论文标题
扭转周期性晶格扭曲和扭曲2D材料的衍射
Torsional Periodic Lattice Distortions and Diffraction of Twisted 2D Materials
论文作者
论文摘要
扭曲的2D材料形成了复杂的Moiré结构，这些结构通过中尺度晶格内的Picoscale变形自发地减少对称性。我们显示扭曲的2D材料包含一个由三个横向周期晶格扭曲（PLD）组成的扭转位移场。扭转PLD振幅提供了一个单个阶参数，该参数简单地描述了扭曲的双层Moirés的结构复杂性。此外，使用对倒数空间敏感的基本电子衍射方法可以量化扭转周期性晶格失真的结构和振幅。在扭曲的双层石墨烯中，扭转PLD开始以低于3.89°的角度形成，幅度在1.1°的魔法角度左右达到8 pm。在极低的扭曲角（例如低于0.25°）下，振幅增加，并出现其他PLD谐波，以扩大由孤独的孤子边界隔开的Bernal堆叠结构域。分析描述了扭曲的双层石墨烯中的扭转失真场，上限为22.6 pm。在扭曲的WS $ _2 $，CRI $ _3 $和WSE $ _2 $ / MOSE $ _2 $中观察到类似的扭转扭曲。
Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1.1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS$_2$, CrI$_3$, and WSe$_2$ / MoSe$_2$.
