在苯環中心處吸附原子可以用來產生電子的自旋軌道作用。我們對一個最近合成的聯苯奈米環結構的物理性質感興趣，因為該結構與超短碳納米管類似，而該聯苯奈米環結構是由n個苯環鍵頭尾相接成比較大的環形結構。一方面，石墨烯藉由吸附感應的自旋軌道作用會在奈米碳管兩端產生螺旋形的邊緣態而變成像是二維拓撲這樣的材料，另一方面，超短納米管會造成兩個螺旋邊緣狀態相互混合，所以問題是自旋的物理現象會怎麼在類聯苯奈米環中產生，並且藉由填入電子在結構中，我們發現非零自旋流的情況而電子流保持在零。

An adatom or an adsorbate located at the center of a benzene ring give rise to spin-orbit interaction to electrons in the ring. The recent synthesis of [n]Cycloparaphenylenes structure, which are chaining up of n-Benzene rings and connecting head to tail to form a larger ring structure, are of interest from the physics perspective. It is because of the structure’s equivalence to an ultra-short carbon nanotube. On the one hand, with the adsorbate-induced spin-orbit interaction, a bulk graphene becomes a Z2 topological material [1] such that helical edge states are expected at the 2 ends of the nanotubes formed from such a material. On the other hand, an ultra-short nanotube will cause the two helical edge states to mix with each other. So the question would be what spin-related physics will survive in such [n]-CPPs-like structures. In this work we consider the simplest case of one adatom on a [8]-CPP-like structure. Depending on the filling of electrons in the system, we find cases of non-zero persistent spin current, while the persistent charge current remains zero.

Abstract in Chinese ii
Abstract in English iii
List of figures vi
Chapter 1. Introduction 1
Chapter 2. Field-induced spin-flipping through a benzene ring 3
2.1 Hamiltonian in a Benzene ring 3
2.2 Matrix representation for various terms in 6
2.3 Energy levels in Benzene ring 9
2.4 Transmission through Benzene ring 10
2.5 Summary 18
Chapter 3. Quantum states of pristine [n]-CPPs-like 19
3.1 Hamiltonian in [8]-CPP-like 19
3.2 Energy levels in [n]-CPPs-like 23
3.3 Quantum states in [8]-CPP-like 24
3.4 Approaching way to check Quantum states in [8]-CPP-like 26
3.5 Summary 28
Chapter 4. Quantum states of [n]-CPPs-like with adsorbates 29
4.1 Hamiltonian in [n]-CPPs-like with adsorbates 29
4.2 Hamiltonian in [n]-CPPs-like with adsorbate and electric field 34
4.3 Hamiltonian in [n]-CPPs-like with one adatom and electric field 35
4.4 Summary 38
Chapter 5. Persistent current in [8]-CPP-like with/without adsorbates 39
5.1 A ring in Continue and tight-binding model with magnetic flux 39
5.2 [n]-CPPs-like with magnetic flux in tight-binding model 40
5.3 Hamiltonian in [n]-CPPs-like with magnetic flux 42
5.4 Energy levels of [n]-CPPs-like with magnetic flux 44
5.5 Current density in [n]-CPPs-like without adsorbates 46
5.6 Persistent current in [8]-CPP-like without adsorbates 49
5.7 Summary 54
Chapter 6. Persistent spin current in [8]-CPP-like with one adsorbate 55
6.1 Energy level of [8]-CPP-like with one adatom 55
6.2 Persistent spin current of [8]-CPP-like with one adatom 58
6.3 Persistent spin current of [8]-CPP-like with one adatom and electric field 65
6.4 Persistent spin current of [8]-CPP-like with adatoms 67
6.5 Summary 69
Chapter 7. Conclusion 71
Appendix A. 1-D Tight-binding with magnetic flux 72
Appendix B. Reductive algorithm for determinant of [n]-CPPs-like matrix with magnetic flux 75
Appendix C. Persistent charge current of [8]-CPP-like with adsorbates 79
Appendix D. Table of [8]-CPP-like energy levels with/without adatom 84
References 85

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