在Dresselhaus-type 介觀量子環中的持續性電流和自旋密度

Abstract

本論文的工作主要是去探究以及了解在有限寬的介觀環裡Dresselhaus自旋軌道交互作用效應的物理意涵，包含有和沒有外加磁通量兩種情況。而自旋密度和持續性電流是我們關注的物理量。特別地，我們藉由個別獨立打開Dresselhaus自旋軌道交互作用和磁通量，去仔細分析本徵態和能譜來得到物理意涵。

在打開Dresselhaus 自旋軌道交互作用強度的情況下，我們證明所有的能階都是Kramer’s type 的雙重簡併，以及藉由能階排斥原理和相對基底本徵態比重來瞭解能譜的趨勢。在弱自旋軌道交互作用場的範疇下，能譜和Dresselhaus 自旋軌道交互作用強度成二次方關係，此結果與我們的微擾分析相同。

在漸增磁通量的情況下，我們呈現了Kramer 簡併態的分裂，以及確認分裂後能譜的物理原因。對於在打開Dresselhaus 自旋軌道交互作用或磁通量後的本徵態，我們發展了一套有系統的方法去得到它的通式。我們也計算了一個本徵態所對應的自旋密度和淨z 方向投影自旋量。當系統中有N 個電子時，總合每個本徵態就能得到全部的總量。

The work of this thesis is to explore and to understand physical insights on the effects of Dresselhaus spin-orbit interaction (DSOI) in a ‾nite width mesoscopic ring, both with and without a magnetic flux. The physical quantifies of interest are the spin density and persistent current. Specifcally, our insight is obtained from a detail analysis of the eigenstates and the energy spectrum as the DSOI is turned on and, independently, when the magnetic flux is turned on.

For the case of turning on of the DSOI strength, we demonstrate that all energy levels are doubly degenerate, of the Kramer's type, and the trend of the energy spectrum is understood by level repulsions and the relative weighting between the constituent bases state ket. The energy spectrum depends on the DSOI quadratically in the weak SOI field regime, and this is consistent with our perturbation result.

For the case of increasing the magnetic flux, we show that the Kramer degenerate states split and the physical reason for the subsequent order in the energy splitting is identified. For the eigenstate in the presence of the DSOI and the magnetic flux, we have developed a systematic way to produce its general form. We have calculated the spin density and the net spin Sz of an eigenstate. Summing these gives us the total when there are N electrons in the system.