二維異質結構系統和石墨稀內的自旋霍爾效應

Abstract

本文利用非平衡格林函數方法研究二維異質結構系統(two-dimensional heterostructure)和石墨稀(graphene)中的自旋霍爾效應(spin Hall effect)。簡單地來說，自旋霍爾效應就是電流會感應與其垂直方向的自旋電流，自旋堆積通常也會伴隨而生。自旋霍爾效應以及其反效應(inverse spin Hall effect)可以分別被用來產生以及偵測自旋電流，對於自旋電子學，這個效應提供了一個電性方法去控制電子自旋，因此近年吸引來許多實驗學家與理論學家投入。

首先，我們考慮一個Rashba自旋軌道耦合的管狀二維電子氣體，探討管狀幾何結構對於自旋霍爾效應產生的影響。在此系統下，我們發現儘管自旋霍爾堆積消失了，自旋霍爾流仍然存在並且環行於系統中。另外，放入一個非磁性雜質，在雜質附近會感應出自旋堆積。這些現象不同於一般在平面上觀察到的自旋霍爾效應，可以建立我們對管狀系統中自旋霍爾效應的了解。

此外，目前只有少數實驗觀察到本質(intrinsic)自旋霍爾效應，為了讓本質自旋霍爾效應更顯著更容易觀察，我們提出一個方法去增強本質自旋霍爾堆積，此一研究發現在特定能量下自旋霍爾堆積會顯著地增強兩個數量級，增強效應來自於兩個相異對掌性的渦旋電流，利用自旋軌道力的圖像，可以了解兩個渦漩電流會受到自旋軌道力分別將自旋向上及向下的電子向渦漩中心推進，造成自旋堆積增強。進一步研究發現這個局部渦旋態來自於Fano-Rashba效應所造成的電導低谷。

另外，最近實驗上發現鎳基底會增強石墨稀上的Rashba自旋軌道耦合，為了研究此一自旋軌道耦合所產生的自旋霍爾效應，我們應用了Heisenberg運動方程式推導自旋軌道力。這個自旋軌道力不同於常見在半導體內的自旋軌道力，它可以提供石墨稀內自旋分離的物理圖像。此外，我們計算自旋霍爾電導，利用自旋軌道力定性解釋這個自旋霍爾效應。

最後，最近Geim的研究團隊在石墨稀上外加一個磁場做傳輸實驗量測，在Dirac point附近觀察到巨大的非局部電位差，出人意外地，這個信號可以傳遞長達數個微米的距離，並且在室溫下仍然可以觀察到，此一現象可以歸因於Zeeman splitting引起的巨大的自旋霍爾效應。為了進一步了解這個現象，我們利用非平衡格林函數計算這個量子傳輸現象，藉由現象學的多體自能(self energy)提供一個模擬去相位(dephasing)的方式，定性上解釋了高溫到低溫的實驗觀察，給予這個現象完整的理論圖像。

In spintronics, spin-orbit coupling in semiconductors and metals has stimulated a great deal of work devoted to spin-orbit-induced phenomena, such as spin Hall effect, which makes electrical manipulation of electron spins possible. The thesis presents a theoretical study of transport of electron spin, mainly focusing on spin Hall effect, in two-dimensional electron gas (2DEG) systems, including two-dimensional semiconductor heterostructures and graphene by employing the Landauer-Keldysh formalism.

We start our work in the tubular 2DEG with Rashba spin-orbit coupling (SOC). This study reveals that the tubular geometry effect can cause spin-orbit-induced phenomena very different from those in a planar sample. In particular, in spite of the absence of spin accumulation, the spin Hall current can still arise and even circulate in the tubular sample. A spin-independent impurity will induce distinctive spin accumulation patterns around the impurity, which may serve as a novel mechanism to control electron spins by arranging the impurities for spintronic devices.

Next, to make intrinsic spin Hall effect more experimentally observable, we investigate the enhancement of intrinsic spin Hall accumulation in a two-dimensional electron gas with Rashba and Dresselhaus (001) spin-orbit coupling. We show that intrinsic spin Hall accumulation can be strongly enhanced at the specific energy point, where the system develop two charge current vortices with certain chirality. We find the localized vortex state is accompanied by the occurrence of the conductance dip arising from Fano-Rashba effect. The spin-orbit force picture is used to analyze the enhanced spin accumulation patterns.

Then, motivated by the experimental observed large Rashba spin-splitting, we derive the effective spin-orbit force in Rashba coupled graphene from the Heisenberg equation of motion. The spin-orbit force, different from that in conventional semiconductors, can provide us a physical picture of unusual spin separation due to Rashba spin-orbit coupling in graphene. This picture is useful to design the spin generator device based on graphene. Furthermore, we numerically calculate spin Hall conductance and qualitatively explain the result by the spin-orbit force picture in graphene.

Finally, a very recent experiment [D. A. Abanin et al., Science 332, 328 (2011)] observed the giant nonlocal voltage in magnetotransport near the Dirac point in graphene. This giant nonlocal voltage signal, transmitting over several micrometers, is attributed to an unusual giant spin Hall effect induced by Zeeman splitting in graphene without SOC. In order to further understand this phenomenon, we have developed a fully quantum transport theory with dephasing introduced via phenomenological many-body self-energies. By employing this theory, we provide a unified picture of the giant nonlocal voltage and spin Hall effect from the quantum-coherent transport regime at low temperatures to a semiclassical transport regime at higher temperatures.