论文标题
扭曲双层石墨烯的结构放松和低能特性
Structural relaxation and low energy properties of Twisted Bilayer Graphene
论文作者
论文摘要
扭曲双层石墨烯的结构和电子特性是从第一原理和紧密的结合方法作为扭角的函数（从第一个“魔术”角$θ= 1.08^\ cird $到$θ= 3.89^\ circ $的函数，而前者则与前与最大的单位单元相通用，包括11164碳的碳）。通过正确考虑远程范德华相互作用，我们为原子位移提供了模式（相对于理想的扭曲双层）。平面外放松显示出一种振荡（“屈曲”）的行为，对于最小的角度来说非常明显，而AA堆叠区域周围的原子对最大的位移感兴趣。平面外位移伴随着明显的平面弛豫，显示出类似涡流的图案，当从顶部到底层和viceversa移动时，涡度（目的是作为位移场的卷曲）被恢复。总体而言，原子放松导致AA堆叠区域的收缩，有利于更有利的AB/BA堆叠域。 只有在考虑原子弛豫时，才能准确地描述以第一个魔术角出现的测得的扁平带。非常重要的是，只有仅考虑平面内或仅考虑平面外弛豫，就无法再现将平坦带歧管与较高和较低能带分开的实验差距。据估计，在第一个魔术角下放松双层的稳定性为每个原子（或7-10 K）的0.5-0.9 MeV。我们的计算阐明了对VDW相互作用的准确描述以及所得的原子松弛的重要性，以设想这种非常奇特的VDW BiLayers的电子结构。
The structural and electronic properties of twisted bilayer graphene are investigated from first principles and tight binding approach as a function of the twist angle (ranging from the first "magic" angle $θ=1.08^\circ$ to $θ=3.89^\circ$, with the former corresponding to the largest unit cell, comprising 11164 carbon atoms). By properly taking into account the long-range van der Waals interaction, we provide the patterns for the atomic displacements (with respect to the ideal twisted bilayer). The out-of-plane relaxation shows an oscillating ("buckling") behavior, very evident for the smallest angles, with the atoms around the AA stacking regions interested by the largest displacements. The out-of-plane displacements are accompanied by a significant in-plane relaxation, showing a vortex-like pattern, where the vorticity (intended as curl of the displacement field) is reverted when moving from the top to the bottom plane and viceversa. Overall, the atomic relaxation results in the shrinking of the AA stacking regions in favor of the more energetically favorable AB/BA stacking domains. The measured flat bands emerging at the first magic angle can be accurately described only if the atomic relaxations are taken into account. Quite importantly, the experimental gaps separating the flat band manifold from the higher and lower energy bands cannot be reproduced if only in-plane or only out-of-plane relaxations are considered. The stability of the relaxed bilayer at the first magic angle is estimated to be of the order of 0.5-0.9 meV per atom (or 7-10 K). Our calculations shed light on the importance of an accurate description of the vdW interaction and of the resulting atomic relaxation to envisage the electronic structure of this really peculiar kind of vdW bilayers.
