臺灣博碩士論文加值系統

在本論文中，我們提出一個理論模型，來研究近來利用自組裝法(self-assembled)所製造出的同心量子雙環。我們利用電子在量子單環的確切解來形成一組基底，展開同心量子雙環之漢密頓函數(Hamiltonian)，並用數值方法將其對角化，得出相應的能量本徵值和本徵函數。藉由此法，我們可以研究Aharonov-Bohm效應，是否還會發生在中心有外加磁通量的量子雙環中？此外，我們也計算了在量子雙環中存在一個固定的雜質時之能階變化情形，並進一步討論量子環中有兩個對稱且固定的雜質，皆位於內環以及其一在內環而另一在外環的不同情形之能階變化。

In this thesis, we propose a theoretical model to study the spectra of the concentric quantum rings which have been fabricated lately by self-assembled technique. By using the exact diagonalization method, we examine whether the Aharonov-Bohm (AB) effect still appears in the concentric quantum rings threaded by a magnetic flux. Moreover, we study the variations of the energy spectra when impurities are presented in the rings.

1 Introduction 3
2 Formulation 5
2.1 Single Quantum Ring . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Aharonov-Bohm Effect in Single Quantum Ring . . . . . . . . 9
2.3 Energy Spectra of Quantum Rings with Impurities . . . . . . 12
2.4 Theoretical Model for Two Concentric Quantum Rings . . . . 16
3 Results and Discussions 23
3.1 Aharonov-Bohm Effect in Concentric Quantum Rings . . . . . 23
3.2 Energy Spectra of Concentric Quantum Rings with Single Im-
purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Energy Spectra of Concentric Quantum Rings with Two Im-
purities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Relation Between ΦB and Aharonov-Bohm Effect . . . . . . . 39
4 Conclusion 42

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