以第一原理多體理論研究二維二硫化鉬與二硒化鎢的激子能帶及電子能量損失能譜

Abstract

具有非零質心動量的激子 (Exciton) 的可以通過電子能量損失譜（Electron Energy-Loss Spectroscopy, EELS）實驗激發。近期對二硒化鎢單層的電子能量損失譜實驗表明，激子能帶 (Exciton band structure) 可以透過追蹤電子能量損失譜電子能量損失譜中的峰值色散關係 (Dispersion relation) 來量測。然而，如果不能直接與激子能帶比較，就無法徹底理解電子能量損失譜實驗中的激子激發機制。在這篇碩士論文中，我們首先利用第一原理密度泛函理論結合貝特–薩爾皮特方程計算來探索二硒化鎢和二硫化鉬單層中的激子能帶。由於電子-電洞交換作用，能量最低的明激子 (Bright exciton) 能帶在非零激子質心動量時匹裂，形成較低的拋物線激子能帶以及較高的非拋物線激子能帶。我們發現由於電子-電洞直接作用，拋物線能帶的激子的有效質量大幅增加，而二硒化鎢單層中的激子有效速度比二硫化鉬單層大，這表明二硒化鎢單層中有較強的電子-電洞交換作用且可能源於較強的自旋-軌道耦合作用。有趣的是，我們發現在較小的激子動量範圍內，二硒化鎢單層中兩個能量最低的暗激子的能量有 4 meV 的分裂，且在二硫化鉬單層中它們是簡併的。接著，我們仔細檢查了現有準二維系統的電子能量損失譜公式之間的差異和關聯，並確立了適當的電子能量損失譜的公式。使用這個公式，我們透過密度泛函理論結合貝特–薩爾皮特方程方法計算了二硒化鎢和二硫化鉬單層的電子能量損失譜，並發現與現有的實驗能譜非常吻合。我們也證明適當的電子能量損失譜公式能得到與實驗能譜有更好的吻合度的能譜。值得注意的是，在我們計算的電子能量損失譜中的最低能量的峰值色散是各向同性的，且與明激子的非拋物線激子能帶一致。此外，在實驗量測和我們的理論計算中，電子能量損失譜中的能量第二低的峰值都顯示出明顯的非拋物線行為。通過進一步的分析，我們闡明了電子能量損失譜實驗中的激子激發機制。在使用垂直入射高速電子的電子能量損失譜實驗中，徑向激子 (Longitudinal exciton，構成 A 與 B 明激子的非拋物線能帶) 會被選擇性地激發。相反地，軸向激子（Transverse exciton，構成 A 與 B 明激子的拋物線能帶）對能譜幾乎沒有貢獻。這解釋了我們理論計算中觀察到的非拋物線色散行為。最後，我們提出了可以選擇性激發橫向激子的電子能量損失譜實驗設置。這將會啟發電子能量損失譜實驗進一步地探索其他激子能帶，如 A 與 B 明激子的拋物線能帶，從而對準二維材料中的激子動力學有更深刻的理解。

Exciton with finite center-of-mass momentum Q is experimentally accessible by electron energy-loss spectroscopy (EELS) techniques. Recent EELS experiment on the WSe2 monolayer suggests that the EELS techniques can measure the exciton band structure by tracking the peak dispersion in the electron-energy-loss (EEL) spectra. However, the exciton excitation mechanism in EELS cannot be fully understood without knowing the underlying exciton band structure. In this master's thesis, we first utilize ab initio density-functional theory plus Bethe-Salpeter equation (DFT+BSE) approach to explore the exciton band structure in the WSe2 and MoS2 monolayers. Due to the electron-hole exchange interaction, the lowest bright (A) exciton bands split at finite Q, with the lower branch exhibiting a parabolic behavior and the upper branch showing a distinct non-parabolic characteristics. We find the exciton effective masses for the lower band are greatly enhanced by the electron-hole direct interaction, and the exciton effective velocity in the WSe2 monolayer is larger than the MoS2 monolayer, which indicates the stronger electron-hole exchange interaction in the WSe2 monolayer and may result from the stronger spin-orbit coupling (SOC) interaction. Interestingly, we find that in the small Q regime, the excitation energies of the two lowest dark excitons in the WSe2 monolayer exhibit a 4 meV splitting, a feature absent in the MoS2 monolayer. Next, we carefully examine the discrepancies and connections among the existing EEL spectrum formulas for quasi-two-dimensional (2D) systems, and establish a proper definition of the EEL spectrum. Using this proper EEL spectrum formula for quasi-2D materials, we calculate the EEL spectra of WSe2 and MoS2 monolayers within the DFT+BSE framework at non-vanishing Q, finding good agreement with experimental spectra. We demonstrate that the proper EEL spectrum formula yields better agreement with experiment. Notably, the lowest-energy EELS peaks dispersion is isotropic and coincides with the non-parabolic upper band of the A exciton. Additionally, we observe that the second-lowest-energy B peaks in the EEL spectra exhibit a distinctly non-parabolic behavior in both experimental data and our theoretical calculations. Through comprehensive analysis, we clarify the underlying exciton excitation mechanism in EELS. In the previous experimental setup with normally incident high-velocity electrons, EELS will selectively probe the longitudinal exciton, comprising the upper band of the A and B excitons. In contrast, the transverse exciton, corresponding to the lower band of the A and B excitons, contributes negligibly. This validates the non-parabolic A and B EELS peaks dispersion observed in our theoretical EELS peaks. Finally, we propose an experimental setup designed to selectively probe the transverse exciton, which will inspire further EELS experiments to explore other branches of the exciton band structure, such as the parabolic lower band of the A and B excitons, leading to a deeper understanding of exciton dynamics in quasi-2D materials.