武汉大学袁声军教授：揭示双层石墨烯准晶花样

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。该文近期发表于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及其翻译

Dodecagonal bilayer graphene quasicrystal and its approximants (双层石墨烯准晶及其周期性近似结构)

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 M M  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.

摘要双层石墨烯准晶具有十二重旋转对称性，但由于缺乏空间平移对称性很多基于能带理论的研究方法已不再适用。本文运用大尺度的紧束缚近似方法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。通过对由2702个原子组成的周期性近似结构进行能带反折叠，本文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。

文章来源：npj计算材料学