低維材料的電子性質題材研究

Abstract

我們利用第一原理和緊束縛模型的計算去研究低維度材料的電子性質。首先，我們處理兩個負電荷低維度系統：單層奈米碳管以及單層石墨烯，經由計算不同超晶胞下的能帶和電荷密度，我們結果指出了在負電荷系統下有些類自由電子態是假的態。我們同樣地發現了儘管在此系統下有兩種態都像是類自由電子態，但它們的根源和性質是完全不一樣的。我們的研究指出了在負電荷低維度的系統下第一原理計算需更仔細地進行。然後，我們關注另一個有趣的材料：雙層旋轉石墨烯。我們建構了最局域瓦尼爾函數在雙層旋轉石墨烯旋轉角度5.08◦下。接著利用緊束縛模型去分析雙層旋轉石墨烯的兩個有趣的特性：費米速度的重整化以及電荷密度的局域性。相較於之前文獻研究，我們發現在普遍來說電荷密度並不會單純地局域在AA 區域。另外儘管費米速度以及電荷密度局域都會隨著旋轉角度而變動，但這兩種讓人驚豔的特性並不完全相關。這指出了這兩種形質源自於不同的物理機制。

We carry out first-principles and tight-binding calculations to study the electronic properties of low-dimensional materials. First, we have two negatively charged low-dimensional systems, single-walled carbon nanotubes and monolayer graphene. Through calculating the band structure and the charge density with different supercells, we show that some nearly free electron states are artificial states in negatively charged systems. Furthermore, we also reveal that although there are two types of states both looking like nearly free electron states, their origin and properties are totally different. Our results suggest that in first-principles more careful calculations should be implemented in negatively charged low-dimensional systems. Then, we focus on another interesting material, twisted bilayer graphene. We construct maximally-localized Wannier functions for a twist angle 5.08◦ twisted bilayer graphene. By applying tight-binding scheme, we further study two intriguing properties of twisted bilayer graphene: renormalization Fermi velocity and charge density localization. In contrast to previous studies, we show that the charge density localization of twisted bilayer graphene is not in the AA region in general. Furthermore, even though both the Fermi velocity and charge density localization fluctuate with respect with different twist angles, these two fascinating properties are not correlated. This suggests that these two phenomena are originated from different mechanisms.