具自旋軌道交互作用下介觀環的電子傳輸特性

本論文探討介觀環在磁場及自旋軌道交互作用下的量子干涉現象。考慮磁場作用下，對於任意階層的一維Fibonacci 介觀環陣列而言，根據能帶圖提出了能譜的分支規則。任意階層Fibonacci 介觀環的能譜是可以被分成數個擁有相似圖樣的區域。本文提出了當階數大於二時，在每個區域中子能帶分支的特性，包括了零透射率線，包圍群組通帶，主要子禁帶，高階層下的主要子禁帶跟群組通帶之收斂性以及任意階層下的每一個群組通帶中的分裂子能帶個數。此外，從透射光譜中可看出系統的主要子禁帶之電子局限性此外，本文也發現巨大永久電流會出現在準週期Thue-Morse介觀環陣列中。當系統的階層數或磁通量增加時，最大永久電流也會隨指數增加，並且這些最大永久電流都出現在陣列中的中間環位置附近。高階數系統中的巨大永久電流會大於在一般傳統結構中的永久電流。這些永久電流會和傳輸共振點的銳度成正比，且共振點銳度是和能帶結構中的通帶寬度有相關性。此外，文章也確定了在任意階層系統下，巨大永久電流在何處能量出現的規則特性。本論文也提出了可以利用具自旋軌道交互作用介觀環Thue-Morse陣列來達成帶有完全傳輸的高品質因數的電子濾波器與共振器。當Thue-Morse陣列的階層數增加時，不止共振峰的品質因數會指數地增加，且其個數也會增加。在相同的環數下，對於Thue-Morse 陣列的電子濾波器而言，其最大品質因數遠大於週期陣列的結構。

關鍵字

自旋軌道交互作用；量子干涉；自旋電子學；準週期結構； AB 效應； AC 效應；介觀環

並列摘要

Quantum interference phenomena in mesoscopic rings under the influence of the magnetic field and spin-orbit interaction are studied in this thesis. The branching rules of the energy spectrum for a one-dimensional Fibonacci array of mesoscopic rings under the influence of magnetic field with an arbitrary generation is presented based on the bandedge map. It is found that the energy spectrum for the Fibonacci mesoscopic rings with an arbitrary generation can be divided to several regions, each of which has a similar pattern. As the generation order is greater than two, the characteristics of the subbands branching in each region, including the zero transmission lines, the enveloped group bands, the major subgaps, convergence of the group bands and major subgaps for a higher generation, and number of splitting subbands in each group band for an arbitrary generation, have been proposed in the study. Moreover, electron localization in the major subgaps of the Fibonacci rings is demonstrated by the transmission spectra. Giant persistent currents that occur in quasiperiodic Thue-Morse array of mesoscopic rings are also proposed. As the order or the magnetic flux of the system increases, the maximum persistent current increases exponentially. It is found that the maximum persistent current occurs in the ring near the middle position of the array. The giant persistent current in a system with higher order is greater than that in traditional structures. The persistent current is also proportional to the sharpness of the transport resonance, which is dependent on the width of the allowed band in the band structure. A rule to determine the occurrence energy of the giant persistent currents for a system with arbitrary order is also proposed. A high Q electron filter and resonator with complete transports is achieved using a quasiperiodic Thue-Morse array of mesoscopic rings with spin-orbit interaction. As the generation order of the Thue-Morse array increases, not only does the Q factor of the resonance peak increase exponentially, but the number of sharp resonance peaks also increases. The maximum Q factor for the electronic filter of a Thue-Morse array is much greater than that in a periodic array, for the same number of the rings.