Feuerbacher M
Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany.
Acta Crystallogr A Found Adv. 2021 Sep 1;77(Pt 5):460-471. doi: 10.1107/S2053273321007245. Epub 2021 Aug 19.
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 to 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.
提出了一种实空间方法，用于计算由一组旋转的六方二维晶体（如石墨烯或过渡金属二硫属化物）形成的超结构的莫尔晶格参数。对于所有旋转角度，都会连续形成表观莫尔晶格，并且其晶格参数在良好近似下遵循双曲线角度依赖性。莫尔晶体，即装饰有基元的莫尔晶格，需要对可公度性进行更关键的评估，并导致离散解以及莫尔晶体晶格参数的非连续角度依赖性。特别地，该晶格参数严重依赖于旋转角度，角度的连续变化可能导致晶格参数明显的不规则变化。这些解形成了一个高度复杂的模式，它反映了莫尔晶体形成参数之间的数论关系。该分析还深入了解了构成晶格30°旋转的特殊情况，对于这种情况会形成十二边形准晶结构。
