论文标题
Moiré，Euler和自相似性 - 扭曲的六角形晶体的晶格参数
Moiré, Euler, and self-similarity -- the lattice parameters of twisted hexagonal crystals
论文作者
论文摘要
提出了一种用于计算由一组旋转的六边形2D晶体（如石墨烯或过渡金属二核化剂）形成的上层建筑的Moiré晶格参数的方法。明显的Moiré晶格连续形成所有旋转角度，其晶格参数良好近似遵循的是拼小的角度依赖性。 Moiré晶体，即用基础装饰的Moiré晶格，需要对符合能力进行更关键的评估，并导致离散的溶液和Moiré-Crystal Lattice参数的非连续角依赖性。特别是，该晶格参数严重取决于旋转角度，角度的连续变化可能导致晶格参数的明显不稳定的变化。该溶液形成了高度复杂的模式，它反映了Moiré晶体的形成参数之间的数字理论关系。该分析还提供了对构成晶格旋转30°旋转的特殊情况的见解，该晶格旋转了30°的旋转，为此形成了十二型准晶体结构。
A real-space approach for the calculation of the Moiré lattice parameters for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides, is presented. Apparent Moiré lattices continuously form for all rotation angles, and their lattice parameter in a good approximation follows a hyperbolical angle dependence. Moiré crystals, i.e. Moiré lattices decorated with a basis, require more crucial assessment of the commensurabilities and lead to discrete solutions and a non-continuous angle dependence of the Moiré-crystal lattice parameter. In particular, this lattice parameter critically depends on the rotation angle, and continuous variation of the angle can lead to apparently erratic changes of the lattice parameter. The solutions form a highly complex pattern, which reflects number-theoretical relations between formation parameters of the Moiré crystal. The analysis also provides insight into the special case of a 30° rotation of the constituting lattices, for which a dodecagonal quasicrystalline structure forms.
