Spin Transport through One-Dimensional Systems with Periodic Structures

本論文內容為自旋傳輸於一維週期系統的理論研究。文中探討傳輸現象皆是在彈道模式下，被侷限於一維通道的電子。本文主要探討自旋軌道耦合與外加磁場對自旋傳輸於一維週期系統的影響，特別是關於自旋篩選現象。 固態系統裡，自旋軌道耦合起因於固體結構空間反轉對稱的破壞。 兩種破壞對稱的方式造成的效應分別為： (1) Rashba 自旋軌道耦合與 (2) Dresselhaus 自旋軌道耦合。 由異質結構介面引起的 Rashba 自旋軌道耦合可由電壓閘控制耦合作用的強度，而 Dresselhaus 自旋軌道耦合決定於固體的內在晶格結構則較難被控制。 本研究採用兩種方式展生空間中週期的自旋軌道耦合: (1) 由電壓閘控制 Rashba 自旋軌道耦合 (2) 製造週期彎曲的一維線。這些週期的自旋耦合使得能帶結構產生能隙，而這些能隙的位置與自旋相關。自旋軌道耦合可用一等效磁場描述，而此磁場與一般磁場不同，擁有時間反轉對稱性。本文討論了此等效磁場大小與方向對傳輸的影響。 如果一維系統的時間反轉對稱不被破壞，自旋篩選的過程就不會出現。因此，本文檢驗外加磁場對自旋傳輸的影響。外加磁場將先前自旋軌道耦合造成的能隙移到不同能量高度。如果電子動能落在其中一個能隙上，完全自旋極化的電流就會產生。 本文第一章開始為研究動機，然後介紹了彈道模式下的量子傳輸與自旋軌道耦合的成因。第二章介紹曲面系統的描述方式，推導出曲率對動能與自旋軌道耦合的影響。第三章為文章研究方法，介紹計算能帶結構與穿透率的方式。第四章是本文主要結果，探討了自旋軌道耦合 、磁場與幾何結構對自旋傳輸的影響。第五張為本文結論。The thesis presents a theoretical study of spin transport in one-dimensional systems with periodic structures. In this thesis, all the transport is in the ballistic regime and one-dimensional systems are made by confining electrons in two-dimensional systems. The main purpose of this thesis is to investigate the effects of spin-orbit coupling (SOC) and magnetic field on spin transport, especially spin filtering in one-dimensional systems with periodic structures. In solids, SOC describes the interaction between the momentum of an electron and its own spin. The symmetry breaking of space inversion of the solid structure gives rise to two kinds of SOC: (i) Rashba SOC and (ii) Dresselhaus SOC. Rashba SOC, originated from structure inversion asymmetry (SIA), can be tuned by voltage gates while Dresselhaus SOC, originated from bulk inversion asymmetry (BIA), can be not easily controlled. Two methods are used to create periodic SOC in space: (i) to modulate Rashba SOC periodically by voltage gates and (ii) making a periodically curved wire. The periodic SOC in space can make a band structure with spin-dependent band gaps. SOC contributes an effective magnetic field, which has time reversal symmetry. With the two methods, we can control the effective magnetic field. The influences of the absolute value and the direction of the effective magnetic field are studied. It have been shown that without breaking time reversal symmetry, single-channel one-dimensional systems can not have spin filtering properties. Therefore, the effect of an exterior magnetic filed applied to the one-dimensional systems is examined. This exterior magnetic filed moves the spin-dependent band gaps to different energy levels. When electrons'' energies lie in these spin-dependent band gaps, full spin-polarized current is produced. In chapter 1, the motivation is mentioned in the start and an introduction to electron transport in the ballistic regime and the origin of SOC is given . Chapter 2 will be devoted to confined quantum systems in curvilinear space. The curvilinear effects on kinetic energy and SOC are both described. In chapter 3, the methods for transmittance and band structures are introduced to investigate the properties of spin transport. The transmittance and band structures of specific systems are calculated in chapter 4. The effects of SOC, magnetic filed and geometric structures are discussed in the separate sections. Conclusion of the thesis will be summarized in chapter 5