臺灣博碩士論文加值系統

單層過渡金屬二硫族化合物(TMD-MLs)是由單層的VIB族過渡金屬原子和兩層分別位於過渡金屬原子層上和下的VIA族硫化物原子所構成之二維材料。其優越的光學、自旋和能谷特性使此材料在各樣的研究和應用領域都獲得相當大的關注。其晶體結構的空間反轉對稱性破缺和時間反轉對稱性造成所謂的自旋-能谷鎖效應，使我們能使用光學的方法來對激子的自旋-能谷自由度進行初始化、編碼、控制和讀取等能谷電子學上的應用。由於二維材料本身的介電屏蔽效應十分微弱，TMD-MLs內的激子擁有遠大於塊材半導體材料內激子的束縛能(約百微電子伏特數量級)和劇烈的光物質交互作用效應。根據光學躍遷選擇律對激子進行分類，其中能夠與光反應的激子將被歸類為亮激子(BX)，反之則為暗激子(DX)。更進一步，暗激子又可以細分成自旋禁止(SF)和動量禁止(MF)暗激子。但由於TMD-ML內具有能谷和自旋自由度的帶電載子經過庫倫交互作用後會形成複雜的激子能帶結構，若要能準確地模擬和分析亮暗激子的能量精細結構並且解釋實驗的觀測現象，我們將需要有足夠可靠的電子能帶結構和精確且有效的激子能帶結構計算。在此研究工作中，我們首先利用第一原理密度泛函理論計算TMD-MLs的電子能帶結構，接著藉由Wannierization過程將第一原理計算結果轉化成高精確度的緊束縛模型以降低後續激子計算所需之計算資源。同時，我們也將利用群理論的對稱分析對TMD-MLs的電子能帶結構進行更深入的了解。接著我們會將基於第一原理計算結果之緊束縛模型代入Bethe-Salpeter equation(BSE)進行激子能譜計算。基於完整且準確的激子能帶結構，我們將利用熱統計模型對單層二硒化鎢(WSe2)的變溫光致發光(TD-PL)光譜進行模擬。我們的模擬結果不僅指出了SF/MF暗激子在TD-PL中所對應的低溫T_1-/高溫T_2-特徵，藉由進一步地模擬和分析單層WSe2在外加雙軸應力下的TD-PL光譜，我們將提供一套能判斷BX,SF-DX,和MF-DX能量相對位置的分析方法。最後，我們將探討二維材料中的光激子與帶有軌道角動量(OAM)之扭曲光(twisted-light)間的光物質交互作用。藉由量測由扭曲光所激發之單層二硫化钼(MoS2)之PL光譜，我們的實驗合作者發現其PL光譜的譜線峰值將會隨著扭曲光的OAM增加而產生能量藍移的現象。在此工作中，我們的理論分析顯示帶有越大OAM的扭曲光將能轉移越大的線動量給二維材料內的光激子，因此可以激發具有較大線動量和能量的MF暗激子。此項研究工作不僅為實驗所觀測到的PL譜線藍移現象提供了合理的解釋，也為TMD-MLs中的MF暗激子提供了一個新穎的研究發法。

Atomically thin two-dimensional (2D) transition-metal dichalcogenide monolayers (TMD-MLs), constituted by one atomic layer of group-VIB transition metal atoms and two atomic layers of group-VIA chalcogen atoms, have recently received extensive attention because of the extraordinary photonic, spin and valley properties. The broken inversion symmetry of the crystal structure combined with the time-reversal symmetry leads to the promising spin-valley locking effect in TMD-MLs, which enables one to initialize, encode, control, and read-out the spin-valley degree of freedom of exciton optically and sets up a platform for the opto-valleytronic application. Moreover, due to the reduced dielectric screenings in the low-dimensional materials, a photogenerated exciton in TMD monolayers is very tightly bound with the binding energy so high as hundreds of meV, leading to the large exciton dipole moment and strong light−matter interaction. According to the selection rules of optical transition, one can classify excitons into the optically active/inactive bright/dark exciton (BX/DX), where the DX can be further classified into the spin-forbidden (SF) and momentum-forbidden (MF) ones. In spite of lacking of the optical brightness, the DXs in TMD-MLs have been well recognized to be essential in the photonic and dynamical processes in TMD-ML under photo-excitation. In TMD monolayers, the BX/DX states exhibit rich fine structures, resulting from the intriguing interplay between the spin/valley degree of freedom of the charge carriers and the electron-hole Coulomb interactions. In this thesis, our exciton study begins with the electronic band structure of TMD monolayers computed on the base of the density functional theory (DFT). To reduce the numerical consumption in the exciton band structure calculation, we establish the Wannier tight-binding (TB) model on the basis of maximally localized Wannier functions (MLWFs), transformed via the Wannierization procedure from the DFT-calculated band structures. Besides, we will employ the group theory to analyze the symmetry properties of TMD-MLs, which can help us to acquire a more thorough understanding of the single-particle Bloch states. Next, we successfully integrate the TB model into the Bethe-Salpeter equation (BSE) and compute the exciton spectra with the full consideration of direct and exchange interactions. Simulating the exciton population in Boltzmann statistics, we study the temperature-dependent photo-luminescence (TD-PL) spectra of WSe2 monolayer. Our results reveal the distinctive observable signatures of SF- and MF-DX states in the TD-PL under thermalization, both of which are optically inactive in conventional optical spectroscopies. At last, we extend our exciton theory to the study of the generalized light-matter interaction, specifically the interaction between the twisted-light with orbital-angular momentum (OAM). We will theoretically demonstrate that the twisted-light with increased OAM can transfer finite in-plane linear momentum to the excitons in the 2D material and make it possible to create twisted-light-generated exciton states that involve also the MF-DXs, which not only provides an explanation to the observed PL spectral blue shift but also suggest an alternative route to the activation of the MF-DXs.

