扭轉的雙層石墨烯具有豐富的電子結構和物理性質。當扭轉的角度為30度時，雙層石墨烯組成具有十二重旋轉對稱性的準晶結構。但由於準晶缺乏空間平移對稱性，很多基於能帶理論的研究方法很難直接應用，這使得對近期實驗上製備的雙層石墨烯準晶進行理論研究充滿挑戰。最近，武漢大學袁聲軍教授團隊，運用該小組發展的針對複雜量子體系的緊束縛傳播方法（TBPM），研究了由超過千萬個原子組成的雙層石墨烯準晶，並且提出了一系列周期性近似結構。這些周期性近似結構可以準確還原出雙層石墨烯準晶的電學和光學性質。其中最小的一個精確周期性近似結構包含2702個原子，通過對其能帶結構進行反摺疊運算，得到了雙層石墨烯準晶的有效能帶結構。計算結果表明，除了原有的單層石墨烯狄拉克點外，在兩個單層石墨烯的布裡淵區內部出現了大量新的狄拉克點，同時在M點處出現了能隙。這些特性都和近期的實驗結果一致。此外，雙層石墨烯準晶的準晶特性在其朗道能級和光學性質中也有所體現。本文的研究結果表明，組成準晶的兩層石墨烯晶格常數匹配度是決定其周期性近似結構準確度的最重要因素。本文提出的周期性近似結構可以直接應用於其它的六角蜂窩層狀材料組成的準晶，並且其設計理念可以推廣到任意一種層狀準周期體系。該文近期發表於npj Computational Materials 5:122(2019)。
Editorial Summary
Approximants: Making band theory apply to graphene quasicrystal
Twisted bilayer graphene has rich electronic structures and physical properties. When the twisted angle equals to 30-degree, twisted bilayer graphene forms a quasicrystal with 12-fold rotational order, which has been fabricated in recent experiments. Due to absence of the translational symmetry, the band theory doesn’t apply to quasicrystals, which makes it a big challenge to study theoretically twisted bilayer graphene quasicyrstal. Recently, a team led by Prof. Shengjun Yuan from School of Physics and Technology, Wuhan University, China, studied the electronic structures and physical properties of graphene quasicrystal by means of the large-scale tight-binding propagation method using their home-made simulation package Tipsi. They proposed a series of approximants, which can reproduce electronic and optical properties of bilayer graphene quasicrystal accurately. The effective band structure obtained by unfolding band structure of the smallest approximant with 2702 atoms is in agreement with recent experimental results. This study paved the way for applying band theory to graphene quasicrystal, and design principle of the approximant can be applied for any quasi-periodic layered in commensurate structures. This article was recently published in npj Computational Materials 5:122(2019).
原文Abstract及其翻譯
Dodecagonal bilayer graphene quasicrystal and its approximants (雙層石墨烯準晶及其周期性近似結構)
Guodong Yu, Zewen Wu, Zhen Zhan, Mikhail I. Katsnelson & Shengjun Yuan
Abstract Dodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scale tight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduce accurately the properties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallest approximant with only 2702 atoms, the effective band structure of graphene quasicrystal is derived. The features, such as the emergence of new Dirac points (especially the mirrored ones), the band gap at MM point and the Fermi velocity are all in agreement with recent experiments. The properties of quasicrystal states are identified in the Landau level spectrum and optical excitations. Importantly, our results show that the lattice mismatch is the dominant factor determining the accuracy of layered approximants. The proposed approximants can be used directly for other layered materials in honeycomb lattice, and the design principles can be applied for any quasi-periodic incommensurate structures.
摘要雙層石墨烯準晶具有十二重旋轉對稱性，但由於缺乏空間平移對稱性很多基於能帶理論的研究方法已不再適用。本文運用大尺度的緊束縛近似方法研究了由超過千萬個原子組成的雙層石墨烯準晶，並且提出了一系列周期性近似結構。這些周期性近似結構可以準確還原出雙層石墨烯準晶的電學和光學性質。通過對由2702個原子組成的周期性近似結構進行能帶反摺疊，本文得到了雙層石墨烯準晶的有效能帶結構。計算結果表明，除了原有的單層石墨烯狄拉克點外，在兩個單層石墨烯的布裡淵區內部出現了大量新的狄拉克點，同時在M點處出現了能隙。這些特性都和近期的實驗結果一致。此外，雙層石墨烯準晶的準晶特性在其朗道能級和光學性質中也有所體現。本文的研究結果表明，組成準晶的兩層石墨烯晶格常數匹配度是決定其周期性近似結構準確度的最重要因素。本文提出的周期性近似結構可以直接應用於其它的六角蜂窩層狀材料組成的準晶，並且其設計理念可以推廣到任意一種層狀準周期體系。
文章來源：npj計算材料學
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