在這個研究中，我們假設一個理論的模型來近似一個同軸的量子雙環，此量子雙環是藉由自我組裝的技術組合而成的。首先，我們先分析受交互作用的矩陣元素，然後將這個受到均勻磁場以及Rashba 自旋軌道交互作用的半導體量子雙環的哈米頓算符的數值對角化，我們可以在電子能階上找到由於系統反對稱破壞所造成的自旋之分裂，也可以在AB效應的圖表上找到多個鋸齒狀的週期構造。此外，我們也研究當量子雙環上加入一個扇形的位能方壘，或是當內外環的自旋軌道交互作用強度不同時所造成的變化。

In this thesis, we proposed a theoretical model to study the effect of the spin-orbit interaction on the electronic energy levels in a concentric quantum double ring, which has been successfully fabricated lately by self-assembly technique. We first analyzed the matrix elements of the interactions, and then diagonalized numerically the Hamiltonian of an electron in a semiconductor quantum double ring subjected to the magnetic flux and Rashba spin-orbit interaction. We found that the spin splitting of the electron energy levels was produced by the system inversion asymmetry（the Rashba term）. The multi-zigzag periodic structures were revealed via Aharonov-Bohm energy spectrum. In addition, we also investigated the changes of the energy spectra of a concentric quantum double ring with either one sectorial barrier or different strength of Rashba spin-orbit interaction between inner and outer ring.

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