Chinese Abstract---i
English Abstract---iii
Acknowledgments---v
Contents---vi
Figure Captions---ix
Table Captions---xvii
Chapter 1 Introduction---1
1.1 Excitons in Transition-Metal Dichalcogenide Monolayers---1
1.2 Theoretical Framework---13
Chapter 2 Electronic Structure Calculations---16
2.1 Crystal Structures with Periodic Lattices---17
2.2 Electrons in a Crystal---18
2.3 Density Functional Theory (DFT)---20
2.4 Bloch States---23
2.5 Periodic Boundary Conditions---24
2.6 From DFT to Tight-Binding (TB) Theory---25
2.6.1 Wannierization Process---26
2.6.2 Representations and Basis Transformation---27
2.6.3 Projections with Atomic Orbital Like Functions---28
2.7 General Formalism of TB Theory---30
Chapter 3 Electronic Structures of TMD Monolayers---34
3.1 Symmetries in the Crystal Structures of TMD monolayers---35
3.2 Electronic Structures of TMD Monolayers---39
3.2.1 Electronic Band Structures from Different Calculations---39
3.2.2 Electronic Band Structure of WSe2 Monolayer---44
3.2.3 Reliability of the HSE-DFT Calculations in WSe2 Monolayers---47
3.3 Symmetry Analysis for TMD Monolayers---49
3.4 Symmetry Properties of Strained Systems---54
3.4.1 MoS2 Monolayer with Uniaxial Strain---54
3.4.2 Symmetry of Strain---58
3.5 Single-Particle Transitions in TMD Monolayers---59
3.5.1 Optical Matrix Elements Derived from TB Theory---59
3.5.2 Numerical Simulation Results---61
3.5.3 Optical Dichroism Selection Rules in TMD Monolayers---63
Chapter 4 Excitons in WSe2 Monolayer---66
4.1 Excitonic Structure of WSe2 Monolayer---67
4.1.1 Exciton Band Structure Calculations---67
4.1.2 Strategy for Numerical Computations---68
4.1.3 Simulation Results---69
4.2 Temperature-Dependent PL Spectra of WSe2 Monolayer---74
4.2.1 Excitons at Thermal Equilibrium---74
4.2.2 Temperature-Dependent PL Spectra---75
4.3 Exciton Fine-Structures of Stressed WSe2 Monolayers---82
4.3.1 Strain-Dependent Electronic Band Structures---82
4.3.2 Strain-Dependent Exciton Band Structures---82
4.3.3 Strain-Dependent PL Spectra---84
Chapter 5 Light-Matter Interactions in MoS2 Monolayer---88
5.1 General Formalism of Light-Matter Interactions---89
5.1.1 Light-Matter Interaction (LMI) Hamiltonian---89
5.1.2 Approximations and Gauge Degree of Freedom---90
5.2 Vector Potential of Twisted-Light---91
5.2.1 Paraxial Wave---91
5.2.2 Twisted-Light in Laguerre-Gaussian Mode---92
5.2.3 Vector Potential in Wavevector Space---93
5.3 Effective Pseudospin Model of Excitons in TMD Monolayer---95
5.3.1 The Effective Pseudospin Hamiltonian of Excitons---95
5.3.2 Exciton Band Dispersions and Density of States---97
5.3.3 The Transition Dipole Moment of Valley-Mixed Excitons---98
5.4 Interactions Between Excitons and Twisted-Light---99
5.4.1 Optical Transitions Induced by Twisted-Light---99
5.4.2 Spectral Density Functions of Optical Transitions---100
5.5 Spectral Shifts in MoS2 Monolayer---104
Chapter 6 Summary and Outlook---107
Bibliography---110
Appendix---117
Appendix A: Disentanglement Process in Wannier90---117
Appendix B: Rotated Bloch Sum States---121
Publications---123
Oral and Poster Presentations---124

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