外加應力下砷化鎵/砷化鋁鎵量子點的等效電洞g因子

Abstract

在量子計算中，電洞自旋被視為好的量子位元，故自旋的控制扮演重要角色，為了達到完全的自旋控制(Full spin control)，需使電洞的g-tensor其中一個分量變號，我們關注在量子點形狀與應力對電洞g因子的影響。 在本篇論文中，使用無內建應力的GaAs/AlGaAs量子點，利用k.p理論Luttinger-kohn四能帶模型搭配波包近似法，並考慮外加應力與磁場，磁場包含磁場向量勢與賽曼項，使用的數值方法為考慮規範場守恆的有限差分法，並由能量匹裂計算等效電洞g因子。 由模擬結果，g_z大於g_x,g_y約一個數量級，而量子點幾何形狀的改變會影響輕重電洞混成，進而影響電洞平面g因子，而g_z則變化不大。外加應力也會造成輕重電洞混成，故與量子點的形狀異向性有相互疊加或抵消的關係，共同影響等效電洞g因子。磁場向量勢對g因子的貢獻與賽曼項不同，是未來值得討論的部分。

In quantum computing, hole spin is regarded as a good choice of qubit and spin control plays an important role. Full spin control(FSC) could be realized that one of the components of hole g-tensor be reversed. In this thesis, I focus on how the quantum dot(QD) geometry and external stress affect the hole g-tensor. The hole g-tensor is theoretically calculated using Luttinger-Kohn 4-band model, by considering uniaxial stress and magnetic field. The effect of magnetic field includes vector potential and spin zeeman term. We use the gauge invariant finite difference method as the numerical calculation. It is found that the magnitude of gz is one order larger than in-plane g-factor. The geometry of QD causes the change of valence band mixing(VBM) and then affects in-plane g, while gz is affected little. Uniaxial stress also causes VBM and will improve or reduce the effect of geometry. The effect of vector potential causes different effect to hole g from zeeman term, and we have to study more about the vector potential effect in the future.