吸附原子石墨烯系統中能谷和自旋霍爾效應共存現象的研究

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研究生：	張先鵬 Zhang, Xian Peng
論文名稱：	吸附原子石墨烯系統中能谷和自旋霍爾效應共存現象的研究 Coexistence of valley and spin Hall effects in graphene decorated with adatoms
指導教授：	米格爾 Miguel A. Cazalilla
口試委員:	郭瑞年 Kuo, Ray Nien 唐述中 Tang, Shu Jung 王道維 Wang, Daw Wei
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2016
畢業學年度：	104
語文別：	英文
論文頁數：	47
中文關鍵詞：	能谷霍爾效應、自旋霍爾效應
外文關鍵詞：	Valley Hall effect, Spin Hall effect
相關次數：	點閱：2 下載：0
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我們研究了石墨烯系統中任意分佈的吸附原子的電流響應。我們發現局部的吸附原子如果能誘導自旋軌道耦合并破壞子晶格反演對稱性的話，我們能觀測到能谷和自旋霍爾效應共存現象。我們構造了一個非常簡單的模型去研究這種共存現象，并解釋了最近實驗室上倍受爭議的非局域電信號的物理起源問題。

We show that in the presence of random impurities that both break the sub-lattice inversion symmetry and induce spin orbit coupling, graphene can sustain both spin and valley currents. We develop a simple model to investigate the coexistence of the classical spin and valley Hall effects. Our results are relevant for the existing experimental controversy concerning the origin of the non-local signals observed in graphene devices decorated with various types of adsorbates.

Introduction 
1 Classical and quantum Hall Hall effect …………………………………………5
1.1 Classical Hall effect CHE) ……………………………………………………………………5
1.2 Quantum Hall effect (QHE) ………………………………………………………………………6
2 Classical and quantum spin Hall effects ………………………………………7
2.1 Classical spin Hall effect (CSHE) …………………………………………………7
2.2 Quantum spin Hall effects (QSHE) ……………………………………………………8
3 Quantum valley Hall effect (QVHE) ………………………………………………………9
4 Motivations for this work …………………………………………………………………………10
Physical model ……………………………………………………………………………………………………………14
1 Graphene model ………………………………………………………………………………………………………14
2 Extrinsic localized …………………………………………………………………………………………16
Scattering theory ……………………………………………………………………………………………………18
1 Lippmann-Schwinger equation ……………………………………………………………………18
2 T-matrix ………………………………………………………………………………………………………………………20
Semi-classical Boltzmann equation …………………………………………………………23
1 The classical valley Hall effect ………………………………………………………23
2 Coexistence of spin and valley Hall effects …………………………29
Quantum Boltzmann equation ……………………………………………………………………………34
1 Quantum Boltzmann equation ………………………………………………………………………34
1.1 Uniform quantum Boltamann equation ……………………………………………36
1.2 Non-uniform quantum Boltzmann equation …………………………………37
2 A model for the diffusion source ………………………………………………………38
3 Second-order approximation  …………………………………………………………………40
4 Higher-order approximation  ……………………………………………………………………42
Summary and conclusion ……………………………………………………………………………………47
                                

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