電子自旋於低維系統之空間行為

本論文致力於具有自旋軌道耦合效應之低維系統中，特別是二維，電子自旋之空間行為的理論研究。在固體中，自旋軌道耦合效應源自許多不同的機制，該機制取決於空間倒置的對稱性是如何被破壞。常見的自旋軌道耦合效應包含可存在於半導體異質結構與金屬表面態的Rashba項，以及只存在半導體的Dresselhaus項。這些自旋軌道耦合效應於自旋傳輸中所引發的許多效應，可大致被歸類為三種：(i)自旋進動、(ii)自旋霍爾效應、(iii)電流誘發自旋極化。本論文即以理論推導、解釋、並圖像化這些現象為目標，基於實驗上合理的參數，藉以總結電子自旋於低維系統在自旋軌道耦合效應下的空間行為。本研究由兩種理論方法譜成：量子力學方法、Landauer-Keldysh方法。量子力學方法中，我們假設具有明確方向自旋的電子被注入到自由電子氣。對於無邊界的系統，點注射的情況下，描述電子自旋之量子期望值且為空間函數的一解析公式可被推導出來。由於注入的電子是自旋極化的，此方法所描述的自旋空間行為將只包含自旋進動的部份。相對的，前述之第(ii)與第(iii)，甚至也包含第(i)現象，將在基於Keldysh非平衡格林函數的Landauer-Keldysh方法中有相當完整的描述。這樣描述下的系統，可以是類似於自由電子氣，也可以是保有晶格結構特性的固體，端看Fermi能階距離能帶底部是遠還是近。本論文盡量以獨立而完備的方向撰寫。在第一章中，我們不僅對此領域，也就是半導體自旋電子學，給一概觀，也為讀者準備了充分但並非必要的背景知識。第二章致力於自由電子氣體模型下，基於量子力學方法的自旋進動研究。相較於物理系研究生皆具備的量子力學，最近才出現此一術語的Landauer-Keldysh方法則需要較詳細的介紹。這將是第三章的主要內容。基於Landauer-Keldysh方法的數值結果則在第四章呈現，所有前面提及的三項自旋現象將被一一囊括。並且，所呈現結果的二維系統包含半導體異質結構以及導體金屬表面態。對於自旋進動的部份，兩種不同方法所得結果的一致性，也將被與以展示。本論文的結論以及未來工作的展望則於第五章作總結。

關鍵字

自旋電子學；自旋進動；自旋軌道耦合效應；自旋霍爾效應

並列摘要

The thesis presents a theoretical study of spatial behavior of electron spin in low dimensional, in particular, two-dimensional systems, subject to the spin-orbit coupling. In solids, spin-orbit coupling stems from different mechanisms, based on how the space inversion symmetry is broken. Commonly referred spin-orbit couplings include the Rashba term, which appears in both semiconductor heterostructures and metallic surface states, and the Dresselhaus term, which appears only in semiconductors. These spin-orbit couplings may induce in the spin transport lots of interesting phenomena, which we categorize into three: (i) spin precession, (ii) spin-Hall effect, (iii) current-induced spin polarization. The thesis mainly aims at theoretically deriving, explaining, and imaging these phenomena, based on experimentally reasonable parameters, in order to summarize the spatial behavior of electron spin in spin-orbit-coupled low-dimensional systems. Two methods compose the study: quantum mechanical approach and Landauer-Keldysh formalism. In the quantum mechanical approach, injected electron with definite spin direction in nearly free electron gas is assumed. An analytical spin vector formula describing the position-dependent quantum expectation value of spin can be derived in the case of point injection in boundless systems. The spatial behavior thus described covers only the spin precession since the injected electrons are spin-polarized. Contrarily, phenomena (ii) and (iii), as well as phenomenon (i), can be well described by the Landauer-Keldysh formalism, which is based on the Keldysh nonequilibrium Green's function approach. The system thus described can either be free-electron-like, or preserve the crystal structure information, depending on the location of the Fermi level relative to the band bottom. This thesis is written in a self-contained way. In chapter 1 we not only give an overview for this field, semiconductor spintronics, but also arm the readers with prerequisite knowledge. Chapter 2 will be devoted to the quantum-mechanical approach for studying spin precession in the nearly-free electron gas. Compared to the quantum-mechanical approach, Landauer-Keldysh formalism is formulated only recently, and hence requires detailed introduction. This will be done in chapter 3. Numerical results based on the Landauer-Keldysh formalism will be presented in chapter 4, where all of the three phenomena are covered for both semiconductor heterostructures and metallic surface states. For the spin precession, the consistency between the two different approaches will also be seen. Conclusion of the present work and outlook for the future works will be summarized in chapter 5.

並列關鍵字

spintronics ； spin-Hall effect ； spin-orbit coupling ； spin precession

參考文獻

M.L. ROUKES, A.Y. CHTCHELKANOVA, AND D.M. TREGER. Spintronics: A

spin-based electronics vision for the future. Science 294, 1488 (2001). 1

[2] MARTIN THORNTON AND MICHAEL ZIESE, editors. “Spin Electronics”. Springer,

Berlin (2001). 1

[3] D. D. AWSCHALOM, D. LOSS, AND N. SAMARTH, editors. “Semiconductor Spintronics

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電子自旋於低維系統之空間行為

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