arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2004.14323cond-mat.mtrl-scicond-mat.mes-hallcond-mat.supr-con
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扭曲双层石墨烯的结构弛豫和低能性质

Structural relaxation and low energy properties of Twisted Bilayer Graphene

G. Cantele, D. Alfè, F. Conte, V. Cataudella, D. Ninno, P. Lucignano

摘要:

从第一性原理和紧束缚方法研究了扭曲双层石墨烯的结构和电子性质随扭曲角(从第一个“魔”角$θ=1.08^\circ$到$θ=3.89^\circ$,前者对应于最大的单元格,包含11164个碳原子)的变化.通过适当地考虑长程范德华相互作用,我们提供了原子位移的模式(相对于理想的扭曲双层)。面外弛豫显示出振荡(“屈曲”)行为,对于最小角度非常明显,AA堆叠区域周围的原子受到最大位移的影响。面外位移伴随着显着的面内松弛,表现出类似涡旋的模式,其中涡度(旨在作为位移场的旋度)在从顶部平面移动到底部平面时发生逆转,反之亦然。总的来说,原子弛豫导致AA堆叠区域的收缩,有利于能量更有利的AB/BA堆叠域。在第一魔角处出现的平带只有在考虑原子弛豫的情况下才能得到精确的描述。非常重要的是,如果只考虑面内或面外弛豫,则不能再现将平带流形与较高和较低能带分开的实验间隙。在第一魔角的弛豫双层的稳定性估计为0.5-0.9 meV每原子(或7-10 K)的顺序。我们的计算揭示了准确描述的vdW相互作用和由此产生的原子弛豫的重要性,设想这种真正特殊的vdW双层的电子结构。

英文摘要:

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.

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