介觀自旋軌道耦合系統中的量子傳輸之數值研究

在本篇論文中我們以數值計算討論幾種Rashba自旋軌道耦合介觀系統，由文獻指出在這些系統設置下所計算的量子傳導率和自旋霍爾傳導率會受到Rashba自旋軌道耦合強度及雜質之影響，在本論文中會針對幾個系統之結果做討論及介紹。論文中所有的結果皆由kwant一個由多國研究員共同研發來計算量子傳輸效應進行數值計算。Kwant以Landauer–B ̈uttiker 形式及格林函數（Green’s function）去計算一緊束緮模型（Tight–binding model）。在研究系統幾何的例子中，我們設置了圓形環、方形環以及實心方形系統，而傳導率在圓形環的結果出現震盪現象，且系統傳導率會受到自旋軌道耦合強度的影響。當我們在圓形環、方形環系統中施加一平面內塞曼場（Zeeman field）時，傳導率及自旋霍爾傳導率結果皆呈現一些干涉紋特徵。在研究雜質（隨機亂數）效應的例子，我們發現只要Rashba自旋軌道耦合強度不為零便能誘發自旋霍爾傳導率的產生。介觀下的自旋霍爾傳導率在雜質強度為零時（乾淨系統中）與連續模型所導出的固定常數不同，且傳導率會受雜質強度影響。在某些雜質添加方式下雜質強度不為零時（隨機雜質系統中），雜質會削弱自旋霍爾傳導率且隨強度增加而減弱。根據文獻與我們的結果顯示自旋霍爾傳導率震盪週期顯示此震盪現象係由有限系統下之自旋進動結果。

關鍵字

量子傳輸； Rashba自旋軌道耦合；自旋霍爾效應；自旋霍爾傳導率；量子傳導率；雜質效應

並列摘要

We numerically study quantum transport in mesoscopic two-dimensional electron systems (2DESs) with Rashba spin–orbit coupling (SOC), particularly the effect of disorder and Rashba SOC on spin-Hall conductivities (SHCs) and charge conductance in different limits. The numerical simulations are performed with Kwant, an open–source package for numerically calculating quantum transport for discretized tight-binding models based on the Landauer–B ̈uttiker approach and Green’s function formalism. In this thesis, the geometric structures are rings, square loops and square shapes. For a Rashba ring, the quantum conductance oscillates and depends on the strength of Rashba SOC. When an in–plane Zeeman field is applied to a ring or a square–loop system, the quantum conductance and SHC show interference pattern characteristics. For disorder effects, in the disordered limit, the on–site and Rashba type disorders weaken SHC. Notably, we found that in a system without SOC, SHC can be induced by random Rashba SOC. We show that in the clean limit (W = 0), in contrast to the continuum model, SHC is not universal for a mesoscopic structure. This finding agrees with previous numerical studies. Moreover, the period of SHC indicates that oscillation patterns result from the spin precessional effect in finite–size systems.

並列關鍵字

Quantum transport ； Quantum conductance ； Rashba spin-orbit coupling ； Spin–Hall effect ； Spin–Hall conductivity ； Disorder effect

參考文獻

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