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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)，英文標題與摘要如下，點擊左下角「閱讀原文」可以自由獲取論文PDF。
Dodecagonal bilayer graphene quasicrystal and itsapproximants Guodong Yu, Zewen Wu, Zhen Zhan, Mikhail I. Katsnelson & Shengjun YuanDodecagonal bilayer graphene quasicrystal has 12-fold rotational orderbut lacks translational symmetry which prevents theapplication of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scaletight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduceaccurately theproperties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallestapproximant with only 2702 atoms, the effective bandstructure of graphene quasicrystal is derived. The features, such as theemergence of new Dirac points (especially the mirrored ones), the band gap at M point and theFermi velocity are all in agreementwith recent experiments. The properties ofquasicrystal states are identified in the Landau level spectrum and opticalexcitations.Importantly, our results show that the lattice mismatch is the dominant factor determining the accuracy of layered approximants.The proposedapproximants can be used directly for other layered materials in honeycomb lattice,and the design principles can beapplied for any quasi-periodic incommensurate structures.本文系網易新聞·網易號「各有態度」特色內容
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