操控半導體電子自旋的動力行為與傳輸的研究

Abstract

這份研究計畫主要有下列三個目標： [1].對自旋霍爾效應(spin-Hall)中自旋堆壘效應(spin accumulation)的物理取得更透 徹的瞭解，並全面地瞭解到自旋堆壘與同時結合內秉的(intrinsic)與非內秉的 (extrinsic)自旋軌道交互作用(SOI: spin-orbit interaction)之間的相互對應關係: 內秉的自旋軌道作互交用包括Rashba 和Dresselhaus 兩項，而非內秉的SOI 主要 係由SOI 的散射效應而來，其散射體如一些重雜質的存在即是。其中關於不同SOIs 之間如何相互作用影響的物理圖像更是大家特別感興趣與關注的。其他一併加進來 研究考慮的相關影響因子有如：二維電子氣(2DEG)的有限厚度效應(finite-thickness effect)，晶格的方向性，和局部散射粒子附近的自旋堆壘效應等。我們希望能透過 這些一一的瞭解而藉以在給予直流(dc)電場的環境影響下，能找出「最適化」的條件 以達到最大的自旋堆壘效果。 [2].對直流(dc)磁場和交流(ac)電場與自旋堆壘的現象、機制與影響取得透徹而全面的 瞭解： 垂直於的或平行於(in-plane)樣品方向的直流(dc)磁場都是研究的重點。其中垂直 於的樣品方向的直流(dc)磁場乃作為提供操控系統中自旋對稱(spin-symmetry)的 額外自由由度以獲致最大自旋堆壘的可能。而垂直於樣品方向的直流(dc)磁場，如 調製在弱場(weak field)範圍的影響下的迴旋運動(cyclotron motion)情形；與如 在強場(strong field) 範圍的影響下產生的Landau-quantization 效應，則可來 用以利作為另一種調製觀察自旋堆壘效果的手段。除此之外，於推廣到有限頻率範 圍時(finite frequency regime)，自旋動力學中的同調-非彈性碰撞過程便自然需 要再加以引入進來計算裡。為了能以一種似古典(classical-like)的途徑來加以描 述這些效應和過程，我們也將從Keldysh-Green 函數出發，來推廣目前自旋擴散方 程(spin-diffusion eqn) 讓其進一步能兼顧到同時含有ac 以及dc 外場的作用。 藉此也同時來瞭解這些效應對於塊材(bulk)極化與邊緣(edge)極化情形之影響。 [3].探討透過純粹電性的方法來偵測傳輸自旋的現象(spin transport)： 透過利用SOI 效應，橫向的荷電流(charge current)自然也可以由自旋電流 (spin-current)中加以產生。這也正是所謂的逆向(inverse)自旋霍爾效應的結 果。我們循此觀念將考慮在不同的系統配置中的自旋電流注射(spin-current injection) 的情形：從而分析計算由擴散機制主導範圍(diffusion regime)及彈 道(ballistic) 機制主導範圍裡所可能衍生的各種對應的荷電流表現的情形。這些 結構中將包含一條開放性的導線，和一條與它相交的導線。外在場的作用影響亦在 此放進來考慮。而關於在彈道機制主導的系統中其自旋電流注射(spin-current injection)的實現則可由我們先前的研究工作中的方法：以交流相變(ac biased) 的手指閘極(finger-gate)所給出。對於擴散機制所主導的作用範圍(diffusion regime)裡，自旋擴散方程(spin-diffusion eqn)中的SOI-coupling 參數自然也隨 之需要擴展到兼具時變性和空間變動性。對此於荷電流，荷電堆壘(charge accumulation)，與自旋電流的相關性將被更深入完整地探討。這些瞭解都將可用於 設計發展以純粹電性的方法來達到自旋電流偵測的目標。

There are three major goals in this study: To understand in a comprehensive way the relation of the spin accumulation in the spin-Hall configuration to the combined effects of the intrinsic and the extrinsic spin-orbit-interactions (SOI): Intrinsic SOI includes both the Rashba and the Dresselhaus SOIs, and the extrinsic SOI is resulted from the SOI scatterers such as the heavy impurities. Of particular interest is to obtain physical pictures for the interplay between the various SOIs. Other factors such as the finite thickness effect of the 2DEG, the crystal orientation, and particular spin accumulation around local scatterers will be studied. With these understanding, we are hoping to propose some simple optimal situation for the production of spin accumulation from a given driving dc electric field. To understand in a comprehensive way the effects of dc magnetic fields and ac electric field on the spin accumulations: dc magnetic fields, either perpendicular or parallel to the sample, will be incorporated into our study. The in plane magnetic field will introduce additional handle for monitoring the spin symmetry in the system and thus allows an extra degree of freedom to better achieve maximal spin accumulation. The perpendicular magnetic field will introduce cyclotron motion, in the weak field regime, and the Landau quantization, in the strong field regime, for another possible way of tuning the spin accumulation. Furthermore, extending our calculation to the finite frequency regime, which we will study first the case of ac electric field, may introduce additional coherent inelastic processes to the spin dynamics. To describe these processes in a 「classical」-like approach, we will extend our derivation of the spin diffusion equation to incorporate both the ac and the dc external fields, starting from the Keldysh Green』s function. We will look for the effects on both the bulk and the edge polarizations. To explore pure electrical means of probing the transport of spins: Making use of the SOI, a spin current can generate charge current in the transverse direction. This is the so-called inverse spin-Hall effect. We will consider various system configurations, which include both the diffusive and the ballistic regimes, into which a spin current is injected and calculate the resulting charge current. These structures include a wire, a wire with an opening, and a cross-wire situation. External fields effects will also be taken into consideration. The spin current injection can be generated from an ac biased finger-gate proposed in our recent work for the case of the ballistic regime. For the diffusive regime, we need to extend our spin diffusion equation to the situation when the SOI coupling parameter varies spatially and temporally. The correlation of the resulting charge current, or charge accumulation, with the injected spin current will be studied. These understanding will form a basic for the devising of spin current detection by pure electrical measurements.