自旋相關量子現象:自旋霍爾效應及自旋幫浦

Abstract

本文利用非平衡格林函數方法研究兩個自旋相關的量子現象: 自旋霍爾效應和自旋幫浦。我們將非平衡格林函數方法此方法應用在Landauer setup 上 (即所謂的Landauer-Keldysh理論) 來探討和分析在這個裝置 (setup) 下的一些物理特性，例如: 電荷堆積，自旋堆積，電流，自旋流，以及電導。在存在於半導體異質接面的二維電子氣體中會有Rashba跟Dresselhaus的自旋軌道耦合 (spin-orbit coupling) 。而此自旋耦合便是造成自旋霍爾效應的根源。我們研究了在此系統中的自旋霍爾效應並探討會影響到此效應的另外一個機制: 自旋進動。我們發現在上述兩種耦合下所造成的自旋進動，可以經由引入一個非交換性的規範場來描述。利用此規範場所給出的相位差，我們提出了一個干涉效應的應用，此應用考慮了一個正方型的電線迴路，而此迴路是存在於此二為電子氣體內，並可利用蝕刻此二為電子氣體製作出來。我們探討了磁場，非磁性缺陷，以及磁性雜質對於自旋霍爾效應的影響。值得一提的是，兩個磁性雜質的交換作用 (exchange interaction) 並不止存在於單一軸上 (不是由單一軸來描述) ，這個現象反應出了媒介於兩雜質間的電子是具有自旋進動的。另外，我們更探討了存在於單層石墨 (grapheme) 上的量子自旋霍爾效應，並發現到，自旋電導是否會量子化，是跟被量測的單層石墨的大小有關係 (單層石墨要夠大才會導致自旋電導量子化) 。在自旋幫浦的題目上，我們考慮了一維，二維，與三維的系統。在一維的系統裡，簡單的緊束縛模型 (tight-binding model) 讓我們可以得到解析解。此解析解使我們對於自旋幫浦有一個基本的理解，並提供了一個簡單有用的物理圖像。在二維裡，我們引入單層石墨。單層石墨的量子自旋霍爾效應跟拓樸絕緣體 (topological insulator) 有著密不可分的關係。利用自旋幫浦效應和單層石墨的量子自旋霍爾效應，我們提出了一個設計。此設計使得我們可以在實驗上證明拓樸絕緣體的存在。而在三維的系統裡，我們考慮了磁性穿隧接合體 (magnetic tunneling juction) ，並且得到了跟實驗上量到的自旋幫浦電壓一致的數量級 (這個數量級是目前大部分的理論無法預測到的) 。

Spin-dependent quantum phenomena, the spin-Hall effect and spin-pumping, are investigated with employing the Landauer-Keldysh formalism, the Keldysh-nonequilibrium-Green-function technique applied to the Landauer setup. As one advantage from this method, physical quantities such as, charge and spin occupations, charge and spin currents, and conductance can all be obtained in a unified way. Analysis will be given mainly on these quantities. The spin-Hall effect in the two-dimensional sample made of semiconductor heterostructure with Rashba and Dresselhaus spin-orbit interaction (coupling) is studied. The spin-precession, which originates from these two SO couplings and plays an important role in the spin Hall effect, can be elucidated by the spin propagator constructed via the non-Abelian (non-commutable) spin-orbit gauge. Applications based on the spin-precession are proposed by considering a square ring etched from the two-dimensional system mentioned above. The spin-Hall effect in the presence of magnetic field, non-magnetic defect, and magnetic impurity (-ies) are also discussed. In particular, the exchange between two magnetic impurities is non-collinear, reflecting the existence of the spin precession of mediating electrons. Furthermore, the quantum spin Hall effect in graphene is also examined. We point out that the size of the sample is relevant to the quantization of the spin Hall conductance; the size of graphene has to be large enough to get the quantized conductance. On the issue of spin-pumping, we consider one-, two-, and three-dimensional systems. In the one-dimensional tight-binding model, the analytical form of the pumped spin currents yield fundamental understanding of the pumping; a plain and insightful physical picture is established to explain the pumping mechanism. In the two-dimensional topological-insulator graphene, a setup based on the interplay of the quantum spin Hall effect and spin pumping is proposed. This setup offers an experimental proof via electric means for the existence of the topological-insulator phase. Distinguishable from most of the present theoretical results, in the three-dimensional case, our calculations yield the same order of magnitude of the converted charge voltage measured in a magnetic tunneling junction with spin-pumping.