npj: 周期性近似结构揭示—双层石墨烯准晶花样

来源：知社学术圈

扭转的双层石墨烯具有丰富的电子结构和物理性质。当扭转的角度为30度时，双层石墨烯组成具有十二重旋转对称性的准晶结构。但由于准晶缺乏空间平移对称性，很多基于能带理论的研究方法很难直接应用，这使得对近期实验上制备的双层石墨烯准晶进行理论研究充满挑战。

最近武汉大学袁声军教授团队，运用该小组发展的针对复杂量子体系的紧束缚传播方法（TBPM），研究了由超过千万个原子组成的双层石墨烯准晶，并且提出了一系列周期性近似结构。这些周期性近似结构可以准确还原出双层石墨烯准晶的电学和光学性质。其中最小的一个精确周期性近似结构包含2702个原子，通过对其能带结构进行反折叠运算，得到了双层石墨烯准晶的有效能带结构。计算结果表明，除了原有的单层石墨烯狄拉克点外，在两个单层石墨烯的布里渊区内部出现了大量新的狄拉克点，同时在M点处出现了能隙。这些特性都和近期的实验结果一致。

此外，双层石墨烯准晶的准晶特性在其朗道能级和光学性质中也有所体现。本文的研究结果表明，组成准晶的两层石墨烯晶格常数匹配度是决定其周期性近似结构准确度的最重要因素。本文提出的周期性近似结构可以直接应用于其它的六角蜂窝层状材料组成的准晶，并且其设计理念可以推广到任意一种层状准周期体系。

Dodecagonal bilayer graphene quasicrystal and itsapproximants 

Guodong Yu, Zewen Wu, Zhen Zhan, Mikhail I. Katsnelson & Shengjun Yuan

Dodecagonal 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.