- 學位論文
準一維系統之量子干涉與自旋極化行為
Quantum Interference and Spin Polarization in Quasi-One-Dimensional Systems
摘要
此論文為準一維系統下自旋相關傳輸之理論研究。探討的系統包括耦合量子點結構及量子線狀導體。若考慮單一散射區域，透過若干電極連接至電子庫，格林函數方法尤其適用於此類開放系統。因此於研究中，我們利用薛丁格方程式以及非平衡多體系統下兩者之單一粒子格林函數來討論電子的傳輸特性，而文內分析是藉由相關物理量所組織，如電導、電荷與自旋占據、以及態密度。總結而言，考慮若干具相異幾何結構之元件，研究乃依下列三個主題討論：一、量子干涉效應。二、可調控之自旋堆積及自旋極化電流。三、電場誘發自旋極化率。 基於量子相位同調性於介觀系統之重要性，我們首先以一個簡明的工作來闡釋主題一。考慮多量子點系統伴隨外加磁場，在特定結構下，存於導電帶內一個分子態可以獨立局部化，即完全無耦合於電極。基於此，隨著間接耦合參數及磁通量的變化，此束縛態可以被良好解析。同時，兩個反共振由於破壞性量子干涉而形成。藉由電導圖譜中Fano與Breit-Wigner共振的更迭可以明確得知分子態的漸進侷限化過程。 接著，我們引入此論文的中心主題，即透過Rashba自旋軌道交互作用解析電子的自旋態並操控其行為。其中，Rashba自旋軌道耦合效應已被證實存在於若干缺乏結構反轉對稱性之半導體異質接面處。在主題二裡，我們考慮兩種耦合雙量子點結構。由於自旋軌道耦合效應，電子在空間內的運動行為與其自旋自由度耦合而導致自旋進動。若以序列配置為例，此效應使得高度重疊之Fano共振峰連續地演進至反共振。此外，量子干涉與自旋軌道耦合效應的結合將產生可電性調控之自旋堆積以及自旋極化電流。另一方面，於主題三中，我們證實並說明於高偏壓條件下，有限且失序的二維電子氣體內之自旋極化率。其中，雜質散射與電場驅動之漂移速度致使自旋堆積的演進。於準彈道區域內可得知電子波函數尚未被強烈地擾動；而於漂移區域內則可觀察到堅穩的磁電耦合效應的形成。
並列摘要
Spin-dependent electronic transport through quasi-one-dimensional systems, including coupled quantum dots and wire-shaped conductor, is theoretically studied in this dissertation. Green function approach is particularly useful when considering an open system, i.e., a scattering region in contact with a couple of leads to reservoirs. Single-particle Green function for both one-particle Schrödinger equation and many-body system out of equilibrium are employed herein to investigate the transport properties and relevant physical quantities, such as conductance, charge and spin occupations, and density of states, upon which the analysis is organized. In summary, the discussions over considered devices with different geometry are mainly consisting in three phenomena: (i) quantum interference, (ii) controllable spin accumulation and spin-polarized current, and (iii) electric-field-induced spin polarization. As quantum phase coherence plays an important role in mesoscopic systems we present a simple work of coupled quantum dots in the presence of magnetic flux to illustrate the phenomenon (i). Starting from specific geometry one of molecular states could be totally uncoupled from the leads and becomes localized within the conduction band. As changing indirect coupling parameter and magnetic flux, bound state becomes well resolved, and meantime two antiresonances form due to destructive quantum interference and point out the gradual localization of molecular states, as manifested by the Fano and Breit-Wigner resonances in conductance spectrum, respectively. Then we present the central subjects of this dissertation, i.e., to lift and control the spin states of electrons by utilizing Rashba spin-orbit interaction, which has been shown to exist in semiconductor heterostructures due to the lack of inversion symmetry. Phenomenon (ii) is based on two kinds of coupled double quantum dots configurations. Owing to spin-orbit interaction the spatial motion of electrons are coupled to their spin degree of freedom. This results in spin precession, leading to a continuous evolution of antiresonances from strong overlapping Fano resonances, in serial configuration for example. Meantime combined effects of quantum interference and spin-orbit coupling generate an electrically tunable spin accumulation and a spin-polarized current. On the other hand, in phenomenon (iii) we demonstrate the spin polarization in finite disordered two-dimensional electron gas. Impurity scattering and drift velocity following electric field in strong bias condition lead to an evolution of spin accumulation. In the quasi-ballistic region electron wave function has not yet been strongly perturbed, while robust magnetoelectric effect develops in the diffusive region.
參考文獻
延伸閱讀
- Huang, C. Y. (2012). 自旋系統的量子糾纏量子相變與拓樸序 [doctoral dissertation, National Taiwan Normal University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0021-1610201315281788
- Lai, C. Y. (2007). 自旋量子位元與自旋環境交互作用的相消干現象--與時間相關的密度矩陣重整化群的研究 [master's thesis, National Tsing Hua University]. Airiti Library. https://doi.org/10.6843/NTHU.2007.00412
- Chi, L. Y. (2022). 介觀自旋軌道耦合系統中的量子傳輸之數值研究 [master's thesis, National Chengchi University]. Airiti Library. https://doi.org/10.6814/NCCU202201608
- Hung, J. T. (2008). 自旋量子位元與一維自旋環境交互作用之消相干與糾纏態研究 [master's thesis, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-2002201314450653
- 陳恩誌（2019）。Spin Polarization in Quantum Rings with Spin-Orbit Interaction〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU201901979