2020/07/07 by Michael Feuerbacher, Feuerbacher, Michael · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #cond-mat.mtrl-sci
paper · pdf · doi:10.48550/arxiv.2007.03542
14 pages 7 figures, plus appendix with 5 figures
arxiv created 2020/07/07 · arxiv updated 2020/07/08
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.