本論文主題是一維介觀圓環上的持續電流與持續自旋流。我們先在第一章中回顧一維金屬圓環上的持續電流，電子自旋的自由度暫不考慮在內，從其中我們知道，持續電流的存在與電子繞圓環時獲得的Aharonov Bohm相位有關。接著我們作關於二維自旋-軌道耦合系統中電子行為的研究，在此處，電子的電荷與自旋的自由度同時考慮進去，其中，我們特別探討介觀大小的導電性同心環上電子的行為，研究Rashba自旋-軌道耦合及磁通量對此環的能階結構、持續電流及持續自旋密度等造成的影響。最後，我們探討不均勻磁場環境中亞鐵磁環上的持續自旋流，在這部份，亞鐵磁環為絕緣環，所以電荷的自由度可以不考慮，而持續自旋流的存在與磁波子繞圓環時獲得的Berry相位有關是這部份的主要概念。

In this dissertation, we address the topics of persistent charge current and spin current in one-dimensional mesoscopic rings. In Chap. 1, we review the persistent charge current in a normal metal ring without spin degree of freedom. The existence of the persistent charge current is related to the Aharonov-Bohm phase acquired by the electrons while circling the ring. In Chap. 2, we concentrate on the spin-orbit coupling in two-dimensional system with both charge and spin degrees of freedom. We investigate a mesoscopic and isolated conducting annulus with Rashba spin-orbit coupling. The effect of the Rashba spin-orbit coupling on energy levels, and the behaviors of the persistent charge and spin currents are reported. In Chap. 3, we study the persistent spin current (the current of magnons) in an insulating ferrimagnetic ring subjects to a nonuniform magnetic field. The existence of the persistent spin current is related to the Berry phase acquired by the magnons while circling the ring.

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