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研究生：	歐懿中 Ou, Yih-Jon
論文名稱：	石墨烯磁電子和磁光學性質的調制效應 Modulation effect on the magneto-electronic and optical properties of graphene
指導教授：	林明發 Lin, Ming-Fa
學位類別：	博士 Doctor
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2014
畢業學年度：	102
語文別：	英文
論文頁數：	121
中文關鍵詞：	藍道能階、光吸收譜、選擇定則、調制磁場、調制電場
外文關鍵詞：	Landau levels, optical absorption spectra, selection rule, modulated magnetic field, modulated electric field
相關次數：	點閱：151 下載：4
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這篇論文之中，單層石墨在外加複合場下的電子性質和光吸收譜以廣義化緊束模型以及梯度近似法計算。其中，複合場包含兩種情形:垂直均勻磁場加上調制週期磁場以及垂直均勻磁場加上調制週期電場。單層石墨在垂直均勻磁場下時會產生藍道能階，其能階的能量與開根號的磁場強度和量子數成正比關係。而更進一步外加調制場(週期性的調製電場或磁場)時，藍道能階的特性會被強烈的影響。原本零維的藍道能階會變成一維能帶，這些能帶展現週期性震盪並且具有新的能量邊界態。而這些主要的特性也會反應到態密度上，原本零維的對稱發散峰變成一維的非對稱發散峰。此外，藍道波函數的對稱性會被破壞，局域化中心也可能移動。在光譜特性上，單層石墨在外加均勻磁場時，磁光吸收譜產生許多均勻強度的顯著峰。這些峰遵循著一個特定的光學選擇定則。在外加調制場時，這些吸收峰的頻率、強度、結構、數目和選擇定則會被明顯的改變。原本對稱的顯著峰變成非對稱峰並且有較低的吸收強度。起始吸收頻率發生紅位移現象。更且，有額外的吸收峰產生，並遵循不一樣的光學選擇定則。值得一提的是，對於調制電場而言，這些額外的吸收峰在越大的調制強度以及較高光譜頻率下越容易產生。但是對於調制磁場而言，在一定的調制強度之後以及較低的頻率下反而越容易觀察到。

The influences of modulated electric fields and modulated magnetic fields on Landau levels (LLs) of monolayer graphene are investigated by the general tight-binding model and gradient approximation. Both modulated fields cause the LLs to split into two double-degenerate parabolic subbands; these subbands exhibit periodic oscillations and extra band-edge states. However, the subband dispersions and oscillation amplitudes that are subjected to electric and magnetic modulated fields behave differently. Main features of the electronic structure are reflected in the density of states (DOS), which presents pair-like and square-root divergent structures for both modulated field cases. The LL wave functions are strongly affected by both modulated fields, the altered features including the broken symmetry, displacement of the center location and the varied amplitude strength. As to the optical absorption spectra, the modulated fields have strong influence on the structure, number, intensity and frequency of absorption peaks, and thus the extra selection rules. Each symmetric peak, under a uniform magnetic field, changes into asymmetric ones with lower intensities. The threshold absorption frequency exhibits an obvious evolution in the regard of redshift. Moreover, the extra peaks in the absorption spectrum might arise from different selection rules. For the modulated electric field, the extra peaks can relatively easily be identified at higher frequencies and under stronger modulation strength. For the modulated magnetic field, the extra peaks could be obtained at lower frequencies and under a strong enough modulation strength.

Chapter 1. Introduction......3

References......10

Chapter 2. Electronic properties of monolayer graphene in the presence of the uniform magnetic and modulated electric fields

2.1 Introduction......12

2.2 Theory......13

2.3 Results......14

2.4 Conclusion......19

References......22

Chapter 3. Influence of modulated fields on the Landau level properties of graphene

3.1 Introduction......25

3.2 Band-like Hamiltonian matrix in external fields......27

3.3 Electronic properties in external fields......32

3.4 Concluding remarks......50

References......53

Chapter 4. Electric modulation effect on magneto-optical spectrum of monolayer graphene

4.1 Introduction......57

4.2 Band-like Hamiltonian matrix in external fields......59

4.3 Results and discussion......61

4.4 Conclusion......75

References......77

Chapter 5. The optical spectrum of graphene in a composite magnetic field

5.1 Introduction......82

5.2 Band-like Hamiltonian matrix in external fields......84

5.3 Uniform magnetic eld combined with a modulated magnetic field......88

5.4 Conclusion......103

References......107

Chapter 6. Summary and future research......113

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