Three-filter layout) 36
G. Inter-filter spacer effect 39
H. Uniform strain 44
V. SUMMARY 45
VI. BIBLIOGRAPHY & REFERENCES 47

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